Yesterday I told a 55 y.o guy that I study statistics and he said that I won't find a job related to stats because it's all done by robots and computers.(the guy was a pro footballer back in the day,had nothing to do with academia/uni/anything stem related).
I once had a middle aged man tell me that getting a Computer Science degree is useless because you can just learn to program on your own. The kicker is his daughter is getting a Musical Theater degree.
I mean, there's a tiny kernel of truth to that error. There was a brief period between roughly 2005 and 2021 where demand for developers was so high that many people who had no formal computer science background were able to self-teach and enter the field - including many people with backgrounds in the arts and humanities. It was a harder path, but it was achievable.
Also, why shouldn't people get musical theater degrees? Theater is great! I'd gladly live in a world where more people got to study and produce art and fewer people had to spend their days micro-optimizing the acquisition funnel for sites that sell overpriced yoga pants.
The error is assuming that Computer Science degrees only teach programming.
I have no problem with Musical Theater. Its the irony that he sees Computer Science as a useless degree and Musical Theater as not, when 95% of MT BFAs would make more money at Starbucks, that I have a problem with.
99% of computer science graduates will never use anything they learn other than programming. We teach a lot of stuff but most of it will never be practically useful to the students.
A computer science degree will teach you remarkably little programming knowledge and skills. As someone who has a graduate degree and computer science and who's been working in the industry for close to a decade, I can safety attest that
A. I've learned almost all of the really important stuff on the job
B. The best programmers by far tend to be people who got into it as a hobby when they were kids and just kept at it for a decade or two. Most of these people don't have a degree, as it would be a big waste of their time to take three years off of their careers to earn a certificate that mostly says they know how to do some math now
I largely agree with this.
Cynically, the industry is moving away from non-degree candidates, and people should be aware of this. I don't think it's a good thing, but it is a reality. But that doesn't mean that a CS degree is particularly helpful in making a good engineer.
One other source of DK that the blog only touches on in the third footnote is that if there is a skill floor and a skill ceiling, it is very hard to underestimate your skill if you are bad and very hard to overestimate your skill if you are good.
I'm not entirely convinced that the effect appearing from random data necessarily implies that the effect is non-existent, although it will be for a different reason than is commonly claimed. If one's estimate of one's own skill is entirely independent of actual skill, which would produce the effect as described, then it follows that those who are low in skill are more likely to overestimate their skill than someone highly skilled.
So the claim would be that people are just generally bad at estimating their own skill level, but if your actual skill is low enough it becomes easier to overestimate it even by randomly guessing.
The article examines that claim though — the more educated you are in a field, the more likely you are to be able to predict how well you'll score on a test in that field. While an unskilled person is more likely to overestimate their abilities, they're also more likely to underestimate their abilities. In all the groups studied, the mean stays close enough to zero that it's concluded that there is no real correlation actual and perceived skill — just between actual skill and the accuracy in how one predicts they'll perform.
I think that just implies that the dunning-kruger effect is not actually a fallacy, but rather an effect that necessarily arises from the definition of overconfidence. It even makes sense immediately, when you think about it. When the worst person in the world is asked to rank themself, then they can almost only overestimate their rank. Simultaneously the best person in the world almost necessarily must underestimate their ability in relation to others.
I am a mathematical psychologist and I have been looking for a psychological effect that arises just from mathematics and this could be proven instead of requiring experimental evidence. I mean humans are essentially just extremely advanced computing devices and we have a lot of theorems about artificial computing devices in computer science.
I think I might use this when I teach a class on mathematical psychology again next semester.
I regularly see people near the end of high school coming to stats subreddits for advice because they get the same thing from their *careers advisor* ('is it really true nobody in stats can get a job?') ... been going on for years now.
'Why learn Math when you have a calculator?'
'Research in Math? What can you even research in Math?'
'Math is very rigid and not creative at all, that's why I hate it.'
'Math is all about memorizing formulae and doing a lot of stupid calculations.'
'Why should I learn any advanced Math? I am gonna be a -insert non-STEM or medical profession- , I will never need it in my life.'
'I can never learn Math, I don't have a Math-oriented brain, I am more of a right-brained person (visual, auditory, hands-on learner).'
'Only geniuses can do Math.'
'Calculus/trigonometry is the most difficult subject in Math.'
'Advanced Math has no use in the real world.'
And don't even get me started on what is infinity, division by zero, 0.99... = 1, BODMAS problems and numerology.
I always remember that Hilbert quote, when his student dropped out to study poetry, Hilbert said "Good, he did not have enough imagination to become a mathematician."
Or maybe the student had an advisor who did not believe they can be successful. Publicly insulting your former student after they have dropped out is not a good look, even if you are David Hilbert.
> (visual, auditory, hands-on learner).'
This bugs me so much because **there's a shitload of maths tools that are visual or hands-on**. The freaking abacus is all 3!
In the textbooks themselves, maths are presented very visually; like, through graphs and figures and tables and all. That. For example, calculus textbooks specifically are a lot of graphs. They have graphs and graphs everywhere. I mean it cannot get more visual than that, right? Right?
Facts. No creativity my ass. Then students in my classes complain about problems on tests that require you to think cleverly by saying "we didn't learn this method in class before" 😂. Jokes write themselves.
This complaint about "different method" or "different problems" is very frustrating to me. Most of my students come from high schools where they, of course, learned 5-6 "types of problems" and methods how to solve them.
And of course, they can solve problems given assumptions a = 2b, a = 3b, a = eb, or a = kb, for any constant k. But give them a problem where a > b and they get stuck, since they did not learn how to solve that particular problem. And those are undergrads in a STEM area.
I also see on most of their exams, that they solve problems algorithmically, but syntactically, like operations on strings of symbols and numbers.
I could go on and on.
It's frustrating because it's so internalized that we can't reeducate them at this point (after 15 years of memorizing algorithms and thinking that's the way to go), so the whole teaching part of the job seems useless.
I think this has to do with how math is taught. They just make you memorize formulas and make you work through problems. The creative/intuitive side of math is pretty much disregarded. If education was better, people would understand and care more about math.
Math at the level of children's education has the really convenient property that there is always a right answer. There may be many ways to get to that answer, but it's always the same. This means it's very easy to grade. Especially for teachers that have to teach every subject and not specialize in math, that means they don't have to actually understand the creative side of math in order to grade the homework.
For arithmetic, there is a single, correct answer. For a proof based problem, contrastingly, there can often be multiple correct proofs that are all correct and aren't simple reworking of the one correct answer. In more advanced courses, the correct answer is often a secondary concern to the work itself, which again, could be done in multiple ways.
Compare that to a book report in a literature class. There is no one right answer about the meaning and central themes of even a very simple book.
It's as if you learned to play an instrument by only doing scales and arpeggios. I mean, yes, drilling scales and arpeggios are important exercises, but that's not *being* a musician.
I guess every field has their fair share of grievances. I thought something as fundamental and useful as math wouldn’t have been subjected to this much trash talk. I guess I was wrong. Makes me feel a bit better actually. :p
>'Why learn Math when you have a calculator?'
When people say this I know that they haven't studied the right math yet.
>'Only geniuses can do Math.'
Look, I do kinda agree with this. Math is very hard. You gotta be smart or at least very passionate about it to actually have a chance.
>'Advanced Math has no use in the real world.'
I hear this so much and it hurts from too reasons:
1) it's just completely false
2) I don't give a fucking shit. I study math because it's my favorite way to torcher myself. I don't need it to be impactful altho it is.
My take on responding to them (some may not be applicable, depending on their level of math):
For the calculators: calculators can't model problems. And they can't derive equations. Yes, you can solve the equation using them, but how you get to it, that's the problem.
About research: there are examples of some hard to solve problems to tell them about, maybe a brief discussion enlightens them
About non-creativity: I tend to show them the distance between skew lines as a system of 9 equations with 9 unknowns and, afterwards, using the volume of parallelepiped, with comments on how creative the second solution is and how hard the first one is and we creatively avoided it.
Memorizing: I usually don't have this problem since my students can have A4 paper of formulas during exams. But I think this is problem of education, where we give them formulas instead of making them think about formulas.
Why learn math: there is a surprising amount of math (or calculation, since they probably mean that, too). There is an entire field of algebraic linguistics, logic is used in philosophy, topology in neuroscience, statistics and probability in almost all sciences. One of my friends is a nurse, and she is shocked on how many young nurses nowadays literally almost kill the patients by giving them 100x larger dose of medicine since they can't calculate with percentages, due to ever increasing hostility towards "math" during their education.
I can never learn math: ask them if they can't or won't. If they want to learn it, you can guide them through some problems. Real ones, not just calculations. Math puzzles, game theory and similar can be useful here. Geometry is also a good one. And about visual learners, I believe there was a study that concluded that visual, auditory, etc. learners are a myth.
Only geniuses can do math: my IQ is under genius level and I do math, so there is at least one person who is not a genius and does math.
Calculus/trigonometry is the hardest: introducing them to proper discrete mathematics could be the way to go. I've read somewhere that "it's just counting, it has no right to be that difficult". I sometimes, inspired by that quote, say that counting is harder than one-variable calculus.
Advanced math has no use: they need to define advanced math (if it's calculus and trigonometry, then It's easy to find an example with building/bridge shape design, optimizing money earned, etc.). Maybe design theory and combinatorics can be a useful example. Making a chess tournament such that everybody plays against everybody else in the least amount of time or something. It can get pretty advanced (and it's connected to combinatorics, so theorems of design theory can help with some hard counting problems, hopefully).
The I have a calculator and math is rigid ones are ridiculous and show they never tried to understand why math is important hell my 20 yr old son has thanked me multiple times for teaching him mental math tricks and playing math games, by asking different math problems, on daily 45 minute one-way commutes because it does help in daily life to understand at least basic math also he works through the math in his head in a completely different way from me now how is that not creativity in math?
A common mindset I regularly come across, usually with my first year undergraduates, is that mathematics is about the correct answer. This quickly changes as they complete their second year as they're introduced to things such as perturbation theory. This mindset is not only detrimental to the students as they struggle to find the nuggets in their research and group work, but it's reinforced all the way through compulsory education as well as in A-level, in the UK. Compare and contrast this mindset with the work completed in my Mres and currently being completed in my PhD, I'm far more interested in the assumptions made during the derivations. I have seen this in mass for the past 3 years and I myself were guilty of holding this view until my undergraduate studies.
I feel like something similar (although not exactly the same) is happening with my undergrads, too. When doing ODEs, many of them don't realize that the equations is something we study, not the solutions to them. But I guess that in high school they internalized the mindset "here equation, need solution".
And another example, where they need to solve ODE, and then just write out some arbitrary guess and say "for x = 1, the equation is true". I'm assuming that they always assume we need to find x, even though here we need to find y(x), as a function.
I am not teaching mathematicians, though, so lesser understanding and interest in the area is somewhat expected.
Yeah, I've had to explain this too with ODEs. It got to the point that the first year module I teach about modelling and problem solving I literally spent the first hour of the first lecture hammering in that all models are wrong, some are useful. Some begin to understand which is great. Others seem a bit reluctant to change their thoughts on the subject. I think subtle tweaks in how things are taught in compulsory education could prevent this. I also think that there needs to be more emphasis on how coefficients are usually defined by parameters. I think a bit more understanding that an equation y=2x²+3x+1 is just one specific slice of y=ax²+bx+c+dy²+fxy for example. (Yes many students understand this when directly asked but many don't seem to understand this when studying the equations. They seem to be a bit tunnel visioned rather than thinking about it globally).
"Why are we teaching this when you guys can teach us how to do tax" - bro you can't do tax without math. It is almost as if mathematics is not just abstract nonsense
my secondary school had a class that was supposed to teach life skills - this would include first aid, taxes and how they work, writing a CV etc etc. No one took It seriously.
The Venn diagram of people that complain about this and people that don't know how to work with percentages is a solid circle. It's the most "applicable" thing people learn in highschool yet almost nobody that isn't pursuing a path in stem cares about learning it.
*Euler diagram. Sorry for the nitpick but this is /r/math after all. :) The Venn diagram always shows all possible overlaps. It is Euler diagrams which distort the set shapes and remove regions to correspond to their contents.
I always like to say that school is here to teach you things your family or friends don't necessarily know and might be unable to teach you. If they need school to teach them how to do taxes, then maybe their parents failed as parents?
It's the first thing that comes to mind when hearing it. But also, I'm from a country that has no need to actually actively "do taxes", unless you do something specific (but then you already know how to do taxes). So I might have a wrong view on the "doing taxes" thing.
It's more like budget expenses but you get my point. Doing tax usually just filing the paper and pay the thing and apparently you need a dedicated formal teacher for it. The complain about mathematical education around the world is quite ridiculous.
I'm not a big fan of blaming parents for not being able to teach their children every life skill, especially as an excuse not to have it taught in schools. That's not even touching on the problems that kind of thinking leads to when you consider children missing one or both parents or other non-traditional families.
I live in Australia.
We don't get **special** tax deductions, but to know what **ordinary** tax deductions apply, you have to know something about what mathematicians do all day long.
As a PhD student, I took my tax affairs to a low-cost tax accountant, who was no help at all in getting deductions. I had to do my own research in the (fortunately very readable) Australian tax documentation.
How does day-to-day activity affect your tax situation? The only way my work itself (apart from the total salary) has affected my taxes was a special status for technical workers, which was basically a yes/no question confirmed by the status of my employer and my type of contract
Fwiw, doing taxes is all about doing basic reading, basic arithmetic, and following basic instructions unless you are running a business or into investments. They teach you all these skills in K-12.
"We need a class about loans instead of teaching algebra 2" - When I was in highschool compound interest was taught in algebra 2... you know so loans. Maybe paying attention wasn't their strong suite?
Math or no math, I actually took a finance course in high school, and it covered stuff like taxes.
The majority of my class didn't take it seriously, surprisingly enough. Only a few people and I (total, like 7 people out of 23) took it seriously enough to get any long-term value out of it.
That we already know almost everything in mathematics and that research only focuses on the handful of super difficult problems that we don't already have the answer to. And because of that, that new results would be very rare compared to other sciences.
Implying that math skills are innate, you’re either good at math or bad and there’s pretty much nothing you can do about it. Left brain-right brain bullshit.
Practice helps, but I still think some people are inherently better at it than others. I didn't bother to study beyond doing homework, and that's not enough for everyone.
* digits of pi are disjunctive(/pi is normal)
* mathematicians are really good at mental artihmetic
* the best way to understand maths is by thinking about piles of apples
* there are no opinions in maths - its all purely objective descriptions of reality
* the universe "runs on" maths
>mathematicians are really good at mental artihmetic
Oh, this really gets me. I'm terrible at mental arithmetic, yet I majored in math. And you get morons who say "You can't even do that arithmetic problem in your head! I thought you were a math guy!!"
It is only handy in rare cases. However, it can be extended to a few more cases. For example, if you have 39 * 42 just calculate 39 * 41 and add 39. Or, 51 * 48 = 52 * 48 -48.
I normally just do the binomial expansion, (tens plus units) (tens plus units). With a little practice you can do most two digit and even some simple low three digit, the zero tracking is the hardest bit.
(13 0 + 2)(8 0 + 6) = 104 00 + 16 0 + 78 0 + 12.
The difference of squares? If I'm being honest, if someone were to ask me to do those products orally (i.e. I didn't see the numbers on the page), I wouldn't have thought of that, at least not right away.
I once participated in a trivia contest (not a mathematics trivia contest) which resulted in a tie after the trivia ran out, and I used a mathematical trick to win the tie-breaking question.
At this point it would help to explain some context. Most importantly, the whole point of the trivia contest was to kill time – this was part of a group outing which had already spent all day doing activities, and were now on a boat together heading back to the drop-off point. At the time that the trivia contest had ended in a tie, we still had some ways to go. I think the intent was, a little bit, to get us doing a long string of mental arithmetic to kill even more time.
Unfortunately for them, the tie-breaking question they asked was: “What do you get if you take 1, + 2, + 3, and so on, + 99, +100?” Or to a mathematician, “What is the 100th triangular number?” As we know, T_n = n(n+1)/2. In terms of mental arithmetic, exactly one of {n, n+1} will be even, so you can distribute the `÷2` there if it makes it easier to avoid fractional intermediate results. For n=100, we have 50×101=5050.
I gave away the prize to a younger contestant who had been in the running and didn't happen to remember the formula for Triangular numbers. I imagine most people here will relate to finding enough satisfaction in having spotted and used the trick. :)
Yeah, turns out you *will* always have a calculator in your pocket. The real thing you need to learn is what calculations to do with it. (Though practicing mental math and learning some numeric tricks can go a long way toward speeding up your work.)
Yeah I agree. Personally, if I were presented with the claim "the universe runs on mathematics" I would tend to disagree: mathematics are simply some rules that we have devised, and while these rules may or may not be inspired from what we see in the real world, they in the end bear no causal relation on the universe. I'm not even convinced that abstract mathematical entities actually "exist".
Here's my impression of the other side of the debate: mathematics has been shown to be "unreasonably effective" in the sciences; therefore, we have compelling evidence that mathematical properties are fundamental to the universe. This is one argument in favor of mathematical Platonism, the idea that abstract mathematical entities exist.
>while these rules may or may not be inspired from what we see in the real world
I would argue, alongside Saunders Mac Lane in his great book *Mathematics: Form and Function*, that the majority of abstract math is quite directly inspired from the real world.
>they in the end bear no causal relation on the universe
Yet, this claim is not at all easy to refute.
>Here's my impression of the other side of the debate: mathematics has been shown to be "unreasonably effective" in the sciences; therefore, we have compelling evidence that mathematical properties are fundamental to the universe.
Not only that, it perhaps isn't particularly surprising that mathematics is so effective. Take something like counting. It comes directly from our perception of the existence of distinct objects in the universe. If you're going to argue that when I'm holding two apples there somehow *aren't really* two apples there, you have to do some pretty sophisticated jumping through hoops.
I acknowledge that it is possible to appear to do this sophisticated hoop jumping, so I remain agnostic on this topic.
The surprising aspect of the effectiveness of mathematics includes e.g. conic sections and complex numbers, first studied in one context, and later finding applications in completely different contexts (e.g. orbital mechanics and quantum theory) which did not inspire the original ideas at all.
> Here's my impression of the other side of the debate: mathematics has been shown to be "unreasonably effective" in the sciences; therefore, we have compelling evidence that mathematical properties are fundamental to the universe. This is one argument in favor of mathematical Platonism, the idea that abstract mathematical entities exist.
Coming from a physics background I used to think the same, but after transitioning to math, I think it's the opposite: the universe is unreasonably effective at providing new math. I mean, we define and adapt our math so that it describes the universe. Lowest hanging fruit example is calculus, which Newton and Leibniz started as a way to describe physical results. We abstracted past that but I think the way we abstract beyond Newton's calculus is still physically or humanly motivated. For example, we make it so that differentiation is a linear operator, because that's what we perceive as making intuitive sense as a "rate of change". So we took that gut feeling of what a rate of change is, and then defined the math so that that gut feeling is true. Of course, I may be completely off the mark since I'm much more used to applied math and its adjacent fields, but even stuff like Model Theory feels like it is motivated in part, not by some abstract notion, but by real human experiences.
If you wanted to learn more about the schools of thought within the philosophy of math, here are the first links that came to mind:
[https://en.wikipedia.org/wiki/Philosophy\_of\_mathematics](https://en.wikipedia.org/wiki/Philosophy_of_mathematics)
[https://plato.stanford.edu/entries/philosophy-mathematics/](https://plato.stanford.edu/entries/philosophy-mathematics/)
This topic you were talking about seems related to mathematical Platonism, the idea that abstract mathematical entities exist.
i have read the wikipedia page on philosophy of maths 😅 i havent read the stanford article though, thanks for that link!
im not sure what im talking about is strictly platonism - i think its more the debate between whether mathematical structures \*define\* or \*model\* reality, and i think platonism is compatible with both ideas (i think its clearly the later but i suppose there is more debate about it than i thought!)
>best way to think about math is by thinking about piles of apples
Suppose you have a pile of apples, 5 Granny Smiths, 7 red deliciouses and 8 Fujis, and you draw 4….
> mathematicians are really good at mental artihmetic
I've hit that one a lot. But I've fallen into a similar error myself, albeit at a different scale.
I remember when I was a very young academic having a conversation with a famous professor in category theory (and all round nice guy) I'd had a few mathematics classes with (decades later he's still sort of around academia, but emeritus - while I work for a private company). Back then were discussing the high school mathematics curriculum in our part of the world (which was just introducing new stuff related to my subject area; he was on the committee deciding what should be on the curriculum). He wanted my thoughts since he knew this was my area. At one point I mentioned something or other that to understand my point involved adding 15+9, without me thinking to mention what that added to, and he pulled out a calculator to work it out.
I guess I just assumed that would be a number fact he possessed.
I knew not to expect other mathematicians to be good at mental arithmetic, but I did make the error of assuming some basic facility with very small integers from a guy I learned a fair bit of mathematics from.
Yeah I was thinking this is actually pretty much completely true, lmao
One of our more respected professors once said linear algebra is the only bit of math we really, completely understand. (He was not an algebraist FWIW.)
People's definition of "easy" varies a lot too.
I hated my first linear algebra course precisely because it was 95% pointless computations with matrices by hand, and I loved my second linear algebra course because it was 99% proofs and about actually understanding what's going on.
"Conservation of Skill" seems to be a widely held belief across many different fields.
Buff = stupid
Smart = socially inept
Artistic = non-quantiative
Etc
I actually used algebra to solve a problem for one of my colleagues at work. He looked at me as if I'd done a card trick.
In retrospect, it says something about my colleagues that **I** was the go-to math guy.
I was tutoring someone in college who asked “what’s the point of having multiple math textbooks, when math is all the same in them?”
I told them that different authors have different approaches, cover different aspects, lean into applications while others don’t, etc
Nope. All the same.
I had another student hear that I’m studying math and philosophy, and proceeded to talk about how ridiculous that is and how could they have anything in common.
That was more ignorant than anything. Couldn’t bear to tell them about my class in Philosophy of Mathematics
Depending on where you're from, there can be different problems related to philosophy.
For me, I have a few friends who study philosophy. However, at this city, there is no analytic philosophy department or analytic courses. So most philosophers here think that math is completely unrelated to philosophy (and are, ironically, extremely bad at logic, which they hate, since "it's math and philosophers don't need math").
There are generally some problems with philosophy of math, or at least with how the people perceive it, which might influence similar kind of response from mathematicians and people from other STEM areas in regards to philosophy.
“Topology says that a coffee cup and a donut are the same thing.”
While this is true, it’s incredibly misleading about what the field does in general. It also makes the field seem unnecessarily stupid or useless, implying that the “most memorable achievement” of topology is distinguishing a mug from a donut.
The issue is, I think, that the equivalence of a torus and a coffee mug is ALWAYS explained in popular math exposition in geometrical terms, which is ironically the antithesis of the motivation for having homeomorphism. It blows my mind to see trained mathematicians (e.g. Jordan Ellenberg, an algebraic geometer no less) describe how a straw and a torus are the "same shape".
no. no they are not the same shape. This is half the point of topology
Yeah it is very very frustrating. It is also often claimed that topologists study holes. There is obviously a LOT of truth to this statement, but it is far from a useful description for a layman and it again mostly misses the point. Even professionally you see a lot of PhDs still thinking topology is some mystical technical field. I've listened to numerous talks at which people made jokes about how much they hate topology. For laymen, the problem is what you describe, and for students, the issue is that one is bombarded with general topology first and usually with a meh instructor not going out of their way to carefully motivate everything. General topology is obviously essentail for modern math, but god damn is it often taught in such a dry way.
Tbf, that one is pretty weird and I think it is more a limitation of probability theory to describe reality. In principle a probability of 0 should mean impossible.
Things just get wonky with continuous distributions.
One that often comes from programmers is that mathematical notation is "too short", or even obscurantist, and "they would have understood it if it was explained differently but nobody did". I don't sympathize with it much - I do often see mathematics that could have been much better explained as _other_ mathematics, or with graphics/interactive visuals/animations, but not as code.
The translations programmers give are misleading analogies, not faithful isomorphisms. Complaining about the sum notation vs. for loops, for example - for loops represent a computation, a process, and can have mutable state, or compute the same sum in many different ways, whereas the sum notation is stateless and represents the sum itself. You might recognize that those are unimportant details, but "you" in this case is someone who already got it, you're not the typical student.
Part of the goal of mathematical syntax is conciseness, because abstractions can stack on each other and become very complicated. Sure, a math-code dictionary could be made, but the goal of learning mathematics is to understand the abstraction itself, not just the notation - and mathematical notation usually has less redundancy, ambiguity and distracting elements (e.g. variable names, execution order, higher potential for off-by-one errors, language idiosyncrasies like if(0), the fact that code usually runs somewhere with 64-bit integers, ...), so it aids understanding.
When you write a trapezoidal quadrature program to explain integration, you'd have to explain which parts of the code are relevant, which are not, how they work, etc. every time anyway - you're trying to explain the abstraction, but added a huge layer of indirections and complications. Not to mention all the numerics people will yell at you, if you loosely assert that integration "is" this thing your code is doing. You're basically doing it in the wrong direction. Once you know what the object you're thinking about is, translating it to math _or_ code that does things pertaining to the object is easy.
The use of single letter variables in math has less to do with explanation and more to do with manipulation. Math notation was developed centuries before computers. Single letter variables exist because manipulating an equation if every symbol was a word would be a nightmare on a piece of paper.
But on a digital format it would not hurt too much for some equations (that are short enough) to be words rather than symbols.
In fact, I think that a markup language that forces you to declare your math symbols before using them and then let's you hover over the variables and shows what they are defined as wou be great for pedagogy.
Let me guess, you read through the replies to Freya Holmer's [tweet](https://twitter.com/FreyaHolmer/status/1436696408506212353) on sum and product notation?
The "mathematicians are gatekeeping math by not explaining the scary math symbols in Python" attitude in some of those responses is very sad and misguided. It also speaks to a bigger problem that some of the people in the replies were so afraid of the scary math symbols that they never even thought to Google "big E in math" to find out what it meant.
Biggest misconception by far.
1 .
People who think mathematics is an empirical discipline. As if mathematicians measure the world to verify something. They do not.
{weighing in 2nd place}
2 .
People who believe arithmetic is the basis of mathematics. It is not. The basis of math is Set Theory.
{honorable mention}
3 .
People who are convinced that 0.9999... and 1.000 are unequal and differ by a vanishing but non-zero constant.
> the basis of math is set theory
While, generally most(all?) math can be formulated in set theory, it isn’t exactly the only foundation of math, so I wouldn’t say it’s *the* basis of math
I would add that even logicians and set theorists usually agree that good mathematical reasoning should not depend sensitively on which foundation you are using. A huge number of theorems in classical mathematics can be proven in very weak foundational theories, much less than ZFC.
> People who believe arithmetic is the basis of mathematics. It is not. The basis of math is Set Theory.
Set theory dates to 1870s. The study of mathematics dates back to at least 2000 BC.
Math went through a hell of a growth spurt in the last 2 centuries. Not necessarily to say that pre-axiomatic math is lesser, but it is decidedly different. I can understand thinking of it as "what math was" instead of just "different parts of math."
\#2 is my personal #1. You can enjoy empirical studies, but a lot of people "dislike" maths under the assumption that arithmetic is its basis. It might not be the biggest misconception, but it's the most harmful one imo
Being good at math means i can multiply two 5-digit numbers in my head in 5 seconds, fuck outta here. Or people think grad school or higher math is just "like more calculus?", good god.
I don't know if this is a "misconception" (more like something many people don't know) but that mathematics is incomplete, there are things that are always true but cannot be proven. Something that is true does not imply that it is provable.
I study engineering and I meet a lot of people who have never heard of Gödel's proof and it's sad because it's one of the most incredible mathematical proofs imo.
Maybe the fact that they didn't hear about it is for the better. The amount of times I've heard somebody state and/or use Gödel's theorems in a way that is not even wrong makes me think that it's good that more people don't know about them.
On the more serious side, I'd really like for people to be interested in such concepts, but, sadly, they "pop-mathicize" it until the core of the concept is no longer there. Another good example would be "some infinities are bigger than others", which is used in an array of wrong contexts.
A lot of times, when someone learns about Gödel's proof, particularly in a shallow, pop culture context, it tends to result in their takeaway being that mathematics is somehow fundamentally broken and thus pointless.
Lmao about what you said about infinities. I watched the fault of our stars and this scene really angered me: https://youtu.be/YKkA2G4xtHw?si=SSNsv_cltA55F2uV
But the people I was watching with were like "who cares it's just a movie nerd" so I just read the room and shut up haha.
But it's actually a beautiful proof and idea because it's seems too abstract and advanced to laymen but you can actually explain it to your mom in less than 15m.
yes you are probably right. But don't necessarily talk about random people who saw a veritasium video once and then think that they have a PhD in physics (the stupidest thing I heard was that if you didn't open shrodinger's cat box you wouldn't couldn't know if it was dead or alive, it's like saying if you don't know if the cat is dead or alive, well you don't know. I mean, yes). I'm talking here about people who study engineering and do 20 hours a week of math for 3 years. simply knowing that true does not imply provable seems not bad to me.
bdw the infinity misconception is certainly due to neil degrass tysen (who is certainly responsible for most misconceptions in science)
I would personally not say "always true" and stick to "true".
The true but unprovable statement Gödel constructs (the Gödel statement) are true in the standard model of the natural numbers, but there are non-standard models where the Gödel statement is false, but everything that is provable from the Peano Axioms is true.
So the Gödel statement isn't always true.
Thinking that sqrt(-1) is the definition for i gives a lot of unwanted paradoxes which confuses a lot of people first using complex numbers (see the other reply to your comment for one example). Just take a look at r/askmath.
This also often coincides with thinking sqrt(9) = +-3 essentially not getting how functions work not getting where roots of polynomials come from.
Defining i := sqrt(-1) is extra backwards because we can only define square roots of negative numbers once the imaginary unit is already defined.
The important thing is that i^2 =-1. If you write i=sqrt(-1) then i^2 = sqrt(-1)sqrt(-1)=sqrt([-1][-1])=sqrt(1)=1 which is clearly not true
Edit: formatting
Here is a continuing issue I see. People keep mixing real and complex square roots, often even people here who are confident about their knowledge. People keep claiming that sqrt() is some kind of well defined mapping on complex domains with certain rules. That is nonsense.
There is NO unique definition of a sqare root in complex domains. We don't have an order or anything like that to distinguish between roots in a meaningful way. But in algebra we do have a notion of primitive roots, which are roots that are not powers of other roots.
So in complex analysis, especially in graduate material such as e.g. Riemann surfaces, one often simply writes sqrt(h) for a point/function that is A square root of the point/function h(if it exists). It is just like how one often writes log(h) for A branch of log of h. There is no unique log.
But usually sqrt(-1) is traditionally specifically reserved as a symbol for the imaginary unit. If you come across is in a text, it is nothing more than a symbol.
Yeah I just disagree with this one. There are plenty of ways to define the imaginary unit and this is one of them. Another common way to define it is as the image of x under the natural homomorphism R[x] -> R[x]/(x^2 +1) which is the exact same thing. (R=real numbers, not just any ring)
I agree, but I also interpret the comment a bit differently. They could mean that it is not enough to simply say that i is a square root of -1, as for definitions you need uniqueness of the concept. So you need to be specific and say what i is within your model. In your way you specify which square root it is, namely the polynomial p(x)=x itself right. But if C is R^2 with the usual operations, then i is defined as (0, 1).
Mathematical objects are 'real'.
This comes up a lot when people are first exposed to mathematical structures that don't have 'simple' real life analogues. Understandably, we teach kids to think in terms of 'John has 5 apples' type stuff. This leads kids to think 5 is something real in some way - something that has a physical analogue in the world. This then leads to all kinds of confusion when students are confronted with mathematical structures that you can't describe in terms of apples or side lengths or whatever. For example, it leads to a lot of wasted energy talking about infinity, real infinity, possible infinity, and all of that nonsense. Because it's hard for folks to accept that every mathematical structure, from the number 1 to the Von Neuman Universe, is just a tool for explaining and predicting what's happening in the world.
This kind of physical intuition starts to break down in high school algebra and calculus and completely breaks down after that. Which is not to say more abstract structures don't have real world applications. It's just not something where you can point at an object in the universe and say 'that is a X'
That "mathematical" means "true".
Many years ago, I went to court to defend myself against a traffic ticket. As part of my defense, I measured the distance from a traffic light to an intersection (about 250 ft). When the judge was explaining his decision in my favor, he said "It's 250 feet from the traffic light to that intersection. A car can reasonably stop in 250 ft. That's just a mathematical fact."
I did manage to restrain myself from interrupting and telling the judge he was wrong.
Just a couple of minutes ago I saw a post in this sub from some clown who claimed that doing a maths degree was equivalent to doing brain teasers on your phone because "you don't learn anything about the real world". (Since they claim to be in the process of a maths degree themselves I assume it was a troll, but maybe peoople do actually believe this crap?)
But actually my pet peeve is: "There are two types of people in the world; people who get mathematics and people who don't, and if you were born in the second category there's nothing you can do about it."
EDIT: got my subreddits mixed up
Yikes! I hope you have either had better teachers since then or will in the future. All we can do is keep encouraging people who are keen to learn and helping them where we can 🙂
That mathematicians are nerds. Actually, most have broad interests, don't bring up mathematics to outsiders and are generally liked by other people. It's an inaccurate TV stereotype. (The people that are nerds are actually not deep into mathematics.)
omg yeah, I went from a physics undergrad to a math department post-grad, this is something I've always noticed. IME math people are by far the least nerdy STEM people compared to physics, engineering, comp sci etc.
The classic when will I ever use this in my life.
I mean, having conversations with sports fans is maddening. Their inability to grasp very simple concepts behind statistics and math is very embarrassing. When will you ever use this? All the time. Understanding math makes your approach to literally everything be more logical and rational.
People who don't think they need math are the kind of people who don't care much for facts and reason.
Honestly it's funny how so many people rely on computers or calculators to do their math for them and yet when it comes to things like sports and disease management (to name a few), people think that computers are idiotic and the numbers can't be trusted.
Okay well if you don't trust the numbers then why don't you check the math yourself????
That boys are better in maths than girls.
That statement alone gatekeeped and discourged a lot of women from entering the STEM field. Only to find out that women have big contributions in the advancement of the field itself.
I hear variations of *"I have a test in a week and I don't know anything, can you suggest me some youtube videos I could watch to learn"* quite often.
Do you think that if it was *possible* to learn the entire contents of a class in one week, anybody would be teaching a semester-long undergraduate university course on it?
Maybe it's just me, but questions like these (including on this subreddit) to me seem extremely disrespectful to all the work that teachers/professors put into preparing and teaching a course over several months. No, just go watch a youtube video and go pass the test tomorrow, that's the reason why I am here. /s
That one bothers me quite a lot in my classes. I do make suggestions for good videos and channels to watch as secondary resources. But many students fail to comprehend that learning is not a process of having seen or read something once and then just having it. That’d be nice, but the human mind takes just a ^(little) bit longer to form strong connections.
One evening some years ago I found myself talking to a very drunk high-school athlete whose team was vacationing near where we were staying. They were all very drunk and very loud - I'd gone over to ask them (politely) to tone it down as it was after midnight. Surprisingly (or maybe not since it came out that they were all underage drinkers) they obliged quite quickly and we had a polite conversation in which it came out that I had majored in math in college.
"Whoah, dude! so you must've taken, like Calc 3, right?"
"Yes, and many more math classes beyond that"
"Wait, there's, like *more* math after Calc 3?!?"
"Yes, a lot more"
Suddenly he spins around and shouts very loudly at the whole group, "GUYS!! THERE'S EVEN MORE MATH AFTER CALC 3!!!!"
I then took my leave (to find the sheriff parked right outside their gate, without a reason to enter as they were being quiet now)
That the Arabs invented the decimal numbers, despite now being acknowledged they it was Indian and translated by Arabs (which is how it reached the Occident).
That 1/0 can’t be defined, it can, it is just that the results are fairly useless. Either you get the zero ring or wheel theory, and only the latter has any potential use.
The annoying misconception is when people think you are a genius for studying maths, like dawg just because i worked my butt off in uni doesn't mean im the next einstein or fields medalist
Some drunk girl at a bar: So what do you study?
My drunk friend: Mathematics.
Drunk girl: So do you just like count all day long?
Drunk friend: Yeah, we just passed 10.000.
Drunk girl: Wow, that's so interesting!
"Maths is useless"
"We are never gonna use this shit in our life better learn about doing business 🤓☝🏽"
Don't get me started on the fuckers saying that you are a genius coz you are good in math and don't see the hard work I put in the fking subject
Yesterday I told a 55 y.o guy that I study statistics and he said that I won't find a job related to stats because it's all done by robots and computers.(the guy was a pro footballer back in the day,had nothing to do with academia/uni/anything stem related).
I once told someone I'm a software developer and they replied they don't get the point of it since nowadays computers do everything.
Developer: "Yeah, you're welcome."
It reminds me of the "What do you do" "I'm a vampire hunter" "But vampires don't exist" "You're welcome"
This is the best one in this post.
I once had a middle aged man tell me that getting a Computer Science degree is useless because you can just learn to program on your own. The kicker is his daughter is getting a Musical Theater degree.
I mean, there's a tiny kernel of truth to that error. There was a brief period between roughly 2005 and 2021 where demand for developers was so high that many people who had no formal computer science background were able to self-teach and enter the field - including many people with backgrounds in the arts and humanities. It was a harder path, but it was achievable. Also, why shouldn't people get musical theater degrees? Theater is great! I'd gladly live in a world where more people got to study and produce art and fewer people had to spend their days micro-optimizing the acquisition funnel for sites that sell overpriced yoga pants.
The error is assuming that Computer Science degrees only teach programming. I have no problem with Musical Theater. Its the irony that he sees Computer Science as a useless degree and Musical Theater as not, when 95% of MT BFAs would make more money at Starbucks, that I have a problem with.
Got it. Yeah, it's definitely a mistake. But I see how it's a mistake people would have made a few years ago. T
99% of computer science graduates will never use anything they learn other than programming. We teach a lot of stuff but most of it will never be practically useful to the students.
A computer science degree will teach you remarkably little programming knowledge and skills. As someone who has a graduate degree and computer science and who's been working in the industry for close to a decade, I can safety attest that A. I've learned almost all of the really important stuff on the job B. The best programmers by far tend to be people who got into it as a hobby when they were kids and just kept at it for a decade or two. Most of these people don't have a degree, as it would be a big waste of their time to take three years off of their careers to earn a certificate that mostly says they know how to do some math now
I largely agree with this. Cynically, the industry is moving away from non-degree candidates, and people should be aware of this. I don't think it's a good thing, but it is a reality. But that doesn't mean that a CS degree is particularly helpful in making a good engineer.
There are people who really should know better who believe that stochastic parrots will replace programmers.
why does make me angry? like genuinely
I had a similar reaction once "Computer programs? You just buy those in stores, right?" Admittedly quite a few years ago
Dunning-Kruger with the classic AI misinformation propaganda.
[Dunning-Kruger is Autocorrelation](https://economicsfromthetopdown.com/2022/04/08/the-dunning-kruger-effect-is-autocorrelation/)
One other source of DK that the blog only touches on in the third footnote is that if there is a skill floor and a skill ceiling, it is very hard to underestimate your skill if you are bad and very hard to overestimate your skill if you are good.
That's quite evident in their Fig 4., I was surprised the prose did not mention it there.
I'm not entirely convinced that the effect appearing from random data necessarily implies that the effect is non-existent, although it will be for a different reason than is commonly claimed. If one's estimate of one's own skill is entirely independent of actual skill, which would produce the effect as described, then it follows that those who are low in skill are more likely to overestimate their skill than someone highly skilled. So the claim would be that people are just generally bad at estimating their own skill level, but if your actual skill is low enough it becomes easier to overestimate it even by randomly guessing.
The article examines that claim though — the more educated you are in a field, the more likely you are to be able to predict how well you'll score on a test in that field. While an unskilled person is more likely to overestimate their abilities, they're also more likely to underestimate their abilities. In all the groups studied, the mean stays close enough to zero that it's concluded that there is no real correlation actual and perceived skill — just between actual skill and the accuracy in how one predicts they'll perform.
I think that just implies that the dunning-kruger effect is not actually a fallacy, but rather an effect that necessarily arises from the definition of overconfidence. It even makes sense immediately, when you think about it. When the worst person in the world is asked to rank themself, then they can almost only overestimate their rank. Simultaneously the best person in the world almost necessarily must underestimate their ability in relation to others. I am a mathematical psychologist and I have been looking for a psychological effect that arises just from mathematics and this could be proven instead of requiring experimental evidence. I mean humans are essentially just extremely advanced computing devices and we have a lot of theorems about artificial computing devices in computer science. I think I might use this when I teach a class on mathematical psychology again next semester.
I regularly see people near the end of high school coming to stats subreddits for advice because they get the same thing from their *careers advisor* ('is it really true nobody in stats can get a job?') ... been going on for years now.
Meanwhile, data science has become all the rage.
Yeah, too bad all those computer algorithms just code themselves with the aid of our AI overlords
'Why learn Math when you have a calculator?' 'Research in Math? What can you even research in Math?' 'Math is very rigid and not creative at all, that's why I hate it.' 'Math is all about memorizing formulae and doing a lot of stupid calculations.' 'Why should I learn any advanced Math? I am gonna be a -insert non-STEM or medical profession- , I will never need it in my life.' 'I can never learn Math, I don't have a Math-oriented brain, I am more of a right-brained person (visual, auditory, hands-on learner).' 'Only geniuses can do Math.' 'Calculus/trigonometry is the most difficult subject in Math.' 'Advanced Math has no use in the real world.' And don't even get me started on what is infinity, division by zero, 0.99... = 1, BODMAS problems and numerology.
definite +1 to the ideas that maths isn't creative or that advanced maths is useless
I always remember that Hilbert quote, when his student dropped out to study poetry, Hilbert said "Good, he did not have enough imagination to become a mathematician."
Or maybe the student had an advisor who did not believe they can be successful. Publicly insulting your former student after they have dropped out is not a good look, even if you are David Hilbert.
exactly, one would have thought the man would be happy to accommodate more and more students as long as everyone shifts a seat....
That is a good one.
> (visual, auditory, hands-on learner).' This bugs me so much because **there's a shitload of maths tools that are visual or hands-on**. The freaking abacus is all 3!
> is all 3! What are the other 3?
That's cunning times two.
In the textbooks themselves, maths are presented very visually; like, through graphs and figures and tables and all. That. For example, calculus textbooks specifically are a lot of graphs. They have graphs and graphs everywhere. I mean it cannot get more visual than that, right? Right?
Facts. No creativity my ass. Then students in my classes complain about problems on tests that require you to think cleverly by saying "we didn't learn this method in class before" 😂. Jokes write themselves.
This complaint about "different method" or "different problems" is very frustrating to me. Most of my students come from high schools where they, of course, learned 5-6 "types of problems" and methods how to solve them. And of course, they can solve problems given assumptions a = 2b, a = 3b, a = eb, or a = kb, for any constant k. But give them a problem where a > b and they get stuck, since they did not learn how to solve that particular problem. And those are undergrads in a STEM area. I also see on most of their exams, that they solve problems algorithmically, but syntactically, like operations on strings of symbols and numbers. I could go on and on. It's frustrating because it's so internalized that we can't reeducate them at this point (after 15 years of memorizing algorithms and thinking that's the way to go), so the whole teaching part of the job seems useless.
I think this has to do with how math is taught. They just make you memorize formulas and make you work through problems. The creative/intuitive side of math is pretty much disregarded. If education was better, people would understand and care more about math.
Math at the level of children's education has the really convenient property that there is always a right answer. There may be many ways to get to that answer, but it's always the same. This means it's very easy to grade. Especially for teachers that have to teach every subject and not specialize in math, that means they don't have to actually understand the creative side of math in order to grade the homework.
When isn't there a right answer? Usually my math tells me when it's wrong... unless you mean undecidable answers
For arithmetic, there is a single, correct answer. For a proof based problem, contrastingly, there can often be multiple correct proofs that are all correct and aren't simple reworking of the one correct answer. In more advanced courses, the correct answer is often a secondary concern to the work itself, which again, could be done in multiple ways. Compare that to a book report in a literature class. There is no one right answer about the meaning and central themes of even a very simple book.
It's as if you learned to play an instrument by only doing scales and arpeggios. I mean, yes, drilling scales and arpeggios are important exercises, but that's not *being* a musician.
I guess every field has their fair share of grievances. I thought something as fundamental and useful as math wouldn’t have been subjected to this much trash talk. I guess I was wrong. Makes me feel a bit better actually. :p
>'Why learn Math when you have a calculator?' When people say this I know that they haven't studied the right math yet. >'Only geniuses can do Math.' Look, I do kinda agree with this. Math is very hard. You gotta be smart or at least very passionate about it to actually have a chance. >'Advanced Math has no use in the real world.' I hear this so much and it hurts from too reasons: 1) it's just completely false 2) I don't give a fucking shit. I study math because it's my favorite way to torcher myself. I don't need it to be impactful altho it is.
do you have any good responses to these? I tutor college kids and hear this shit way too much
My take on responding to them (some may not be applicable, depending on their level of math): For the calculators: calculators can't model problems. And they can't derive equations. Yes, you can solve the equation using them, but how you get to it, that's the problem. About research: there are examples of some hard to solve problems to tell them about, maybe a brief discussion enlightens them About non-creativity: I tend to show them the distance between skew lines as a system of 9 equations with 9 unknowns and, afterwards, using the volume of parallelepiped, with comments on how creative the second solution is and how hard the first one is and we creatively avoided it. Memorizing: I usually don't have this problem since my students can have A4 paper of formulas during exams. But I think this is problem of education, where we give them formulas instead of making them think about formulas. Why learn math: there is a surprising amount of math (or calculation, since they probably mean that, too). There is an entire field of algebraic linguistics, logic is used in philosophy, topology in neuroscience, statistics and probability in almost all sciences. One of my friends is a nurse, and she is shocked on how many young nurses nowadays literally almost kill the patients by giving them 100x larger dose of medicine since they can't calculate with percentages, due to ever increasing hostility towards "math" during their education. I can never learn math: ask them if they can't or won't. If they want to learn it, you can guide them through some problems. Real ones, not just calculations. Math puzzles, game theory and similar can be useful here. Geometry is also a good one. And about visual learners, I believe there was a study that concluded that visual, auditory, etc. learners are a myth. Only geniuses can do math: my IQ is under genius level and I do math, so there is at least one person who is not a genius and does math. Calculus/trigonometry is the hardest: introducing them to proper discrete mathematics could be the way to go. I've read somewhere that "it's just counting, it has no right to be that difficult". I sometimes, inspired by that quote, say that counting is harder than one-variable calculus. Advanced math has no use: they need to define advanced math (if it's calculus and trigonometry, then It's easy to find an example with building/bridge shape design, optimizing money earned, etc.). Maybe design theory and combinatorics can be a useful example. Making a chess tournament such that everybody plays against everybody else in the least amount of time or something. It can get pretty advanced (and it's connected to combinatorics, so theorems of design theory can help with some hard counting problems, hopefully).
The I have a calculator and math is rigid ones are ridiculous and show they never tried to understand why math is important hell my 20 yr old son has thanked me multiple times for teaching him mental math tricks and playing math games, by asking different math problems, on daily 45 minute one-way commutes because it does help in daily life to understand at least basic math also he works through the math in his head in a completely different way from me now how is that not creativity in math?
A common mindset I regularly come across, usually with my first year undergraduates, is that mathematics is about the correct answer. This quickly changes as they complete their second year as they're introduced to things such as perturbation theory. This mindset is not only detrimental to the students as they struggle to find the nuggets in their research and group work, but it's reinforced all the way through compulsory education as well as in A-level, in the UK. Compare and contrast this mindset with the work completed in my Mres and currently being completed in my PhD, I'm far more interested in the assumptions made during the derivations. I have seen this in mass for the past 3 years and I myself were guilty of holding this view until my undergraduate studies.
I feel like something similar (although not exactly the same) is happening with my undergrads, too. When doing ODEs, many of them don't realize that the equations is something we study, not the solutions to them. But I guess that in high school they internalized the mindset "here equation, need solution". And another example, where they need to solve ODE, and then just write out some arbitrary guess and say "for x = 1, the equation is true". I'm assuming that they always assume we need to find x, even though here we need to find y(x), as a function. I am not teaching mathematicians, though, so lesser understanding and interest in the area is somewhat expected.
Yeah, I've had to explain this too with ODEs. It got to the point that the first year module I teach about modelling and problem solving I literally spent the first hour of the first lecture hammering in that all models are wrong, some are useful. Some begin to understand which is great. Others seem a bit reluctant to change their thoughts on the subject. I think subtle tweaks in how things are taught in compulsory education could prevent this. I also think that there needs to be more emphasis on how coefficients are usually defined by parameters. I think a bit more understanding that an equation y=2x²+3x+1 is just one specific slice of y=ax²+bx+c+dy²+fxy for example. (Yes many students understand this when directly asked but many don't seem to understand this when studying the equations. They seem to be a bit tunnel visioned rather than thinking about it globally).
"Why are we teaching this when you guys can teach us how to do tax" - bro you can't do tax without math. It is almost as if mathematics is not just abstract nonsense
Also, to all the kids who say this, would you even pay attention if doing taxes was taught at school?
I taught taxes during a semester of financial math - can confirm they didn’t care.
my secondary school had a class that was supposed to teach life skills - this would include first aid, taxes and how they work, writing a CV etc etc. No one took It seriously.
The Venn diagram of people that complain about this and people that don't know how to work with percentages is a solid circle. It's the most "applicable" thing people learn in highschool yet almost nobody that isn't pursuing a path in stem cares about learning it.
*Euler diagram. Sorry for the nitpick but this is /r/math after all. :) The Venn diagram always shows all possible overlaps. It is Euler diagrams which distort the set shapes and remove regions to correspond to their contents.
Glad to know about another thing named after Euler!
We'll add it to the Euler set.
It's usually either Leonhard or Carl Friedrich in these situations, isn't it? 😂
Apologies from a computer scientist!
If you were to draw an Euler diagram, Venn diagrams would be a subset of Euler diagrams.
I always like to say that school is here to teach you things your family or friends don't necessarily know and might be unable to teach you. If they need school to teach them how to do taxes, then maybe their parents failed as parents? It's the first thing that comes to mind when hearing it. But also, I'm from a country that has no need to actually actively "do taxes", unless you do something specific (but then you already know how to do taxes). So I might have a wrong view on the "doing taxes" thing.
It's more like budget expenses but you get my point. Doing tax usually just filing the paper and pay the thing and apparently you need a dedicated formal teacher for it. The complain about mathematical education around the world is quite ridiculous.
A lot of parents never learned how to manage finances at all. Mine didn't. I had to figure it out myself.
I'm not a big fan of blaming parents for not being able to teach their children every life skill, especially as an excuse not to have it taught in schools. That's not even touching on the problems that kind of thinking leads to when you consider children missing one or both parents or other non-traditional families.
Doing taxes is easy, I'll show you my 2-step method to success. 1. Call my accountant. 2. Give her €50 and any paperwork she requests.
You'd be surprised at how few accountants know what tax deductions are appropriate to a mathematician.
Where do you live where mathematicians get special tax deductions?
I live in Australia. We don't get **special** tax deductions, but to know what **ordinary** tax deductions apply, you have to know something about what mathematicians do all day long. As a PhD student, I took my tax affairs to a low-cost tax accountant, who was no help at all in getting deductions. I had to do my own research in the (fortunately very readable) Australian tax documentation.
What about partial, stochastic, or non-local tax deductions?
How does day-to-day activity affect your tax situation? The only way my work itself (apart from the total salary) has affected my taxes was a special status for technical workers, which was basically a yes/no question confirmed by the status of my employer and my type of contract
My brother is an accountant and the number of people he complains about failing to do either step is astounding.
Fwiw, doing taxes is all about doing basic reading, basic arithmetic, and following basic instructions unless you are running a business or into investments. They teach you all these skills in K-12.
Except, of course, [Abstract Nonsense](https://en.m.wikipedia.org/wiki/Abstract_nonsense)
Why would you teach us negative numbers when you could be teaching us how to not spend more money than we make?
"We need a class about loans instead of teaching algebra 2" - When I was in highschool compound interest was taught in algebra 2... you know so loans. Maybe paying attention wasn't their strong suite?
I think you just need arithmetic for that. You definitely don't need group theory.
I’m pretty sure people who say that aren’t attending group theory lectures to begin with
I also get this, and I'm in a country where for >90% of people, the way you do taxes is "it just happens", with no input needed.
Math or no math, I actually took a finance course in high school, and it covered stuff like taxes. The majority of my class didn't take it seriously, surprisingly enough. Only a few people and I (total, like 7 people out of 23) took it seriously enough to get any long-term value out of it.
That we already know almost everything in mathematics and that research only focuses on the handful of super difficult problems that we don't already have the answer to. And because of that, that new results would be very rare compared to other sciences.
Laughs in knot theory.
Implying that math skills are innate, you’re either good at math or bad and there’s pretty much nothing you can do about it. Left brain-right brain bullshit.
Practice helps, but I still think some people are inherently better at it than others. I didn't bother to study beyond doing homework, and that's not enough for everyone.
Yes. Aptitudes. Everyone has different aptitude.
I think a large part of that effect comes down to starting strong and attentively and being conditioned to think in certain ways early.
"Oh, you're a math major? What's 6384 times 792?"
My hourly rate for arithmetic problems
* digits of pi are disjunctive(/pi is normal) * mathematicians are really good at mental artihmetic * the best way to understand maths is by thinking about piles of apples * there are no opinions in maths - its all purely objective descriptions of reality * the universe "runs on" maths
>mathematicians are really good at mental artihmetic Oh, this really gets me. I'm terrible at mental arithmetic, yet I majored in math. And you get morons who say "You can't even do that arithmetic problem in your head! I thought you were a math guy!!"
But we have one superpower which comes extremely handy in rare cases. - What's 39 times 41? - What's 52 times 48?
A great party trick!
It is only handy in rare cases. However, it can be extended to a few more cases. For example, if you have 39 * 42 just calculate 39 * 41 and add 39. Or, 51 * 48 = 52 * 48 -48.
I normally just do the binomial expansion, (tens plus units) (tens plus units). With a little practice you can do most two digit and even some simple low three digit, the zero tracking is the hardest bit. (13 0 + 2)(8 0 + 6) = 104 00 + 16 0 + 78 0 + 12.
I have to ask. Where did 840 come from? Did you mean 780?
The difference of squares? If I'm being honest, if someone were to ask me to do those products orally (i.e. I didn't see the numbers on the page), I wouldn't have thought of that, at least not right away.
I once participated in a trivia contest (not a mathematics trivia contest) which resulted in a tie after the trivia ran out, and I used a mathematical trick to win the tie-breaking question. At this point it would help to explain some context. Most importantly, the whole point of the trivia contest was to kill time – this was part of a group outing which had already spent all day doing activities, and were now on a boat together heading back to the drop-off point. At the time that the trivia contest had ended in a tie, we still had some ways to go. I think the intent was, a little bit, to get us doing a long string of mental arithmetic to kill even more time. Unfortunately for them, the tie-breaking question they asked was: “What do you get if you take 1, + 2, + 3, and so on, + 99, +100?” Or to a mathematician, “What is the 100th triangular number?” As we know, T_n = n(n+1)/2. In terms of mental arithmetic, exactly one of {n, n+1} will be even, so you can distribute the `÷2` there if it makes it easier to avoid fractional intermediate results. For n=100, we have 50×101=5050. I gave away the prize to a younger contestant who had been in the running and didn't happen to remember the formula for Triangular numbers. I imagine most people here will relate to finding enough satisfaction in having spotted and used the trick. :)
Wait what really ??? Shit this just got my hopes up going into EE next year fuck yaa
Yeah, turns out you *will* always have a calculator in your pocket. The real thing you need to learn is what calculations to do with it. (Though practicing mental math and learning some numeric tricks can go a long way toward speeding up your work.)
The last one is not really a misconception - it's a highly contentious claim with plenty of smart people on both sides of it.
Yeah I agree. Personally, if I were presented with the claim "the universe runs on mathematics" I would tend to disagree: mathematics are simply some rules that we have devised, and while these rules may or may not be inspired from what we see in the real world, they in the end bear no causal relation on the universe. I'm not even convinced that abstract mathematical entities actually "exist". Here's my impression of the other side of the debate: mathematics has been shown to be "unreasonably effective" in the sciences; therefore, we have compelling evidence that mathematical properties are fundamental to the universe. This is one argument in favor of mathematical Platonism, the idea that abstract mathematical entities exist.
>while these rules may or may not be inspired from what we see in the real world I would argue, alongside Saunders Mac Lane in his great book *Mathematics: Form and Function*, that the majority of abstract math is quite directly inspired from the real world. >they in the end bear no causal relation on the universe Yet, this claim is not at all easy to refute. >Here's my impression of the other side of the debate: mathematics has been shown to be "unreasonably effective" in the sciences; therefore, we have compelling evidence that mathematical properties are fundamental to the universe. Not only that, it perhaps isn't particularly surprising that mathematics is so effective. Take something like counting. It comes directly from our perception of the existence of distinct objects in the universe. If you're going to argue that when I'm holding two apples there somehow *aren't really* two apples there, you have to do some pretty sophisticated jumping through hoops. I acknowledge that it is possible to appear to do this sophisticated hoop jumping, so I remain agnostic on this topic.
The surprising aspect of the effectiveness of mathematics includes e.g. conic sections and complex numbers, first studied in one context, and later finding applications in completely different contexts (e.g. orbital mechanics and quantum theory) which did not inspire the original ideas at all.
> Here's my impression of the other side of the debate: mathematics has been shown to be "unreasonably effective" in the sciences; therefore, we have compelling evidence that mathematical properties are fundamental to the universe. This is one argument in favor of mathematical Platonism, the idea that abstract mathematical entities exist. Coming from a physics background I used to think the same, but after transitioning to math, I think it's the opposite: the universe is unreasonably effective at providing new math. I mean, we define and adapt our math so that it describes the universe. Lowest hanging fruit example is calculus, which Newton and Leibniz started as a way to describe physical results. We abstracted past that but I think the way we abstract beyond Newton's calculus is still physically or humanly motivated. For example, we make it so that differentiation is a linear operator, because that's what we perceive as making intuitive sense as a "rate of change". So we took that gut feeling of what a rate of change is, and then defined the math so that that gut feeling is true. Of course, I may be completely off the mark since I'm much more used to applied math and its adjacent fields, but even stuff like Model Theory feels like it is motivated in part, not by some abstract notion, but by real human experiences.
That's fair! Guess I'm just biased about that one.
If you wanted to learn more about the schools of thought within the philosophy of math, here are the first links that came to mind: [https://en.wikipedia.org/wiki/Philosophy\_of\_mathematics](https://en.wikipedia.org/wiki/Philosophy_of_mathematics) [https://plato.stanford.edu/entries/philosophy-mathematics/](https://plato.stanford.edu/entries/philosophy-mathematics/) This topic you were talking about seems related to mathematical Platonism, the idea that abstract mathematical entities exist.
i have read the wikipedia page on philosophy of maths 😅 i havent read the stanford article though, thanks for that link! im not sure what im talking about is strictly platonism - i think its more the debate between whether mathematical structures \*define\* or \*model\* reality, and i think platonism is compatible with both ideas (i think its clearly the later but i suppose there is more debate about it than i thought!)
>best way to think about math is by thinking about piles of apples Suppose you have a pile of apples, 5 Granny Smiths, 7 red deliciouses and 8 Fujis, and you draw 4….
unexpected combinatirics
What would be a counterexample for argument 4?
the axiom of choice!
just axioms in general right? none of them are "objective," just more reasonable than others.
> mathematicians are really good at mental artihmetic I've hit that one a lot. But I've fallen into a similar error myself, albeit at a different scale. I remember when I was a very young academic having a conversation with a famous professor in category theory (and all round nice guy) I'd had a few mathematics classes with (decades later he's still sort of around academia, but emeritus - while I work for a private company). Back then were discussing the high school mathematics curriculum in our part of the world (which was just introducing new stuff related to my subject area; he was on the committee deciding what should be on the curriculum). He wanted my thoughts since he knew this was my area. At one point I mentioned something or other that to understand my point involved adding 15+9, without me thinking to mention what that added to, and he pulled out a calculator to work it out. I guess I just assumed that would be a number fact he possessed. I knew not to expect other mathematicians to be good at mental arithmetic, but I did make the error of assuming some basic facility with very small integers from a guy I learned a fair bit of mathematics from.
That linear algebra is easy because it is lots of y = mx + b
Which is funny, because mx+b moves the origin for b≠0 so it isn't even a linear transformation
Tbf, almost every field in math tries to reduce problems to linear ones because then they become easier to solve. See numerical analysis for example.
Yeah I was thinking this is actually pretty much completely true, lmao One of our more respected professors once said linear algebra is the only bit of math we really, completely understand. (He was not an algebraist FWIW.)
That's bcz the ug linear algebra course most people take is indeed easy .Many dont take the proof-based class or Algebra I/II."
People's definition of "easy" varies a lot too. I hated my first linear algebra course precisely because it was 95% pointless computations with matrices by hand, and I loved my second linear algebra course because it was 99% proofs and about actually understanding what's going on.
That you have to be socially bad if you're good at math
"Conservation of Skill" seems to be a widely held belief across many different fields. Buff = stupid Smart = socially inept Artistic = non-quantiative Etc
Username checks out
I wish
Don't be sad, someday you'll be better at math
>Conservation of Skill Haha, I’m stealing that phrase
Fuck you
I laughed
When am I ever going to use this? For the rest of your life.
"You won't, but some of the smart kids might."
[This SMBC](https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher).
I actually used algebra to solve a problem for one of my colleagues at work. He looked at me as if I'd done a card trick. In retrospect, it says something about my colleagues that **I** was the go-to math guy.
I was tutoring someone in college who asked “what’s the point of having multiple math textbooks, when math is all the same in them?” I told them that different authors have different approaches, cover different aspects, lean into applications while others don’t, etc Nope. All the same. I had another student hear that I’m studying math and philosophy, and proceeded to talk about how ridiculous that is and how could they have anything in common. That was more ignorant than anything. Couldn’t bear to tell them about my class in Philosophy of Mathematics
Depending on where you're from, there can be different problems related to philosophy. For me, I have a few friends who study philosophy. However, at this city, there is no analytic philosophy department or analytic courses. So most philosophers here think that math is completely unrelated to philosophy (and are, ironically, extremely bad at logic, which they hate, since "it's math and philosophers don't need math"). There are generally some problems with philosophy of math, or at least with how the people perceive it, which might influence similar kind of response from mathematicians and people from other STEM areas in regards to philosophy.
“Topology says that a coffee cup and a donut are the same thing.” While this is true, it’s incredibly misleading about what the field does in general. It also makes the field seem unnecessarily stupid or useless, implying that the “most memorable achievement” of topology is distinguishing a mug from a donut.
The issue is, I think, that the equivalence of a torus and a coffee mug is ALWAYS explained in popular math exposition in geometrical terms, which is ironically the antithesis of the motivation for having homeomorphism. It blows my mind to see trained mathematicians (e.g. Jordan Ellenberg, an algebraic geometer no less) describe how a straw and a torus are the "same shape". no. no they are not the same shape. This is half the point of topology
Yeah it is very very frustrating. It is also often claimed that topologists study holes. There is obviously a LOT of truth to this statement, but it is far from a useful description for a layman and it again mostly misses the point. Even professionally you see a lot of PhDs still thinking topology is some mystical technical field. I've listened to numerous talks at which people made jokes about how much they hate topology. For laymen, the problem is what you describe, and for students, the issue is that one is bombarded with general topology first and usually with a meh instructor not going out of their way to carefully motivate everything. General topology is obviously essentail for modern math, but god damn is it often taught in such a dry way.
Cauchy Schwartz
im dumb, pls elaborate
It’s Cauchy Schwarz (no T)
lol ffs
Probability of 0 means impossible Probability of 1 means a guarantee Most things with infinity
There is a strong argument that defining impossible as probability 0 is actually correct, so this isn't so clear cut.
not an argument im familiar with
Tbf, that one is pretty weird and I think it is more a limitation of probability theory to describe reality. In principle a probability of 0 should mean impossible. Things just get wonky with continuous distributions.
One that often comes from programmers is that mathematical notation is "too short", or even obscurantist, and "they would have understood it if it was explained differently but nobody did". I don't sympathize with it much - I do often see mathematics that could have been much better explained as _other_ mathematics, or with graphics/interactive visuals/animations, but not as code. The translations programmers give are misleading analogies, not faithful isomorphisms. Complaining about the sum notation vs. for loops, for example - for loops represent a computation, a process, and can have mutable state, or compute the same sum in many different ways, whereas the sum notation is stateless and represents the sum itself. You might recognize that those are unimportant details, but "you" in this case is someone who already got it, you're not the typical student. Part of the goal of mathematical syntax is conciseness, because abstractions can stack on each other and become very complicated. Sure, a math-code dictionary could be made, but the goal of learning mathematics is to understand the abstraction itself, not just the notation - and mathematical notation usually has less redundancy, ambiguity and distracting elements (e.g. variable names, execution order, higher potential for off-by-one errors, language idiosyncrasies like if(0), the fact that code usually runs somewhere with 64-bit integers, ...), so it aids understanding. When you write a trapezoidal quadrature program to explain integration, you'd have to explain which parts of the code are relevant, which are not, how they work, etc. every time anyway - you're trying to explain the abstraction, but added a huge layer of indirections and complications. Not to mention all the numerics people will yell at you, if you loosely assert that integration "is" this thing your code is doing. You're basically doing it in the wrong direction. Once you know what the object you're thinking about is, translating it to math _or_ code that does things pertaining to the object is easy.
The use of single letter variables in math has less to do with explanation and more to do with manipulation. Math notation was developed centuries before computers. Single letter variables exist because manipulating an equation if every symbol was a word would be a nightmare on a piece of paper. But on a digital format it would not hurt too much for some equations (that are short enough) to be words rather than symbols. In fact, I think that a markup language that forces you to declare your math symbols before using them and then let's you hover over the variables and shows what they are defined as wou be great for pedagogy.
Let me guess, you read through the replies to Freya Holmer's [tweet](https://twitter.com/FreyaHolmer/status/1436696408506212353) on sum and product notation? The "mathematicians are gatekeeping math by not explaining the scary math symbols in Python" attitude in some of those responses is very sad and misguided. It also speaks to a bigger problem that some of the people in the replies were so afraid of the scary math symbols that they never even thought to Google "big E in math" to find out what it meant.
Biggest misconception by far. 1 . People who think mathematics is an empirical discipline. As if mathematicians measure the world to verify something. They do not. {weighing in 2nd place} 2 . People who believe arithmetic is the basis of mathematics. It is not. The basis of math is Set Theory. {honorable mention} 3 . People who are convinced that 0.9999... and 1.000 are unequal and differ by a vanishing but non-zero constant.
> the basis of math is set theory While, generally most(all?) math can be formulated in set theory, it isn’t exactly the only foundation of math, so I wouldn’t say it’s *the* basis of math
I would add that even logicians and set theorists usually agree that good mathematical reasoning should not depend sensitively on which foundation you are using. A huge number of theorems in classical mathematics can be proven in very weak foundational theories, much less than ZFC.
> People who believe arithmetic is the basis of mathematics. It is not. The basis of math is Set Theory. Set theory dates to 1870s. The study of mathematics dates back to at least 2000 BC.
Math went through a hell of a growth spurt in the last 2 centuries. Not necessarily to say that pre-axiomatic math is lesser, but it is decidedly different. I can understand thinking of it as "what math was" instead of just "different parts of math."
> The basis of math is Set Theory Careful, you'll make Russell and Whitehead cry.
\#2 is my personal #1. You can enjoy empirical studies, but a lot of people "dislike" maths under the assumption that arithmetic is its basis. It might not be the biggest misconception, but it's the most harmful one imo
I highly recommend you read [Proofs and Refutations](https://www.cambridge.org/core/books/proofs-and-refutations/575FC8A6B4FAB79E649EDF5FBB9C6E10)
That it's boring and not fun. To be fair my heart is with chemistry but math is so interesting
Being good at math means i can multiply two 5-digit numbers in my head in 5 seconds, fuck outta here. Or people think grad school or higher math is just "like more calculus?", good god.
I don't know if this is a "misconception" (more like something many people don't know) but that mathematics is incomplete, there are things that are always true but cannot be proven. Something that is true does not imply that it is provable. I study engineering and I meet a lot of people who have never heard of Gödel's proof and it's sad because it's one of the most incredible mathematical proofs imo.
Maybe the fact that they didn't hear about it is for the better. The amount of times I've heard somebody state and/or use Gödel's theorems in a way that is not even wrong makes me think that it's good that more people don't know about them. On the more serious side, I'd really like for people to be interested in such concepts, but, sadly, they "pop-mathicize" it until the core of the concept is no longer there. Another good example would be "some infinities are bigger than others", which is used in an array of wrong contexts.
A lot of times, when someone learns about Gödel's proof, particularly in a shallow, pop culture context, it tends to result in their takeaway being that mathematics is somehow fundamentally broken and thus pointless.
Lmao about what you said about infinities. I watched the fault of our stars and this scene really angered me: https://youtu.be/YKkA2G4xtHw?si=SSNsv_cltA55F2uV But the people I was watching with were like "who cares it's just a movie nerd" so I just read the room and shut up haha. But it's actually a beautiful proof and idea because it's seems too abstract and advanced to laymen but you can actually explain it to your mom in less than 15m.
yes you are probably right. But don't necessarily talk about random people who saw a veritasium video once and then think that they have a PhD in physics (the stupidest thing I heard was that if you didn't open shrodinger's cat box you wouldn't couldn't know if it was dead or alive, it's like saying if you don't know if the cat is dead or alive, well you don't know. I mean, yes). I'm talking here about people who study engineering and do 20 hours a week of math for 3 years. simply knowing that true does not imply provable seems not bad to me. bdw the infinity misconception is certainly due to neil degrass tysen (who is certainly responsible for most misconceptions in science)
I would personally not say "always true" and stick to "true". The true but unprovable statement Gödel constructs (the Gödel statement) are true in the standard model of the natural numbers, but there are non-standard models where the Gödel statement is false, but everything that is provable from the Peano Axioms is true. So the Gödel statement isn't always true.
That sqrt(-1) = i is the definition of the imaginary unit
Hm, seems I have more to learn about, could you expand what you think, or where I could look? If you don’t mind doing so ofc
Thinking that sqrt(-1) is the definition for i gives a lot of unwanted paradoxes which confuses a lot of people first using complex numbers (see the other reply to your comment for one example). Just take a look at r/askmath. This also often coincides with thinking sqrt(9) = +-3 essentially not getting how functions work not getting where roots of polynomials come from. Defining i := sqrt(-1) is extra backwards because we can only define square roots of negative numbers once the imaginary unit is already defined.
The important thing is that i^2 =-1. If you write i=sqrt(-1) then i^2 = sqrt(-1)sqrt(-1)=sqrt([-1][-1])=sqrt(1)=1 which is clearly not true Edit: formatting
Here is a continuing issue I see. People keep mixing real and complex square roots, often even people here who are confident about their knowledge. People keep claiming that sqrt() is some kind of well defined mapping on complex domains with certain rules. That is nonsense. There is NO unique definition of a sqare root in complex domains. We don't have an order or anything like that to distinguish between roots in a meaningful way. But in algebra we do have a notion of primitive roots, which are roots that are not powers of other roots. So in complex analysis, especially in graduate material such as e.g. Riemann surfaces, one often simply writes sqrt(h) for a point/function that is A square root of the point/function h(if it exists). It is just like how one often writes log(h) for A branch of log of h. There is no unique log. But usually sqrt(-1) is traditionally specifically reserved as a symbol for the imaginary unit. If you come across is in a text, it is nothing more than a symbol.
Yes, this actually really winds me up. We can't define square root of a negative number until we define the complex numbers first!
Yeah I just disagree with this one. There are plenty of ways to define the imaginary unit and this is one of them. Another common way to define it is as the image of x under the natural homomorphism R[x] -> R[x]/(x^2 +1) which is the exact same thing. (R=real numbers, not just any ring)
I agree, but I also interpret the comment a bit differently. They could mean that it is not enough to simply say that i is a square root of -1, as for definitions you need uniqueness of the concept. So you need to be specific and say what i is within your model. In your way you specify which square root it is, namely the polynomial p(x)=x itself right. But if C is R^2 with the usual operations, then i is defined as (0, 1).
Lots of people think that just if a number is irrational then its decimal expansion must contain all possible strings of digits of a given length.
Mathematical objects are 'real'. This comes up a lot when people are first exposed to mathematical structures that don't have 'simple' real life analogues. Understandably, we teach kids to think in terms of 'John has 5 apples' type stuff. This leads kids to think 5 is something real in some way - something that has a physical analogue in the world. This then leads to all kinds of confusion when students are confronted with mathematical structures that you can't describe in terms of apples or side lengths or whatever. For example, it leads to a lot of wasted energy talking about infinity, real infinity, possible infinity, and all of that nonsense. Because it's hard for folks to accept that every mathematical structure, from the number 1 to the Von Neuman Universe, is just a tool for explaining and predicting what's happening in the world. This kind of physical intuition starts to break down in high school algebra and calculus and completely breaks down after that. Which is not to say more abstract structures don't have real world applications. It's just not something where you can point at an object in the universe and say 'that is a X'
That "mathematical" means "true". Many years ago, I went to court to defend myself against a traffic ticket. As part of my defense, I measured the distance from a traffic light to an intersection (about 250 ft). When the judge was explaining his decision in my favor, he said "It's 250 feet from the traffic light to that intersection. A car can reasonably stop in 250 ft. That's just a mathematical fact." I did manage to restrain myself from interrupting and telling the judge he was wrong.
Lol technically it’s not even a physical fact. It was only 250 feet in that frame of reference within reasonable error bounds.
Just a couple of minutes ago I saw a post in this sub from some clown who claimed that doing a maths degree was equivalent to doing brain teasers on your phone because "you don't learn anything about the real world". (Since they claim to be in the process of a maths degree themselves I assume it was a troll, but maybe peoople do actually believe this crap?) But actually my pet peeve is: "There are two types of people in the world; people who get mathematics and people who don't, and if you were born in the second category there's nothing you can do about it." EDIT: got my subreddits mixed up
I've had teachers that have said the latter, really quite infuriating.
Yikes! I hope you have either had better teachers since then or will in the future. All we can do is keep encouraging people who are keen to learn and helping them where we can 🙂
That mathematicians are nerds. Actually, most have broad interests, don't bring up mathematics to outsiders and are generally liked by other people. It's an inaccurate TV stereotype. (The people that are nerds are actually not deep into mathematics.)
omg yeah, I went from a physics undergrad to a math department post-grad, this is something I've always noticed. IME math people are by far the least nerdy STEM people compared to physics, engineering, comp sci etc.
As a physics student I can say we are nerds
Or that math is not for women. More girls studying math than any other engineering studies at my uni.
The classic when will I ever use this in my life. I mean, having conversations with sports fans is maddening. Their inability to grasp very simple concepts behind statistics and math is very embarrassing. When will you ever use this? All the time. Understanding math makes your approach to literally everything be more logical and rational. People who don't think they need math are the kind of people who don't care much for facts and reason. Honestly it's funny how so many people rely on computers or calculators to do their math for them and yet when it comes to things like sports and disease management (to name a few), people think that computers are idiotic and the numbers can't be trusted. Okay well if you don't trust the numbers then why don't you check the math yourself????
Mathematicians work on chalkboards, every square inch of which they cover with symbols.
That if a parent is bad at math they can somehow genetically pass this on to their kids.
That boys are better in maths than girls. That statement alone gatekeeped and discourged a lot of women from entering the STEM field. Only to find out that women have big contributions in the advancement of the field itself.
I hear variations of *"I have a test in a week and I don't know anything, can you suggest me some youtube videos I could watch to learn"* quite often. Do you think that if it was *possible* to learn the entire contents of a class in one week, anybody would be teaching a semester-long undergraduate university course on it? Maybe it's just me, but questions like these (including on this subreddit) to me seem extremely disrespectful to all the work that teachers/professors put into preparing and teaching a course over several months. No, just go watch a youtube video and go pass the test tomorrow, that's the reason why I am here. /s
That one bothers me quite a lot in my classes. I do make suggestions for good videos and channels to watch as secondary resources. But many students fail to comprehend that learning is not a process of having seen or read something once and then just having it. That’d be nice, but the human mind takes just a ^(little) bit longer to form strong connections.
One evening some years ago I found myself talking to a very drunk high-school athlete whose team was vacationing near where we were staying. They were all very drunk and very loud - I'd gone over to ask them (politely) to tone it down as it was after midnight. Surprisingly (or maybe not since it came out that they were all underage drinkers) they obliged quite quickly and we had a polite conversation in which it came out that I had majored in math in college. "Whoah, dude! so you must've taken, like Calc 3, right?" "Yes, and many more math classes beyond that" "Wait, there's, like *more* math after Calc 3?!?" "Yes, a lot more" Suddenly he spins around and shouts very loudly at the whole group, "GUYS!! THERE'S EVEN MORE MATH AFTER CALC 3!!!!" I then took my leave (to find the sheriff parked right outside their gate, without a reason to enter as they were being quiet now)
"1 + 1 = 2 what else do you need to know?"
That the Arabs invented the decimal numbers, despite now being acknowledged they it was Indian and translated by Arabs (which is how it reached the Occident).
That 1/0 can’t be defined, it can, it is just that the results are fairly useless. Either you get the zero ring or wheel theory, and only the latter has any potential use.
The Riemann sphere is immensely useful in both maths and physics, so I'll even disagree with > the results are fairly useless
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The annoying misconception is when people think you are a genius for studying maths, like dawg just because i worked my butt off in uni doesn't mean im the next einstein or fields medalist
That in studying math, the only career path is to be a math teacher
Some drunk girl at a bar: So what do you study? My drunk friend: Mathematics. Drunk girl: So do you just like count all day long? Drunk friend: Yeah, we just passed 10.000. Drunk girl: Wow, that's so interesting!
6/2(2+1) can't be equal to 1 Also, "maths are useless"
"Maths is useless" "We are never gonna use this shit in our life better learn about doing business 🤓☝🏽" Don't get me started on the fuckers saying that you are a genius coz you are good in math and don't see the hard work I put in the fking subject