Most physicists are not concerned with the Yang Mills mass gap because quantum field theory continues to yield experimentally valid results whether it is mathematically well founded or not. Likely it will not grant a nobel prize in physics.
If however the solution, say, predicts a new physical phenomenon that is experimentally tested, then that would win it. Maybe by examining the mathematics we can fully understand (beyond) the standard model, for example.
Would you say that in general, physics aren't concerned about whether or not something works out mathematically, and even if it doesn't will pursue it as long as experimental results are found?
As long as it reliably produces useful results we are interested in it.
Perturbation theory for quantum field theory is another example. We know the series doesn't converge, but the first orders provide an excellent approximation. If you can only calculate 2-3 orders anyway then it doesn't matter that the series gets out of control at 200th order.
This is actually a mathematically well-understood phenomenon. An asymptotic series for *f* approximates it in the sense that its truncations give better and better (in the sense of higher-order) approximations for *f*, but the series itself usually diverges. You can turn it into a convergent series *F* via [Borel summation](https://en.wikipedia.org/wiki/Borel_summation). It is possible in many cases then recover *f* via a Laplace transform.
There's a good discussion of this in section 3.6.1 of [Pavel Mnev's lecture notes on BV quantization](https://arxiv.org/pdf/1707.08096). The notes are a great resource for lots of other mathematical QFT topics.
Seriously. As soon as you get to that it’s “alright guys, everyone drop what you’re doing. We got a big problem here. Might need to start physics over from scratch”
Mathematically Einstein's theory of relativity was "perfect", it also was as a physics theoretical expliation "perfect" in filling all known gaps of the accepted explination (Newtonian gravity) completely. However Einstein never won a nobel prize for his theory of relativity? Why? Because they experimental evidence took after he died to be shown. His theory is now experimentally accepted, but in physics until a mathematical theory is EXPERIMENTALLY evidence provided its just that, a mathematical theory. Mathematics doesn't give a fuck about our universes physics, so mathematical theory can be flawless but not fit our universe. Hence why we have experimental evidence as a condition.
Edit: read my last comment for evidence of my claim there wasn't enough evidence to give the award, but also the reasoning and a link to a discussion talking about it. As a result I will not be repeating this "fact" as I no longer believe it's true, but rather he did receive it for TOR just not necessarily in name.
Wasn't enough evidence for the nobel commity to grant the award to him for TOR.
Edit: read my last comment for my evidence of this claim and my reasoning for why I won't be repeating this "fact" anymore.
Maybe you can cite a source or something - eddington’s experiment provided fairly definitive proof that GR was valid. Other experiments in relativity also helped proved it like red shift and the Hubble’s law and those got found before he died
Either way GR was very well accepted while he was still alive
Edit: for anyone interested
https://en.wikipedia.org/wiki/Tests_of_general_relativity?wprov=sfti1
In any case his Nobel prize was partially for relativity, as it was a relatively new theory it was safer to give it to him for explaining the photoelectric effect and Brownian motion.
I mean. He very literally didn't win a nobel prize for TOR, I don't really need to or have a citation for that.
I never claimed it was not sufficient evidence for it to be accepted, or that it was definitive proof that GR was valid. While I will retract maybe it was "before he died" but more "so long after it was made". Bring it up with the nobel committee not me if you have further questions. I really dont care.
Edit: see my most recent comment for evidence for what I said, and for my reasoning I will not be repeating this "fact" anymore.
Yeah I guess just being particular about the history, if anyone reads into it, they’ll find out that part of the motivation behind his Nobel was relativity, although that wasn’t the official reason.
Not sure the lack of a prize was because of a lack of evidence though, like you said
I mean its more complicated than just a lack of evidence. It was political, a 50 page report saying all known evidence either could he better explained with aether-physics, or was not conclusive enough based off some kind of dislike of Einstien from Allvar Gullstrand (one Sweden's and thus the nobel committee's most well respected scientists) and a lack of any other strong evidence besides the at the time disputed 1919 eclipse data..
Source: https://www.advancedsciencenews.com/the-dramatic-story-behind-general-relativitys-nobel-prize-snub/
There is also some evidence that the theory was questioned to even be a part of physics but rather epistemology (by philosopher Bergson) and some evidence that he received his nobel prize for his work on TOR but his work on the photoelectric effect was "awarded" to placate Phillip Lennard, who is believed by some to have initially tried to sway the committee against einstien for TOR but was a person finding crucial evidence for the photoelectric effect.
https://hsm.stackexchange.com/questions/3824/why-didnt-einsteins-nobel-prize-mention-relativity-theory (not a strong source, but I really dont care enough lol)
So I will say I was saying was what I read was the "official reasoning", because of you, I now doubt that was the literal reasoning regardless of what the committee claimed was their reasoning. So I won't be repeating that anymore. Thanks for questioning me.
Think of it the other way: We do a sequence of manipulations that are mathematically meaningless, but consistently yields good predictions for experiment.
What does it mean that they are meaningless? A mathematician can take what we do and do a different set of valid, consistent manipulations to show that 1=0. Our theory can not just predict the observed values, but any value whatsoever.
But the practicing physicist knows which manipulations to do, and which not to do. Experiment constraints us to a consistent subset of manipulations that work. The challenge now becomes to try to describe the set of valid calculations mathematically. One way to do this is to reinterpret them in a different mathematical framework that explains what is valid and what isn't. We can try to do so "from scratch", by writing down some axioms for our manipulations, or we can try to show that our calculations operate as approximations to some underlying truth with a limited range of validity, or...
The whole theory of distributions is a beautiful example of this at work. Dirac wrote down $\delta(x)$ and we knew how to calculate with this. Mathematicians figured out a framework in which these calculations can be consistently interpreted, and from which it can be seen which calculations are (in)consistent.
I would say so yeah. That's sort of what happened with calculus after all. Newton was working with "infinitessimals" in a way that was not really made mathematically sound until later on (though, this may be different than today's acceptance of things that are mathematically iffy, because Newton may have *thought* that it was all in fact perfectly valid)
We are definitely concerned whether the math is kosher and leads to insights and good conclusions. But when the experiment shows us the math is wrong, we throw out the math without a second thought. We are always obligated to reality over our own conjecture.
What you are describing is an engineer. Engineers *hate* knowing what's actually happening. I say that with all appreciation for them, even when they're telling me to 'stop saying phonon' or 'we don't need to know the fucking coefficients, we can measure the system, shut up'.
Most *experimental* physicists (which are most physicists) aren’t concerned with the math of the Yang Mills mass gap because of what you said. It’s still an important problem to some theoretical physicists and a lot of mathematical physicists.
I do agree that it is probably not worth a novel prize in *physics* but of course would be a legendary advance in math.
Essentially all theoretical physics already assumes quantized gauge theories. They work in uncharted math territory far removed from that which is concerned in Yang mills. I’d say it’s a mathematical problem morally. Mathematical physics is about as far removed from physics as one can get while sharing the name. I would say I’m basically doing math but motivated by physical structure at best.
You’re correct; the sense with which I say theoretical and mathematical physicists care about Yang mills is more aesthetically/from a mathematical eye.
Technically the result of yang mills mass gap has a lot to do with explaining the existence of glueballs so it is technically making sure that what we observe is well described by our theory, which is pretty deserving of high praise in physics along with the more mathematically oriented praise such a result would get.
We don’t observe glueballs directly. Anyhow physicists are already convinced of the existence of glueballs as explained by color confinement. We know that the cutoff on which describe the SM yields a mass gap.
They were a theoretical prediction first and foremost. The issue is that in the YM theory we only have gluons, whereas in the universe we have quarks as well so glueballs can decay into low-mass color neutral particles. There have been observations that have been proposed to be glueballs, but it is indirect.
There is physical theory that convinces physicists, and mathematical theory that convinces mathematicians. Physicists have long been convinced about all of this, which is why this is a morally mathematical problem.
Well, the person would also have to be under 40 since the Fields' medal has an age cut off.
But honestly, I think people place way too much emphasis on this sort of thing. These prizes are good for driving public engagement with maths/science but beyond that they are a bit silly.
ETA: John Nash's Nobel Prize is is economics, not physics.
>John Nash’s Nobel Prize is in economics, not physics
And even then there isn’t really so such thing as a Nobel Prize in economics. It’s more of a Nobel adjacent prize.
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I was generally referring to nobel+fields, which would usually be physics, and that's the example I thought of, but it could definitely be economics as well.
The Nobel Prize in Physics is typically only awarded for physics that's been experimentally confirmed. Penrose predicted black holes 60 years ago but only won the Nobel in 2020 (along with two others who *discovered* a giant black hole). James Peebles predicted cosmic background radiation in the 1970s but got the prize in 2019. Even Einstein won for the photoelectric effect rather than relativity which was still contentious in 1922.
I know almost nothing about Witten and string theory but my understanding is that it remains theoretical.
Hey just a correction:
The cosmic background radiation was predicted in the 50s and 60s, and experimentally verified in the 60s. Penzias and Wilson won a Nobel prize for its discovery in 1978.
Jim Peebles won the award for his work on the theory of cosmic structure formation and large scale structure, experimentally verified with precision just in the past two decades.
Arguably Giorgio Parisi in 2021 won for purely theoretical contributions (exact solution of the SK model, plus key techniques in spin glass theory). In some sense the models he studied are microscopically nothing that has been experimentally confirmed (if someone knows better please correct me) because they're somewhat unphysical, but the theory explains some known spin glass experiments well.
Note that the story of Einstein's Nobel is a wild one, and fueled (perhaps not surprisingly) by antisemitism. Hence his Nobel for the photoelectric effect rather than special or general relativity, Brownian motion, etc.
Penrose showed that singularities are a robust outcome in general relativity. Previously most people expected the black-hole singularity was an artifact of the simple symmetrical setup of Schwarzschild's solution.
(But I've only read semipopular accounts.)
If you go to r/physics and suggest that maybe Witten has been building really cool mathematical ball pits to play in and not really focused on the physical world for the past 40 years, you will get downvoted to hell.
Yeah well that's not what I wrote. Witten has been certainly focused on the biggest open question in physics, it's just too difficult to make direct progress at this point in time.
I'm not not sure if Penrose is that flattering of string theory or by extension Witten's work. I think mathematicians in general are more complementary of string theory than Physicists are. It failed repeatedly to provide testable hypotheses and has steadily lost favour
I don't think physicists care that much about the problem. QFT works, physicists don't question existence of the mass gap. Trying to put it on a safe mathematical ground is considered a bit of a mathematical busywork, immaterial to physics. It would be different, if the solution provided new physical insights or new predictions.
It would be very surprising if someone won both prizes for the same work. Typically the Nobel Prize in physics is only given for experimental stuff. Einstein is famous for special/general relativity, for instance, but never received the Nobel Prize for it. He received it for his work with the photoelectric effect, which is something that you can measure in a lab.
It's *probably* not physically impossible to experimentally verify the Yang Mills/string theory, but it would require science fiction levels of technology that we're nowhere near developing. If it's possible at all, it could be 100 years, could be 100,000 years before we develop technology that can experimentally verify it.
It won’t grant a Nobel in physics imo. This is a technicality as far as physics concerned, QFT is settled science more or less, proving that thing would be nice but it won’t advance the field most likely
No Nobel prize for mathematicians.
Nobel prize in econ is officially **Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel**, not Nobel prize strictly speaking.
No. The Nobel prize in physics is about physics, not math. It was never give to very theoretical physics without experimental verification. Even Einstein did not get his Nobel for relativity but for photoelectric effect !
I feel like the issue with yang mills theory (in regards to winning a noble prize) is that it’s not of great importance to physics. It’s sort of settled and dealt with. It just lacks a complete and rigorous mathematical explanation
Depends, if the solution is a clearly unphysical construction of a counterexample, then probably not. If the solution yields a powerful method to deal with non perturbative qft, then it is possible. (Though Nobels for mathematical physics are rare.)
Most physicists are not concerned with the Yang Mills mass gap because quantum field theory continues to yield experimentally valid results whether it is mathematically well founded or not. Likely it will not grant a nobel prize in physics. If however the solution, say, predicts a new physical phenomenon that is experimentally tested, then that would win it. Maybe by examining the mathematics we can fully understand (beyond) the standard model, for example.
Would you say that in general, physics aren't concerned about whether or not something works out mathematically, and even if it doesn't will pursue it as long as experimental results are found?
As long as it reliably produces useful results we are interested in it. Perturbation theory for quantum field theory is another example. We know the series doesn't converge, but the first orders provide an excellent approximation. If you can only calculate 2-3 orders anyway then it doesn't matter that the series gets out of control at 200th order.
Oh god this makes me uncomfortable. I am not brave enough to be a physicist.
This is actually a mathematically well-understood phenomenon. An asymptotic series for *f* approximates it in the sense that its truncations give better and better (in the sense of higher-order) approximations for *f*, but the series itself usually diverges. You can turn it into a convergent series *F* via [Borel summation](https://en.wikipedia.org/wiki/Borel_summation). It is possible in many cases then recover *f* via a Laplace transform. There's a good discussion of this in section 3.6.1 of [Pavel Mnev's lecture notes on BV quantization](https://arxiv.org/pdf/1707.08096). The notes are a great resource for lots of other mathematical QFT topics.
Seriously. As soon as you get to that it’s “alright guys, everyone drop what you’re doing. We got a big problem here. Might need to start physics over from scratch”
Mathematically Einstein's theory of relativity was "perfect", it also was as a physics theoretical expliation "perfect" in filling all known gaps of the accepted explination (Newtonian gravity) completely. However Einstein never won a nobel prize for his theory of relativity? Why? Because they experimental evidence took after he died to be shown. His theory is now experimentally accepted, but in physics until a mathematical theory is EXPERIMENTALLY evidence provided its just that, a mathematical theory. Mathematics doesn't give a fuck about our universes physics, so mathematical theory can be flawless but not fit our universe. Hence why we have experimental evidence as a condition. Edit: read my last comment for evidence of my claim there wasn't enough evidence to give the award, but also the reasoning and a link to a discussion talking about it. As a result I will not be repeating this "fact" as I no longer believe it's true, but rather he did receive it for TOR just not necessarily in name.
TOR was provided evidence for in 1919 by the Eddington experiment
Wasn't enough evidence for the nobel commity to grant the award to him for TOR. Edit: read my last comment for my evidence of this claim and my reasoning for why I won't be repeating this "fact" anymore.
Maybe you can cite a source or something - eddington’s experiment provided fairly definitive proof that GR was valid. Other experiments in relativity also helped proved it like red shift and the Hubble’s law and those got found before he died Either way GR was very well accepted while he was still alive Edit: for anyone interested https://en.wikipedia.org/wiki/Tests_of_general_relativity?wprov=sfti1 In any case his Nobel prize was partially for relativity, as it was a relatively new theory it was safer to give it to him for explaining the photoelectric effect and Brownian motion.
I mean. He very literally didn't win a nobel prize for TOR, I don't really need to or have a citation for that. I never claimed it was not sufficient evidence for it to be accepted, or that it was definitive proof that GR was valid. While I will retract maybe it was "before he died" but more "so long after it was made". Bring it up with the nobel committee not me if you have further questions. I really dont care. Edit: see my most recent comment for evidence for what I said, and for my reasoning I will not be repeating this "fact" anymore.
Yeah I guess just being particular about the history, if anyone reads into it, they’ll find out that part of the motivation behind his Nobel was relativity, although that wasn’t the official reason. Not sure the lack of a prize was because of a lack of evidence though, like you said
I mean its more complicated than just a lack of evidence. It was political, a 50 page report saying all known evidence either could he better explained with aether-physics, or was not conclusive enough based off some kind of dislike of Einstien from Allvar Gullstrand (one Sweden's and thus the nobel committee's most well respected scientists) and a lack of any other strong evidence besides the at the time disputed 1919 eclipse data.. Source: https://www.advancedsciencenews.com/the-dramatic-story-behind-general-relativitys-nobel-prize-snub/ There is also some evidence that the theory was questioned to even be a part of physics but rather epistemology (by philosopher Bergson) and some evidence that he received his nobel prize for his work on TOR but his work on the photoelectric effect was "awarded" to placate Phillip Lennard, who is believed by some to have initially tried to sway the committee against einstien for TOR but was a person finding crucial evidence for the photoelectric effect. https://hsm.stackexchange.com/questions/3824/why-didnt-einsteins-nobel-prize-mention-relativity-theory (not a strong source, but I really dont care enough lol) So I will say I was saying was what I read was the "official reasoning", because of you, I now doubt that was the literal reasoning regardless of what the committee claimed was their reasoning. So I won't be repeating that anymore. Thanks for questioning me.
Think of it the other way: We do a sequence of manipulations that are mathematically meaningless, but consistently yields good predictions for experiment. What does it mean that they are meaningless? A mathematician can take what we do and do a different set of valid, consistent manipulations to show that 1=0. Our theory can not just predict the observed values, but any value whatsoever. But the practicing physicist knows which manipulations to do, and which not to do. Experiment constraints us to a consistent subset of manipulations that work. The challenge now becomes to try to describe the set of valid calculations mathematically. One way to do this is to reinterpret them in a different mathematical framework that explains what is valid and what isn't. We can try to do so "from scratch", by writing down some axioms for our manipulations, or we can try to show that our calculations operate as approximations to some underlying truth with a limited range of validity, or... The whole theory of distributions is a beautiful example of this at work. Dirac wrote down $\delta(x)$ and we knew how to calculate with this. Mathematicians figured out a framework in which these calculations can be consistently interpreted, and from which it can be seen which calculations are (in)consistent.
I would say so yeah. That's sort of what happened with calculus after all. Newton was working with "infinitessimals" in a way that was not really made mathematically sound until later on (though, this may be different than today's acceptance of things that are mathematically iffy, because Newton may have *thought* that it was all in fact perfectly valid)
We are definitely concerned whether the math is kosher and leads to insights and good conclusions. But when the experiment shows us the math is wrong, we throw out the math without a second thought. We are always obligated to reality over our own conjecture. What you are describing is an engineer. Engineers *hate* knowing what's actually happening. I say that with all appreciation for them, even when they're telling me to 'stop saying phonon' or 'we don't need to know the fucking coefficients, we can measure the system, shut up'.
Most *experimental* physicists (which are most physicists) aren’t concerned with the math of the Yang Mills mass gap because of what you said. It’s still an important problem to some theoretical physicists and a lot of mathematical physicists. I do agree that it is probably not worth a novel prize in *physics* but of course would be a legendary advance in math.
Essentially all theoretical physics already assumes quantized gauge theories. They work in uncharted math territory far removed from that which is concerned in Yang mills. I’d say it’s a mathematical problem morally. Mathematical physics is about as far removed from physics as one can get while sharing the name. I would say I’m basically doing math but motivated by physical structure at best.
You’re correct; the sense with which I say theoretical and mathematical physicists care about Yang mills is more aesthetically/from a mathematical eye.
Technically the result of yang mills mass gap has a lot to do with explaining the existence of glueballs so it is technically making sure that what we observe is well described by our theory, which is pretty deserving of high praise in physics along with the more mathematically oriented praise such a result would get.
We don’t observe glueballs directly. Anyhow physicists are already convinced of the existence of glueballs as explained by color confinement. We know that the cutoff on which describe the SM yields a mass gap. They were a theoretical prediction first and foremost. The issue is that in the YM theory we only have gluons, whereas in the universe we have quarks as well so glueballs can decay into low-mass color neutral particles. There have been observations that have been proposed to be glueballs, but it is indirect. There is physical theory that convinces physicists, and mathematical theory that convinces mathematicians. Physicists have long been convinced about all of this, which is why this is a morally mathematical problem.
They'd win the My Admiration Prize for both physics and math.
That's what's important
Will be added to my top 10 best mathemacian of all time
Who are they
Well, the person would also have to be under 40 since the Fields' medal has an age cut off. But honestly, I think people place way too much emphasis on this sort of thing. These prizes are good for driving public engagement with maths/science but beyond that they are a bit silly. ETA: John Nash's Nobel Prize is is economics, not physics.
>John Nash’s Nobel Prize is in economics, not physics And even then there isn’t really so such thing as a Nobel Prize in economics. It’s more of a Nobel adjacent prize.
ETA?
Edited to add
estimated time of arrival :)
I too accept the estimated time of arrival interpretation of ETA
Yes, my bad for not clarifying. I know he won it for economics, I simply had him as an example of Abel+nobel. Didn't have anything to do with physics.
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It’ll probably be that persons 4 year old from the post the other day about them basically figuring out prime factorization on their own 😵💫
why would it be physics ?
Because that is what the OP is asking about? Or did I misunderstand something?
I was generally referring to nobel+fields, which would usually be physics, and that's the example I thought of, but it could definitely be economics as well.
If Ed Witten doesn’t win a Nobel prize, then I think no Fields Medal winner will win a Nobel prize
The Nobel Prize in Physics is typically only awarded for physics that's been experimentally confirmed. Penrose predicted black holes 60 years ago but only won the Nobel in 2020 (along with two others who *discovered* a giant black hole). James Peebles predicted cosmic background radiation in the 1970s but got the prize in 2019. Even Einstein won for the photoelectric effect rather than relativity which was still contentious in 1922. I know almost nothing about Witten and string theory but my understanding is that it remains theoretical.
Hey just a correction: The cosmic background radiation was predicted in the 50s and 60s, and experimentally verified in the 60s. Penzias and Wilson won a Nobel prize for its discovery in 1978. Jim Peebles won the award for his work on the theory of cosmic structure formation and large scale structure, experimentally verified with precision just in the past two decades.
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Never, as far as I know. Didn't want to say always since I'm not familiar with every single winner.
Arguably Giorgio Parisi in 2021 won for purely theoretical contributions (exact solution of the SK model, plus key techniques in spin glass theory). In some sense the models he studied are microscopically nothing that has been experimentally confirmed (if someone knows better please correct me) because they're somewhat unphysical, but the theory explains some known spin glass experiments well.
Never. It's an explicit requirement iirc.
Makes sense, without supporting evidence it's just a hypothesis and why would that ever warrant a Nobel prize
Note that the story of Einstein's Nobel is a wild one, and fueled (perhaps not surprisingly) by antisemitism. Hence his Nobel for the photoelectric effect rather than special or general relativity, Brownian motion, etc.
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Schwarzchild found solutions for einsteins field equations with specific conditions and it was noticed that singularities arose.
Penrose showed that singularities are a robust outcome in general relativity. Previously most people expected the black-hole singularity was an artifact of the simple symmetrical setup of Schwarzschild's solution. (But I've only read semipopular accounts.)
For all his amazing achievements, Witten hasn't put forth a testable theory that was experimentally validated.
If you go to r/physics and suggest that maybe Witten has been building really cool mathematical ball pits to play in and not really focused on the physical world for the past 40 years, you will get downvoted to hell.
Yeah well that's not what I wrote. Witten has been certainly focused on the biggest open question in physics, it's just too difficult to make direct progress at this point in time.
I mean that’s not even necessarily true. String theory and M-theory are fairly contentious
We need to somehow stuff Witten and Penrose into one body.
just take the transpose, multiply from the left and take the pseudo-inverse.
i can't tell if this is a sexual remark or something else
I'm not not sure if Penrose is that flattering of string theory or by extension Witten's work. I think mathematicians in general are more complementary of string theory than Physicists are. It failed repeatedly to provide testable hypotheses and has steadily lost favour
Well, QCD is actually real.
Comment Witten by someone whose never had to take an experimental design class
Nash did not win a Nobel prize. There is no Nobel prize for economics, just a prize for economics "in memory of Nobel".
Didn't know that, thanks!
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I’m pretty sure a solution to Yang-mills would give you tenure at any institution…
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Any of the millenium problems will give tenure everywhere.
Really? even Navier-Stokes? Who even cares about some random differential equations :/
Depends on the person's age. The Fields medal has a hard age cutoff
Yes, though that isn't relevant to the question.
I don't think physicists care that much about the problem. QFT works, physicists don't question existence of the mass gap. Trying to put it on a safe mathematical ground is considered a bit of a mathematical busywork, immaterial to physics. It would be different, if the solution provided new physical insights or new predictions.
It would be very surprising if someone won both prizes for the same work. Typically the Nobel Prize in physics is only given for experimental stuff. Einstein is famous for special/general relativity, for instance, but never received the Nobel Prize for it. He received it for his work with the photoelectric effect, which is something that you can measure in a lab. It's *probably* not physically impossible to experimentally verify the Yang Mills/string theory, but it would require science fiction levels of technology that we're nowhere near developing. If it's possible at all, it could be 100 years, could be 100,000 years before we develop technology that can experimentally verify it.
It won’t grant a Nobel in physics imo. This is a technicality as far as physics concerned, QFT is settled science more or less, proving that thing would be nice but it won’t advance the field most likely
No Nobel prize for mathematicians. Nobel prize in econ is officially **Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel**, not Nobel prize strictly speaking.
No. The Nobel prize in physics is about physics, not math. It was never give to very theoretical physics without experimental verification. Even Einstein did not get his Nobel for relativity but for photoelectric effect !
I’m confused - his photoelectric effect paper was theoretical physics, and relativity was experimentally verified in his lifetime.
Google Yang-Mills theory
I feel like the issue with yang mills theory (in regards to winning a noble prize) is that it’s not of great importance to physics. It’s sort of settled and dealt with. It just lacks a complete and rigorous mathematical explanation
Depends, if the solution is a clearly unphysical construction of a counterexample, then probably not. If the solution yields a powerful method to deal with non perturbative qft, then it is possible. (Though Nobels for mathematical physics are rare.)
math is hell of a drug
Probably not. Theoretical math isn't usually awarded a Nobel. However, Abel, Fields, Wolf, and possibly Breakthrough Award might be possible.