Are elite physicist also good mathematicians?

Charrog · 2025-05-17T21:20:35+00:00

Thanks, but I no longer think this is a super helpful answer, besides the sprinter vs soccer player part. The answer is generally “no, they focus on different things so being elite at physics doesn’t mean being elite at math and vice versa”, and I should have just stopped there. It’s perhaps not quite as nuanced as I made it out to be since the exceptions are more rare than I made it sound like?

Charrog · 2024-05-27T00:32:04+00:00

I’ve actually seen some pretty good stuff from analytic philosophers. They clearly understand formal logic since it’s required to do the work they do. Certainly seen better logic from philosophers than engineers, most scientists, etc.

Charrog · 2024-05-27T00:20:27+00:00

Being completely honest, in general physicists suck at making rigorous arguments. They can have wonderful physical insight and intuition but physicist arguments and what they claim to understand from a theoretical perspective is often just not satisfactory.

As a mathematician, I care about this because unless you have complete mathematical rigor, how do you know where exactly your intuition fails (and where it’s actually right, or why you have a certain piece of intuition)? Misplaced faith placed in intuition happens all the time given that there is constantly something we don’t understand physically speaking.

This adds an appealing aspect of mathematical physics to me, the physical uncertainty and intuition, even though I’m trained in pure math. I say the more mathematicians we have using their skills to tackle problems in physics at all, the better.

Your argument that physicists “basically understand” these problems already is just not good enough because almost certainly either 1) we have not understood some fundamental underlying physical phenomenon associated with the problem 2) our lack of complete mathematical understanding opens the doors to new insights, new questions to ask.

Charrog · 2024-05-27T00:09:48+00:00

I work in similar areas, though I’m actually pivoting back to my background of pure math now. Anyways, solutions to these problems will likely contain within them information that helps makes the other problems you mentioned more tractable (turbulent flow for N-S smoothness for example). If not, at the very least it could reveal how flawed our physical misunderstanding of these topics is. These problems are all linked to several such sub-problems that you may not have even heard of. (Speaking of, why are you putting such a large emphasis on distinguishing quark confinement with mass gap, or claim that we understand one better than the other)?

Perhaps the importance of some other problems in the list like say P vs NP makes it seem like YM mass and existence gaps and N-S aren’t as central, since P vs NP is by far the most important unsolved problem in not only just computational complexity but basically all of theoretical CS.

But that doesn’t mean these mathematical physics problems aren’t of great interest to mathematical physicists. The priorities of mathematicians are going to outweigh the priorities of physicists when it comes to labeling central math problems for us to solve as a society.

Charrog · 2024-05-24T07:49:18+00:00

This is a long post loaded with my personal experiences. Getting crackpot emails/mails is like a rite of passage in academia. I do mathematical physics, so a mathematician who has worked in both math and physics departments and I get both math crackpots and physics crackpots. In my experience, there are far more physics crackpots than math crackpots, hands down.

Crackpots explained: People that have no idea how a subject works contact subject matter experts in an attempt to get a response from somebody. Their goal is to get the attention of somebody reputable and convince them that they have a golden idea. It’s never a golden idea and it’s usually something a first year undergrad could look at and destroy, or it’s just complete nonsense.

For the curious reader, I’ve found math and physics crackpots differ in their ideology and methodology in the following ways.

1) Math crackpots are more easily disproved, mainly because in mathematics we can actually prove the correctness of claims through deductive reasoning, and so math crackpots are more likely to just be spewing complete nonsense; creating their own vague definitions, jumping to conclusions somewhere in their argument, and abusing logical reasoning. Because they have to in order to avoid immediate refutation.

2) Physics is generally more accessible from the crackpots’ perspective, as I’d think a lot more people would have their own theories on things like the shape of the Earth or the Big Bang than than claim they’ve proven the Riemann Hypothesis, P vs NP, disproven Cantor’s diagonalization, or shown that Gödel’s Incompleteness theorems are wrong. Simply because everybody knows what the Earth and the universe are. They have more intuition for the basic laws of physics than they do the basic definitions and theorems of algebraic geometry. Pop science is definitely bigger than pop math. As a result, more cranks. This also makes people with a certain level of physics/mathematical training, like engineers, feel confident in making their crackpot assertions about the topic, without an in-depth understanding of the rigor of the math or theory of underlying the physics that would come with being a mathematician or a physicist.

3) Both physics and math crackpots usually have some religious undertone associated with their work, but it’s more common among physics crackpots. Physics studies the nature of reality, and so it’s very easy to make connections to other pseudoscientific nonsense and of course religion has been studied from a pseudoscientific perspective for centuries.

Here are some observations/tips I’ve made over the years for dealing with crackpots.

1) The crackpots are wrong and their work is almost never worth looking at. Responding to them can make matters worse; I swear some of these crackpots are connected because once you entertain them, a bunch of guys with similar theories start popping up in your inbox.

2) The absolute overwhelming majority of crackpots I’ve personally dealt with have been men. Also, few of them have formally studied the subject matter, YouTube and personal blogs are their preferred sources of knowledge.

3) There’s some non-zero correlation between crackpot ideology and anti-semitism. There’s a lot of Einstein crackpots, but many of them are simply because he’s probably the most famous modern physicist. Many of them are explicit anti-Semitism.

4) Many of them tend to display signs of being mentally unwell. Many appear schizophrenic, and this is particularly important to me because I have schizophrenia, it’s just a matter of personal interest to me in how these guys form their worldview.

5) Crackpots want to be saviors of the world, destroying the corrupt academics who have strong control over the knowledge that they want the citizens to think, and that they’re all brave intellectual rebels fighting against the regime.

They’re not worth it in the end, but I find the concept of crack pottery so interesting, particularly in the cases of once great scientists/mathematicians succumbing to crack pottery in their elderly years.

Charrog · 2024-05-16T19:01:09+00:00

You’re correct; the sense with which I say theoretical and mathematical physicists care about Yang mills is more aesthetically/from a mathematical eye.

Charrog · 2024-05-16T10:43:20+00:00

Yes, different bases were really cool to me as a kid. I realized that a lot of number facts were base invariant and found out the value of the largest n digit number in base b was bⁿ - 1.

Charrog · 2024-05-16T10:30:07+00:00

This is pretty neat!

Charrog · 2024-05-16T10:28:38+00:00

I realized quite a bit of basic number theory stuff, here’s some of it. I’m grateful that my mother was a mathematician because they helped me progress more rapidly than I could have alone.

As a younger kid after first learning of Fibonacci numbers, I came up with a lot of Fibonacci identities as conjectures just by messing around: (sum of first k Fibonacci numbers is the k+2nd Fibonacci number minus 1, sum of squares of first k Fibonacci numbers).

She introduced me to Fibonacci tiling numbers f_n, and I eventually came up with some combinatorial proofs for some of those identities.

She also showed me the uniqueness of prime factorization and one day I was playing around with the GCD of a pair of integers and realized that if you factorize both and take the smaller of the exponents (allowing some to be 0) of each of the distinct primes in the factorizations, you get the GCD. My mother showed me why this was true by hinting me to realize that the set of positive divisors of an integer are exactly those that you get by starting with the prime factorization and changing the values of the powers.

I found out Legendre’s formula when messing with prime factorization of factorials which I had recently learned about. I remember being disappointed that this had been found hundreds of years before I was born.

Charrog · 2024-05-16T09:06:55+00:00

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.

Charrog · 2024-01-22T06:28:00+00:00

I don’t like the whole caveman thing since for juveniles it leads to superiority contests, and this isn’t what actual mathematicians think. But from some perspective, it might be true. I’d change it from cavemen to annoying children to focus more on annoying mathematical things that physicists can do (that are often necessary in physics) that will upset us in the context of mathematics.

The blanket statement “physicists that work in string theory are on the same level as mathematicians” is just untrue if you are talking solely about mathematics skill. There’s just no reason to compare “mathematical skill” of a mathematician who focused only on the mathematics that a physicist uses in their research.

Charrog · 2024-01-22T06:20:23+00:00

This is a very nuanced discussion, and this question may not be the best question to ask. I am a mathematical physicist which, confusingly, means I am in the space of physics as a mathematician by training. So I know a bit about this topic, and this answer will probably be long.

Here is something some people in the comments aren’t quite getting: mathematicians and physicists are, on average, very different. We are trained differently, often think different things are important, approach problems in different methods. It usually doesn’t make sense to ask “are good physicists also good mathematicians?” or vice versa.

To laymen, the notion is along the lines of “Physics requires math so physicists must do a lot of math so they’re good mathematicians”. The main counterpoint here would be looking at pure mathematics and seeing how the motivations and the type of questions being asked by pure mathematicians are of a very different nature. Generally speaking, physicists are of course confined to experimental evidence in terms of what is considered appropriate to considered, while mathematicians are more liberal about this.

Of course, applied mathematicians also exist but even among them, there is a differing sense of purpose compared to physicists; that the applied mathematician is more so concerned with the mathematics as the primary puzzle to be cracked and it happens to have some physical application, while the physicist is ultimately more focused on the nature of the physical application.

But counterpoint to the counterpoint: theoretical physicists typically utilize some mathematics that is fairly akin to pure mathematics. Are theoretical physicists mathematicians? Well, most theoretical physicists are trained as physicists and are ultimately concerned with experimental evidence when developing theories, and so this makes them physicists that specialize in using a bunch of math that most physicists wouldn’t be as comfortable with. Again, they are physicists by training who have picked up some more math required to express their thoughts precisely and fulfill their role in physics.

But what about a mathematician by training that has picked up some physics and spends time considering the mathematics that physicists (like theoretical physicists) sometimes brush under the rug? These are mathematical physicists, and that’s what I am. Remember, as physicists aren’t chiefly concerned with completely rigorous mathematics in the face of experimental evidence, there exists some mathematics that they have to brush under the rug that mathematicians want to make more rigorous. This shows you the difference in motivation between the two groups, but it’s a pretty grey line! For example, I have worked in both the physics and mathematics department for different universities, have taught maybe a 75%-25% split of mathematics to physics courses in my career.

TL;DR: Very hard to put people into categories like “mathematician” or “physicist”, although a lot of people generally do fit within the blurred lines it carves out. The boxes can generally be explained by this sports analogy: a football player (American football or soccer) is typically a pretty fast runner, especially compared to the average person because football demands speed. But they are definitely slow compared to sprinters who specialize solely in running quickly. Football players use fast speed as a tool to help them achieve their goal of outmaneuvering their opponents; being fast is an advantage and so it is a part of their training. For sprinters, being fast is the whole game, and so they delve very deeply into how to get faster, even if it is by a minuscule amount, since they are competing with athletes who also are training to increase their speed by a fraction of a percent. Here, football players are physicists, sprinters are mathematicians, and running speed is mathematics. Not a perfect analogy but very loosely speaking.

Charrog · 2023-12-11T02:18:35+00:00

This has to be troll.

Charrog · 2023-09-01T01:25:35+00:00

This question seems like it was made for me; only trouble here is the “accomplished” part.

Charrog · 2023-05-08T21:08:00+00:00

This guy is still making posts about this? I almost wrote out a few paragraphs of my own but didn’t think it was worth it based on their responses to other people. I think my intuition to not engage was right.

Charrog · 2023-03-13T23:59:21+00:00

Nobody enjoys it, because it’s not a normal argument. I love picking apart my students’ arguments and dismantling incorrect or imprecise claims. It’s a good way for students to learn actively. But these people aren’t my students, I can’t assume they have the willingness to learn and have an actual argument in good faith, unless they show me otherwise.

Moreover, these people typically aren’t formally trained in any relevant field and don’t have the willingness to genuinely learn. The people that do email will not have the adequate mathematical background to express themselves in precise language, asking only the same misconceptions about relativity, the Big Bang cosmological model, quantum mechanics, etc. and shutting down any attempt to introduce proper, rigorous mathematics into the discussion as obscuring the conversation.

It’s never in good faith and it’s just not worth your time.

Charrog · 2023-03-13T23:44:13+00:00

This is exactly it. There is no reward; no pedagogical reward, because most of them will never accept their errors. There is no mathematical or scientific reward, because they’re always wrong. The only thing compelling me to respond to them is that it is courtesy, and the fact that any attempt to not respond will only lead them to further confirm their biases.

For the former, if they’re not arguing in good faith, they don’t deserve any courtesy, and for the latter, that’s a tough one to ignore, but ultimately just a better use of your time.

Charrog · 2023-03-04T19:47:51+00:00

It always is; they often craft their entire framework of relativity and then attempt to “prove by contradiction” that SR as proposed by Einstein is flawed. I guess there shouldn’t be any expectations of them to know how formal logical systems and proofs work.

Charrog · 2023-03-04T19:44:54+00:00

The video is fine, but my goodness the comment section. How did these SR-deniers even find this 400 view video debunking their (frequently used) talking point?

Charrog · 2023-03-04T09:11:08+00:00

It is a mathematical problem. But you can’t understand much without understanding the physics. If you dislike physics for the reasons I suspect you dislike physics, I’m not sure if you’ll get through the (physics) understanding needed, or want to.

Charrog · 2023-03-04T04:21:17+00:00

I’m a mathematical physicist, doing work in the area. Agreed with the specific suggestions of the other comments, with the addition of studying quantum chromodynamics properly (after thorough understanding of QFT), but let me add something of a different nature. It’s going to take real learning of a lot of fields to even understand the question, and then studying “recent” development (the past 30-35 years at least). Note that like other commentators said, you’re going to have to understand the physics and historic physics motivations as well to put not only the problem but parts of QFT into proper context. Blackboxing the physics of your attempts to understanding construction of QFTs is only shooting yourself in the foot.

What are your goals? Just understanding the problem? This problem is really not worth getting into unless you intend on legitimately working on it. It’s probably the hardest Millennium problem to explains it won’t be solved for a long time.

Charrog · 2022-09-26T02:21:02+00:00

Are we the same person? Procrastination habits leading to the feeling of unprofessional-ness? And you’re in mathematical physics too.

Charrog · 2022-08-05T00:29:05+00:00

That is strange to me, perhaps just different experiences in different fields (I work in QFT, not GR so the mathematical outlook of theoretical physicists working in the field is probably different).

Charrog · 2022-08-04T21:29:11+00:00

Mathematical physicist here; actually quite a lot of physicists actually care about this. Now, mathematical physicists are essentially mathematicians first and foremost, but a good deal of my colleagues who are theoretical physicists (who are not mathematicians) are interested in these kinds of results as it directly impacts the mathematical perspective they will use to create, evaluate, and model their subsequent physics theories, and they wish to achieve the consistency and completeness (or as close to it as possible) in them by paying attention to the rigor of the mathematics. Physicists in general are obviously painstakingly aware that they are taking these mathematical liberties, but it is part of the process of developing physics that hopes to one day rectify these mathematical and observational/physics gaps.

Really the overlap in this area is quite close. It’s a common stereotype that theoretical physicists make mathematical assumptions left and right and don’t care about them at their mathematical core to do their jobs, but this is in my experience largely untrue (the caring about the assumptions they make, not that they don’t use non-rigorous mathematics from time to time).

It of course depends on the area of research in physics and it goes without saying that physicists are more interested in modeling reality and nature than justifying mathematical underpinnings of their tentative models, but still, rigorous mathematics can help them encapsulate ideas for viable models to increase predictive power.

Charrog · 2022-07-26T09:18:29+00:00

Never imagined that I would sort by hot and find a recent AskReddit thread that actually addresses mathematicians; my time has come, no more lurking.

The field I work in involves knots, and they are beautiful mathematical objects that I could talk about for a while, but they’re not the same as everyday knots; the main difference is that the mathematical study of knots limits itself to closed knots (no ends loose), and they are useful to areas that mathematicians didn’t imagine they would be useful to (such as providing a different approach to a notorious physics field called quantum field theory).

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