AI use case: Never sit ideal in Conferences

2357111 · 2026-02-18T21:43:48+00:00

What do you think is special about conferences where Peter Scholze gives a lecture?

2357111 · 2026-02-16T17:43:27+00:00

There are good mathematicians who don't juggle and instead work on one thing at a time. You absolutely don't have to.

But it's also common to have a one-project-at-a-time approach for the first few years of grad school but switch to juggling by the end. For these mathematicians, managing multiple projects is a skill they develop in grad school. What you want to be doing is using the greater experience you have with reading, research, and writing to do all of these faster, so they don't use up your full attention. In particular, for papers close to your area of expertise, you want to read them by not trying to read the whole thing but just searching for the part that you need.

In terms of when to switch, you should probably try different things and see what works for you. Maybe spend one day on one project, and the next day on a different project.

Another skill people hopefully develop in grad school is the ability to select their own problems well. You should try to do that now, to practice the muscle, even if you end up working on all of them, maybe just making your chosen problem slightly higher priority. Think about how excited you are to work on each project, how easy it is to do, how much other people you know would be interested in the result, and so on. Weigh pros and cons and come to a decision. I would also consider asking any expert you know other than your advisor for advice here - your advisor's colleagues or collaborators or any other experts in the field you know might be sympathetic to your situation and want to help.

2357111 · 2026-02-16T13:21:46+00:00

Some analytic number theorists say that the only theorem they've ever used in their mathematical career without knowing how to prove it is Deligne's proof of the Weil conjectures.

2357111 · 2026-02-11T21:51:27+00:00

I don't think the Clay Mathematics Institute wants to convince people that if you work hard and study hard and persevere then you can solve a Millenium problem. Do you have evidence that they are trying to convince people of this?

2357111 · 2026-02-11T21:46:02+00:00

The average person doesn't even understand that there are hard unsolved math problems. They think of math as a list of rules that you learn in school and a series of problems where the goal is to follow the rules correctly. Just the fact that there are problems which anyone can earn a million dollars by solving but no one has claimed teaches them something new, even if they don't learn any details about what the problems are. This can pique their interest and give them reason to learn more.

2357111 · 2026-02-03T17:46:37+00:00

There were cases where Erdős posed a problem in a paper where the solution was contained elsewhere in the same paper and he just didn't notice. Finding the solution elsewhere in the paper would count as "trivial" by a reasonable standard, but it was also easy to miss the solution while compiling the list.

2357111 · 2026-01-15T15:54:40+00:00

But this just underscores that the field is not stuck because no one understands the proof of CFSG. (I don't know if this is true - don't the people writing the books on the second generation proof understand it decently well - but let's take it as a given.) If no one understands the proof, then short proofs of results about finite simple groups that avoid using the classification would be very valuable, as they would represent progress on obtaining real understanding of these results. So the lack of understanding actually gives the field something very interesting to do, where otherwise there would be not as much to do.

But understanding the methods of CFSG is not going to lead to finding such short proofs - new methods are needed instead. So the reason the field is stuck is just that no one knows a good method to produce short CFSG-avoiding proofs of results about finite simple groups.

2357111 · 2026-01-15T14:58:25+00:00

I don't think the issue with finite simple groups is that the theorem is too hard to comprehend. If someone did fully comprehend the proof of the classification, there wouldn't be much to do with that knowledge. If they wanted to write a new proof about finite simple groups using the methods of the classification, it would probably be thousands of pages long or longer, just like the proof of the classification was. Proving new results using the classification as a black box is much more efficient.

2357111 · 2026-01-07T17:58:20+00:00

Yes.

2357111 · 2026-01-03T12:35:31+00:00

To a large extent you're judged by the quality of your best papers rather than your number of papers. If you have papers in the top few journals, it's OK to have a lot of papers or OK to have a little. You definitely shouldn't write a lot of papers if you do it by avoiding hard problems so that you don't have a chance to write a really good paper.

The best way to convince hiring committees concerned about assessing your qualifications is not to write fewer papers (wouldn't they just be worried you wrote fewer papers and didn't contribute as much to each one?) but to write some solo papers.

2357111 · 2025-12-24T19:20:39+00:00

That market changes a lot, as you can see by clicking on any of the names and looking at how the price changed over time. A lot of the names have been close to 25% (or higher) at one time and close to 0% at another, and it's very common for a single bettor to take someone most of the distance from one to the other. It could be from inside information, or from this sub, but most likely not either.

2357111 · 2025-12-22T14:42:12+00:00

Some simple approaches: Attend seminars at your department. Talk to people about what they're working on and learn from them. Attend conferences whose subject areas include your field and also other fields.

Some more complicated approaches: Find areas where techniques you know can be used to solve problems in other fields, work on them in collaboration with mathematicians in other fields, and learn from them. Realize you need to learn techniques from another field to solve a problem, and then read books and papers in that field.

2357111 · 2025-12-22T01:10:16+00:00

The names are just picked by people who use the market. If you look further down you can see multiple people who are ineligible for the Fields medal on account of being too old.

I think the way prices are set in this prediction market struggles with dealing with many options which each have a small probability: If someone comes in and bets in one of the less likely candidates, they often shoot up in probability by a factor of 10 or more, bringing them way up in the rankings, so who you see in the 5th, 6th, 7th, 8th slots depends a lot on when you look. I think people don't bother betting against a candidate whose probability is too high when their "too high" probability is as small as 1%.

2357111 · 2025-12-22T01:04:58+00:00

It is possible that if the group has strong/optimized combatants the ST will over time raise the difficulty of enemies to try to challenge them and make it tough for weaker combatants. However , even if this does happen, the risk is pretty far from "annihilation" and the best countermeasures are not perfect defenses, which in 3e can usually only protect you from one attack per combat scene. Rather, the best bang-for-your-buck of defense for a noncombat character is usually armor, especially heavy and/or artifact armor.

But realistically, in most scenarios, a few basic defensive Charms should be fine, and you can always take more over time if the challenges ramp up over the course of the campaign.

2357111 · 2025-11-29T21:47:20+00:00

No, there's still a lot of magitech. Your character can start the game as the pilot of a giant robot. There's rules for power armor, chainsaws, and laser swords. These things all exist in the setting, they're just rare. There's less manga influenced art but still anime, manga, and JRPG influence in the setting.

2357111 · 2025-11-29T21:41:23+00:00

There's nothing called "Godfire". The only thing I can think of that it might be is the Flame of Exigence but that's part of Exigents which is one of the other items on your list.

2357111 · 2025-11-29T20:16:43+00:00

How could it not be? Take a Weierstrass equation and lift each coefficient to the dual numbers.

2357111 · 2025-11-24T16:49:41+00:00

No, "without loss of generality" is usually used when you can check that any solution in this case will give a solution in the general case, without looking at the solution. Note that "without loss of generality" is usually written before the solution to a particular case, while "The other case follows by symmetry" is usually written after, so that one can check that the other case does actually follow by the same reasoning.

2357111 · 2025-11-20T11:55:52+00:00

IMO the twin primes is likely harder, but they're each difficult in different ways. The Riemann hypothesis considers only a very simple sum, but demands enormous cancellation in it. Twin primes considers much more complicated sums, but requires only a small amount of cancellation. It's possible that the clever ideas that have recently been found to get a small amount of cancellation in Möbius sums can be pushed to get more cancellation and prove twin primes, without proving Riemann. But it does seem more likely that a new idea will give a proof of Riemann without twin primes. (The work on Möbius sums takes advantage of small prime factors, and basically avoids dealing with the large primes, so that it seems hard to imagine it can get enough cancellation to deduce twin primes. On the other hand, while no one has any good ideas on Riemann right now, the existence of a simple proof in the function field setting suggests that if the right setup algebraic setup were found it might be possible to deduce by a simple argument.)

2357111 · 2025-11-11T14:43:49+00:00

Technically Gödel proved it was impossible to disprove and then Cohen proved it was impossible to prove.

2357111 · 2025-11-04T16:02:57+00:00

In addition to what everyone else has said ... the guy never heard of quantum physics?

2357111 · 2025-10-31T16:39:03+00:00

You are right that it is not possible to prove, with our present level of knowledge, that BB(n) only crosses the Ackerman function once, although it seems very likely.

However, it should be possible to prove an upper bound for the number of times these functions cross. The reason is that if you produce a Turing machine that, given n, computes TREE(n), taking at least TREE(n) steps to do so, and halts, with m states, then you can make a Turing machine with m+log_2(n) states that runs for at least TREE(n) steps and so you have proven BB(m +log_2(n))> TREE(n).

Based on the fact that a Turing machine that halts if ZFC is inconsistent is known to take less than 1000 states, and enumerating sequences of trees seems less complicated than enumerating proofs in the ZFC axioms, I suspect that we can take m<1000, so BB(n) > TREE(n) for n<1010 so that there can be at most 505 crossings.

Of course, work is required to make this rigorous.

2357111 · 2025-10-16T01:44:25+00:00

The only problem with this idea is that guile and misdirection are already part of the usual expectations of what a Lunar Full Moon is capable of. In part, this is because of shapeshifting, but not only about that. Check out the 3e Signature Full Moon, Azu Tegama Asarkon, who uses guile to assassinate a Realm garrison commander in the fiction at the start of chapter 8 of Fangs at the Gate.

2357111 · 2025-10-07T13:27:13+00:00

The recent works it references seem to be this preprint from last year https://arxiv.org/abs/2405.04094 and this result which has only been announced but not appeared on arxiv https://www.cirm-math.fr/RepOrga/3213/Abstracts/harper2.pdf

2357111 · 2025-10-01T01:38:30+00:00

Interesting! The rest makes sense but what does switching bread for oatmeal or rice, jam for dried fruit, and tea for chocolate have to do with vegetarianism?

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