johnnylemmon.bsky.social @johnnylemmon.bsky.social · 03/10/2026Not really? Given enough time, if the game is random, many "strange" sequences will appear... I would bet the sequence 1 2 3 4 5 has appeared sometime in the past year, for example. Is there any way to check? 110
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 03/10/2026I guess it's 0.3% ? Anyway, not something I'd bet on 110
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 29/09/2026Saving this thread. I am afraid small labs with limited resources like mine will almost disappear from the active research community. Next week we're having a departmental meeting to discuss LLMs and math and I'd like to convey this 011
Reposted by @johnnylemmon.bsky.socialAlexander Kasprzyk @amkasprzyk.bsky.social · 27/09/2026An engineer, a physicist, and a mathematician are at a high-school math event, and have been asked to explain a trigonometry problem to the students. #MathSky 1124
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 21/09/2026Especially if its a bazillion lines. Are we sure there are no extra assumptions hiding somewhere? Or that all definitions are what they should be? 110
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 20/09/2026I think I saw the thread that prompted this question. Related to that, part of the issue is that "the proof of a theorem" has to be symbol manipulation, but is not necessarily what we as mathematicians value in a paper. It has proven to be easy to train an LLM against, however... 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 20/09/2026Do you know of similar other projects that have a different perspective? It'd be good to contrast and compare, make sure that AHM grows in the good direction 111
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 20/09/2026I guess it might be a reflection of the fact that the AI attack on mathematics is very US-centric? And it is threatening a certain western math culture the most (solve the big problem posed by a famous white guy 100 years ago). But it is a good start, no? 211
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 03/09/2026As in, you can compile a single-page pdf and rearrange it for printing using pdfpages 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 21/08/2026From what I understand, what they are disproving was not widely believed to be true. Rather, no explicit counterexample was known because people moved on to modify what K-stability "should" rather be 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 18/08/2026Yes exactly! Just to add some variety 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 18/08/2026Personally, I find the small puzzles a bit easy? It could be fun to have a random target for the games, maybe 10, 15, or 20, that changes game to game. Is that a pro feature? Keep up the good work, I really enjoy the puzzles (: 211
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 18/08/2026Oh, it's not a big deal :') it's just that I liked the challenge! 100
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 16/08/2026Wikipedia has a nice explanation, in the examples section of the article about modules 100
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 16/08/2026I remember realising that all those criteria were equivalent to "count how many points at infinity" and then I felt so upset about having to learn the other stuff 120
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 15/08/2026Yep, hyperbola. Substitute t=y-x and plot in the (x,t) plane 150
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 14/08/2026As vector spaces, rings, modules... ? 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 09/08/2026Depends on theoremstyle and the documentclass. An option is to look at some paper on the arxiv whose style you like, and download the source file to use part of the preambole as a template for your things. 100
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 08/08/2026There's a retraction of R to 0, x \mapsto x/(1+t|x|). This is a family of contractions (for t>0) but the "contraction factor" varies a lot. I think this might be an example in the direction you want, let me know! 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 07/08/2026If you care about your numbers being comparable to each other (<), R is the way to go 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 07/08/2026If you're factoring polynomials, R is terrible 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 06/08/2026Hence we can get a,b integers such that a+b*beta is as close as we want to 0 (without actually hitting 0), which is not good if we were looking at a lattice 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 06/08/2026Ah! Thank you, this clarifies it. I am unfamiliar with this notation. Here is my attempt: first, we scale everything by 1/alpha, this should let us assume alpha=1 and beta is a irrational real. Then we can approximate it arbitrarily well with rationals. 110
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 06/08/2026Did you mean R^2? Or should it be a sum instead of a product? 100
Reposted by @johnnylemmon.bsky.socialSunJester @sun-jester.bsky.social · 31/07/2026Still not really sure how to feel about this tbh… Like, on the one hand, it is really cool that another famous problem has been solved. On the other hand, as someone hoping to at least do a phd in math, I find this quite terrifying... (1/n) #mathsky #mathematics #math #maths 301
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 01/08/2026Also, consider that asking good questions is at least as important as finding the answers! 011
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 01/08/2026A lot of what successful mathematicians do is also finding new techniques. If you can come up with a great new technique to solve a problem, even if its already known that it has a solution, you will have done extremely important maths 111
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 12/07/2026It's usually important to remember the order! For example if you discuss orientation-preseving linear maps. I think it's easiest to consider a basis as an element of the set of n-uples of elements of V, the space V^n. 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 12/07/2026If a solution exists, it must be 12. But how to show that the iterated roots converge? It's way too hot for that today. 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 11/07/2026Sorry, I meant *increasing* instead of declining, I dont know why I wrote declining! 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 11/07/2026...their time and attention on. As in, it might help people overcome some technical hiccups very regularly, so that a mathematician will focus on other things? I am not sure, but it is a distinct possibility. 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 11/07/2026Reviewing the literature on something, to bouncing off ideas, to getting help to prove some technical lemmas. Results vary a lot. These uses are very rarely disclosed. I get the impression that in a couple of years LLMs will be used very liberaly. It might just reshape which tasks one spends 110
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 11/07/2026And the fact that in some subfields the typical proofs have different level of details, so that it's sometimes harder to reach a consensus. 2) in the last few months, the number of colleagues that never used LLMs for research-related things is rapidily declining. This goes from help with 2/ 220
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 11/07/2026Hey, working mathematician here. Two comments: 1) for now, these LLM proofs seem to better fit some subfields than others (e.g. PDE theory seems to have been less impacted than combinatorics). I suspect that this is a combination of lack of interest from experts in the field and openai itself and 1/ 130
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 09/07/2026Isn't there a formula like cos(alpha) = (v.w)/(|v||w|)? Here alpha is the angle between v and w. If this is correct then I guess the answer should be yes, but maybe only up to a sign 120
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 28/06/2026Must be an artifact of how you choose the eigenvectors. Have you tried normalising to be unit length, for example? 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 24/06/2026Maybe the angle is not invariant under projective transformations, but the criterion could be? Since points lyin on a quadric is. I wonder! 000
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 23/06/2026Are they projective dual to each other? 120
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 20/06/2026Trace as derivative of determinant sounds very geometric to me! 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 19/06/2026I 100%agree with you on this. My perspective is that of a mathematician who's trying to understand what's coming and how to adapt. Thank you for the discussion! 010
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 19/06/2026"Not done the correct way" does not mean that the LLM's argument was wrong though: it might be bad LEAN, and sloppy mathematics, but it is not incorrect in the sense that it allows you to prove something false, it's still internally correct 100
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 19/06/2026It seems to me that the paper says something different. They just show that the LLM produced definitions and arguments that are bloated and useless beyond the specific problem it was assigned to solve. Am I misunderstanding? 100
Reposted by @johnnylemmon.bsky.socialSociété Mathématique de France @socmathfrance.bsky.social · 14/06/2026En se rendant à Erevan le spécialiste de géométrie complexe Mikhail Verbitsky a été arrêté par les autorités arméniennes le 12 juin sur demande de la Russie. Il risque l'extradition. La SMF appelle les autorités arméniennes à le libérer et appelle à signer la pétition www.change.org/p/free-misha... 22222
johnnylemmon.bsky.social @johnnylemmon.bsky.social · 12/06/2026Never heard anyone doing this in my subfield. You might also ask a colleague which journals they'd recommend. 000
Reposted by @johnnylemmon.bsky.socialMichael Okun @michael-okun.bsky.social · 10/06/2026I’ve officially resigned as Associate Editor for Frontiers in Systems Neuroscience. It used to be a reputable journal, but became a case study in how forced automation destroys academic integrity. 👇 5435861430
