thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/09/2026In particular note Buckmaster's statement that "The ideas making this line of attack possible are due to Cordoba and Martınez-Zoroa.. in view of this body of work, I believe Luis Martinez-Zoroa deserves a Fields Medal." 000
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/09/2026I recommend reading in full this statement from Buckmaster, which has more information on the rushed announcement and unfinished nature of the proof: cims.nyu.edu/~tristanb/st...cims.nyu.edu 110
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/09/2026Looks like we are indeed close to Navier Stokes (pending checking final details and peer review/formalisation)! See the description on Tao's blog discussing recent work of Alpöge and Buckmaster, (with assistance in various forms from AI). terrytao.wordpress.com/2026/09/07/f...terrytao.wordpress.comFinite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equationsThere’s some exciting very recent work by Alpöge and Buckmaster, building upon prior work by Córdoba and Martínez-Zoroa, in the general topic around the infamous global regularity problem for… 131
Reposted by @thomasfbloom.bsky.socialEpoch AI @epochai.bsky.social · 31/07/2026We’ve launched an expansion of FrontierMath: Open Problems! The benchmark now contains 50 significant, unsolved problems from research mathematics. AI has solved three so far, and solving all of them would be an incredible mathematical feat. Thread with more. 3214
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026I do think this required intelligence, but to be pedantic I don't think "every expert" in discrete geometry had tried seriously to solve the unit distance problem (although I'm sure many did). 140
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026And also don't get too excited if you see 6-7 new solutions all updated at once; this is just a reflection of me having a block of free time to update the website from the backlog of claims, and doesn't mean that suddenly there was a dramatic leap in AI capabilities. 7/7 010
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026So be wary of extrapolating from "average 1-2 new solved problems a day, at this rate they'll all be done by next year!". As with previous new model releases, there will be a spike of new solutions for several weeks, and then it will slow down substantially. 6/7 120
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026There are still a few more unchecked proof claims, and no doubt more to come in the next couple of weeks while people continue to run problems through this new model. Then things will slow down once the new model has proved all of those it can. 5/7 110
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026A fascinating proof to read (see my comment for an exposition), and a great example of 'we thought this problem was a lot harder than it was'! (With echoes of problem 1196, previous work took a different route which involves substantially more technical difficulties.) 4/7 110
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026They don't all start from an existing proof; one exception is erdosproblems.com/119 in which GPT (prompted by Korsky) proves a stronger result than a 44 page Annals paper of Beck from 1991, using only 1 page of simple harmonic analysis tricks. 3/7erdosproblems.com119 | Erdős Problems 110
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026They are still mainly of the same 'type' of argument that we've come to expect from AI (start from an existing weaker proof and refine it, with particular emphasis on quantitative elementary tools and ad hoc anatomy-of-integers type manipulations). 2/7 110
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 19/07/2026So far GPT 5.6 Sol is the most interesting new model mathematics-wise for me - those of the new proof claims on erdosproblems.com that I've looked at in detail have all been correct, and moreover contained some interesting ideas. 1/7erdosproblems.comErdős Problems 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 07/07/2026Combinatorics has the advantage that the problems are mostly pure reasoning, with very little definitional depth, so it seemed more feasible that LLMs could 'reason' successfully about such problems even with a short context window. 030
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 07/07/2026Playing around with some early LLMs showed (very weak) signs of the kind of 'combination reasoning' that one sees in some solutions to open problems. (e.g. "problem A looks like problem B except with a couple of changes, so take a solution to problem B and tweak it accordingly") 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 07/07/2026But if I was told the unit distance conjecture was actually false, and then asked how long before AI would find the counterexample, I'd probably have said "6 months-1 year". I'll record here my prediction that AI will solve at least one other of those top 10 problems in at most 1 year from now. 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 07/07/2026A couple of months ago I wrote a blog post mentioning the unit distance problem as one of my top 10 Erdos problems. At that time, if asked to estimate how long before AI would solve it, I'd probably have said "3+ years". 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 07/07/2026I made the prediction (in private conversations) back in 2021 that "AI will be solving some open problems in combinatorics/number theory within the next 5 years", so feel somewhat vindicated! I didn't make any specific predictions about which conjectures. 120
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 15/06/2026A new blog post on Erdős, aliens, and evil spirits. www.erdosproblems.com/forum/thread...erdosproblems.comBlog - Erdős, aliens, and evil spirits | Erdős Problems 010
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 07/06/2026I have started a collection of essays, blog posts, etc discussing AI in mathematics. I do not agree with everything written, but all are valuable to read - the more different views the better! Please reply with your own suggestions. thomasbloom.org/AIlinks.html 020
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 31/05/2026I have written a blog post giving my personal sketch of the recent disproofs of the sum-product and unit distance conjectures. www.erdosproblems.com/forum/thread...erdosproblems.comBlog - Sum-product, unit distances, and number fields | Erdős Problems 020
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 30/05/2026I recently had someone accuse me of using an AI to write something, until they noticed there was a typo in the final sentence, and then they said "never mind, clearly it's human". The more flaws the better! 000
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 30/05/2026Yes,this is accurate; Will and I saw the OpenAI construction a few days before the general public, but the AI proof was already written before I saw it, and I had no involvement other than contributing to the 'Remarks...' companion paper. 020
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 12/05/2026Yeah, the Dual view is probably buggy in a few ways, view it as an 'experimental feature' that I'll try and fix properly some day soon. Hopefully no bugs on the main site itself. 020
Reposted by @thomasfbloom.bsky.socialDaniel Litt @littmath.bsky.social · 12/05/2026New project: problemsilike.com, a website collecting open problems that I, personally, like, with comments on their context, difficulty, and interest. 2449
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 17/04/2026Some dismiss Erdős problems as trivialities - this couldn't be further from the truth! While many are amusing novelties, some of them are the most central problems in number theory and combinatorics. A blog post with, in my view, the 10 most important: erdosproblems.com/forum/thread...erdosproblems.com Erdős Problems Blog - Top 10 Erdős Problems 010
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 26/01/2026A new blog post by @acerfur.bsky.social describing his experience as a pioneer of using AI tools to solve Erdős problems: www.erdosproblems.com/forum/thread...erdosproblems.com Erdős Problems Blog - A retrospective on problem 728 and the use of AI on Erdős problems 061
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 14/01/2026I think that having zero research should count as a 'defect in your research'. 020
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 14/01/2026AI is capable now of generating new interesting mathematics. But it's much easier for it to generate plausible-sounding nonsense. I am concerned that the latter, copied and promoted by users with no understanding of the mathematics, is going to drown out the former. 0103
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 11/01/2026I expect new human insights to happen first - the AIs can be a powerful force multiplier, so once the initial big new idea/insight is had AI can quickly fill in the details and find other applications. (At least for some problems, certainly not most/all.) 010
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 11/01/2026My prediction is that by the end of the month there'll be between 4 and 8 new Erdos problems with solutions mostly or entirely AI generated. But then we'll have seen all the easy wins available, and progress will slow until a significant jump in model capability or new human insights. 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 11/01/2026If you don't have an Erdos number and would like one, I'm open to an exciting collaboration on the intersection of Erdos-style mathematics and Old English literature and the benefits of free borders. (The first important question being whether this intersection is empty.) 250
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 11/01/2026This may lead to mathematicians becoming (even more) closed off than now about their half-baked ideas and insights - why share an observation on MathOverflow which solves 50% of a problem when a week later someone will ask GPT, which will fill in the other 50%, and give it 100% of the credit. 061
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 11/01/2026This leads to people viewing proofs as more 'purely AI-generated' than they are. Often AI is capable of correcting this when prompted, and can dig up references/sources, but people sometimes don't dig deeper when they should. 131
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 11/01/2026One of the big challenges now in using AI for mathematics is the credit/attribution problem. AI has a tendency to use observations/techniques without giving credit as to where it 'learnt' about them (mainly because it's forgotten itself). 132
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 10/01/2026Presumably with the same construction again? 120
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 10/01/2026Yes, Cloudflare...not heard about La Liga before! 100
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 10/01/2026I haven't checked the original paper again, but I suspect it's just another way they thought of to ask about a!b! dividing n! " up to small primes", and they didn't necessarily give much thought to the precise question. But surely infinitely many n, not all n. 120
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 10/01/2026In fact via a very similar argument to the previous one? (And there may be another to follow, since there at least three very similar problems. ) 160
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 10/01/2026I'm confused by what you say, since this very thread is evidence where it has written novel proofs? 1110
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 10/01/2026Hmm, it's working fine for me? It is behind a CDN already. 100
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026Any scenario involving Tom the Clown. 010
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026If you want something to read for the next couple of years, I highly recommend The Wandering Inn - 16 million words and still in progress! wanderinginn.com (It even has a mathematician canine character, with cool shades, though you have to wait about 10+ million words for them to show up.)wanderinginn.comOverviewTable of Contents Latest Patreon Chapter loading… Latest Public Chapter loading… Where I left off loading… New here? START YOUR JOURNEY Welcome to the Innverse, a captivating web serial where stories ... 000
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026There are certainly teams trying to make things like this (e.g. AlphaProof), so we will see... (The number of 'rules' and 'moves' is orders of magnitude greater than that of Go though, so not sure how much harder this will be.) 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026But we haven't (yet!) seen any genuinely new ideas/techniques come from AI in maths. But I'd expect those to come from an AlphaGo style AI rather than an LLM based one. 140
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026They're still doing 'new research' since a lot of research is applying standard techniques to new problems. (There are really, at the end of the day, very few people thinking about these problems compared to how many problems there are.) 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026I agree - part of what made AlphaGo so interesting is that it was doing (successful) things that no human had ever tried or thought of trying. We haven't seen any evidence of that from public AIs, since they're trained on all the tricks and techniques that humans have become familiar with. 130
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026Yeah, it's definitely an interesting time. I keep being surprised by what they can do. At the moment the most it's done is not very deep, judging by human standards, but it's definitely the sort of output that I'd expect from a human graduate student, rather than a machine. 1120
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026A famous quote by Renyi (often falsely attributed to Erdős) is "A mathematician is a machine for turning coffee into theorems." I recently learnt that in German this is actually a great pun: the word 'satz' for 'theorems' can also be translated as 'coffee grounds'. 150
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026(Your thread is, I mean. The website itself is a summary of all states of all problems for experts and non-experts alike.) 1140
thomasfbloom.bsky.social @thomasfbloom.bsky.social · 08/01/2026Hi Zach! Owner/maintainer of erdosproblems.com here. Just wanted to say how exciting is for me personally to see one of my favourite comic artists/authors posting about Erdos problems. This is a great summary of the state of play for non-experts.erdosproblems.comErdős Problems 2552
