N-gated Hacker NewsMay 10
Ah, the age-old existential crisis: what *is* a mathematician supposed to do? 🤔 Apparently, hang out on #MathOverflow, the place where number nerds unite to swap proofs and procrastinate on real problems. Who knew infinite wisdom could be found in a 183-site rabbit hole of Stack Exchange? 🙄🔢
https://mathoverflow.net/questions/43690/whats-a-mathematician-to-do #mathematics #existentialcrisis #StackExchange #numbernerds #HackerNews #ngated
What's a mathematician to do?

I have to apologize because this is not the normal sort of question for this site, but there have been times in the past where MO was remarkably helpful and kind to undergrads with similar types of

MathOverflow
Hacker NewsMay 10

What's a Mathematician to Do?

https://mathoverflow.net/questions/43690/whats-a-mathematician-to-do

#HackerNews #Mathematics #Problem #Solving #MathOverflow #HackerNews #AcademicDiscussion

What's a mathematician to do?

I have to apologize because this is not the normal sort of question for this site, but there have been times in the past where MO was remarkably helpful and kind to undergrads with similar types of

MathOverflow
Vladimir SavićApr 5

Epic!

Pierre Bohanna's answer to "Project Hail Mary, question? (Spoiler)" on #MathOverflow https://mathoverflow.net/a/509624

P.S. "It works in practice, but does it work in theory?"

Project Hail Mary, question? (Spoiler)

I just watched the movie Project Hail Mary yesterday, and I have a question about the ending of the movie. (Spoilers) At the end, they show the alien nicknamed “Rocky” in a protective clear polyhed...

MathOverflow
Hacker NewsNov 29, 2025

Every mathematician has only a few tricks (2020)

https://mathoverflow.net/questions/363119/every-mathematician-has-only-a-few-tricks

#HackerNews #mathematics #tricks #mathematician #mathoverflow #problem-solving #2020

Every mathematician has only a few tricks

In Gian-Carlo Rota's "Ten lessons I wish I had been taught" he has a section, "Every mathematician has only a few tricks", where he asserts that even mathematicians like Hilbert...

MathOverflow
Terence TaoOct 7, 2025
A third update on my previous posts https://mathstodon.xyz/@tao/115306424727150237 https://mathstodon.xyz/@tao/115316787727719049 https://mathstodon.xyz/@tao/115325228243131134 on the #MathOverflow problem https://mathoverflow.net/questions/501066/is-the-least-common-multiple-sequence-textlcm1-2-dots-n-a-subset-of-t . Out of curiosity, I asked an AI deep research tool for the known literature on this problem: https://g.co/gemini/share/0d41fcadfbaf . As is often the case with these frontier models, the results were mixed. On the one hand, the tool correctly identified a relevant paper of Alaoglu and Erdos from 1944 https://users.renyi.hu/~p_erdos/1944-03.pdf , where they claimed that the authors knew that the conjecture was false, but did not provide a proof. The AI then hallucinated by asserting that n=17 was a counterexample, which I knew to be false. Based on this latter failure, I did not initially give much credence to the initial statement; but later, after reading the Alaoglu-Erdos paper carefully, I did find (on pages 466-467) that they did indeed make the observation that "it would be easy to see" that the conjecture could only be true finitely often, without providing any hint of a proof. (1/4)
Terence Tao (@[email protected])

I was able to use an extended conversation with an AI https://chatgpt.com/share/68ded9b1-37dc-800e-b04c-97095c70eb29 to help answer a MathOverflow question https://mathoverflow.net/questions/501066/is-the-least-common-multiple-sequence-textlcm1-2-dots-n-a-subset-of-t/501125#501125 . I had already conducted a theoretical analysis suggesting that the answer to this question was negative, but needed some numerical parameters verifying certain inequalities in order to conclusively build a counterexample. Initially I sought to ask AI to supply Python code to search for a counterexample that I could run and adjust myself, but found that the run time was infeasible and the initial choice of parameters would have made the search doomed to failure anyway. I then switched strategies and instead engaged in a step by step conversation with the AI where it would perform heuristic calculations to locate feasible choices of parameters. Eventually, the AI was able to produce parameters which I could then verify separately (admittedly using Python code supplied by the same AI, but this was a simple 29-line program that I could visually inspect to do what was asked, and also provided numerical values in line with previous heuristic predictions). Here, the AI tool use was a significant time saver - doing the same task unassisted would likely have required multiple hours of manual code and debugging (the AI was able to use the provided context to spot several mathematical mistakes in my requests, and fix them before generating code). Indeed I would have been very unlikely to even attempt this numerical search without AI assistance (and would have sought a theoretical asymptotic analysis instead).

Mathstodon
Terence TaoOct 6, 2025
A second update on my previous posts https://mathstodon.xyz/@tao/115306424727150237 https://mathstodon.xyz/@tao/115316787727719049 on the #MathOverflow problem https://mathoverflow.net/questions/501066/is-the-least-common-multiple-sequence-textlcm1-2-dots-n-a-subset-of-t that had a first initial counterexample located with #AI assistance, and then the minimal counterexample obtained through a crowdsourced effort. As has happened with several previous projects, the crowdsourced effort has acquired a life of its own. In particular, the task of classifying *all* the counterexamples - which I had previously dismissed in my previous post as "somewhat tedious to perform", has in fact been completed, with the problem alternating between true and false for n between the first counterexample 71 and the last example 172, before settling down to a unending string of counterexamples. We now have some very efficient ways to either prove or disprove that a given number is highly abundant; some of the asymptotic analysis initially required some high powered number theory hypotheses such as the generalized Riemann hypothesis (GRH), but as our arguments became more efficient, this became unnecessary. We even have some recent contributions from the #LeanLang community, formalizing some of the counterexamples in Lean, almost in real-time! (1/3)
Terence Tao (@[email protected])

I was able to use an extended conversation with an AI https://chatgpt.com/share/68ded9b1-37dc-800e-b04c-97095c70eb29 to help answer a MathOverflow question https://mathoverflow.net/questions/501066/is-the-least-common-multiple-sequence-textlcm1-2-dots-n-a-subset-of-t/501125#501125 . I had already conducted a theoretical analysis suggesting that the answer to this question was negative, but needed some numerical parameters verifying certain inequalities in order to conclusively build a counterexample. Initially I sought to ask AI to supply Python code to search for a counterexample that I could run and adjust myself, but found that the run time was infeasible and the initial choice of parameters would have made the search doomed to failure anyway. I then switched strategies and instead engaged in a step by step conversation with the AI where it would perform heuristic calculations to locate feasible choices of parameters. Eventually, the AI was able to produce parameters which I could then verify separately (admittedly using Python code supplied by the same AI, but this was a simple 29-line program that I could visually inspect to do what was asked, and also provided numerical values in line with previous heuristic predictions). Here, the AI tool use was a significant time saver - doing the same task unassisted would likely have required multiple hours of manual code and debugging (the AI was able to use the provided context to spot several mathematical mistakes in my requests, and fix them before generating code). Indeed I would have been very unlikely to even attempt this numerical search without AI assistance (and would have sought a theoretical asymptotic analysis instead).

Mathstodon
theHigherGeometerMay 19, 2025
Less than 24 hours for users to self-nominate for the #MathOverflow moderator elections https://mathoverflow.net/election the button/text link to click is at the bottom of the page.
2025 Moderator Election

Q&A for professional mathematicians

MathOverflow
theHigherGeometerMay 14, 2025
Community moderation election on #MathOverflow is happening! Currently in nomination phase: https://meta.mathoverflow.net/q/6199/4177 We are looking to fill two positions.
2025 Community Moderator Election

The 2025 Community Moderator Election is now underway! Community moderator elections have three phases: Nomination phase Primary phase Election phase Most elections take between two and three wee...

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Terence TaoMar 11, 2025

An interesting (unscientific) experiment on #MathOverflow from a few months ago, where a user gave 15 different MO problems for o1 to answer, with the aim of verifying and then rewriting the answer into a presentable form if the AI generated answer was correct. The outcome was: one question answered correctly, verified, and rewritten; one question given a useful lead, which led the experimenter to find a more direct answer; one possibly correct answer that the experimenter was not able to verify; and the remainder described as "a ton of time consuming chaos", in which the experimenter spent much time trying to verify a hallucinated response before giving up. https://meta.mathoverflow.net/questions/6114/capabilities-and-limits-of-ai-on-mathoverflow This success rate largely tracks with my own experience with these tools. At present this workflow remains less efficient than traditional pen-and-paper approaches; but with some improvement in the success rate, and (more importantly) an improved ability to detect (and then reject) hallucinated responses, I could see one soon reaching a point where a non-trivial fraction of the easier problems in MO could be resolved by a semi-automated method.

I found the discussion for possible AI disclosure policies for MO in the post to also be interesting.

Capabilities and limits of AI on MathOverflow

I did a small informal test over the last few weeks to see if AI could give helpful answers to MathOverflow questions. I want to discuss the results, in case it helps the community work through pos...

MathOverflow Meta
theHigherGeometerDec 20, 2024

In the spirit of old questions, here's another one without an answer: can we get a "holomorphic model" for a K(Z,2)?

https://mathoverflow.net/q/237837/4177

#mathoverflow

Holomorphic contractibility of GL(H)?

Kuiper's theorem is well-known to give the triviality of the homotopy groups of ${\rm GL}(\mathcal{H})$ for $\mathcal{H}$ a (separable) infinite-dimensional complex Hilbert space. Work of Palais la...

MathOverflow