@Techmeme@techhub.socialA group of 25 Fields Medal recipients says AI companies' push to solve mathematical problems as a benchmark is detrimental to the science of mathematics (Terence Tao/What's new)
https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-a…
@fanf@mendeddrum.orgfrom my link log —
Additional publications in mathematics by Jeremy L. Martin.
https://jeremymartinmath.github.io/morepubs.html
saved 2026-08-12 http…
@cdarwin@c.imMathematicians are broadly not anti-AI.
They’re more culturally open to using AI as a tool than, say, artists or writers
However, now that more and more genuinely prestigiousproblems have fallen to AI,
that might be changing.
Almost five thousand mathematicians
(including twenty-five Fields medalists)
have signed a declaration called
"A Severe Misalignment of AI in Mathematics".
The core argument goes something like this:
In re…
@arXiv_csHC_bot@mastoxiv.pageFine-Tuning Large Language Models for Codebook-Guided Coding of Students' Mathematics Metaphor Responses
Liang Zhang, Stephen Hwang, Yue Ma, Jinfa Cai
https://arxiv.org/abs/2608.10276 https://arxiv.org/pdf/2608.10276 https://arxiv.org/html/2608.10276
arXiv:2608.10276v1 Announce Type: new
Abstract: Student-generated metaphors about mathematics can reveal students' attitudes, beliefs, identities, and experiences, but human expert coding of these thematically and semantically complex open-ended responses is time-intensive and difficult to scale. This study examines whether LoRA-based supervised fine-tuning of large language models (LLMs) can improve their performance on codebook-guided coding tasks for student mathematics metaphors. We used a human-coded corpus of 2,265 Grade 6-8 responses to food- and animal-based metaphor prompts and instructed the LLMs to perform two coding tasks: valence-intensity coding to capture the direction and strength of students' affective orientations toward mathematics, and thematic coding to capture students' framings of mathematics as expressed through their metaphors. We compared two proprietary models, GPT-4o mini and GPT-5 mini, under prompt-only conditions with two open-weight models, DeepSeek-R1 1.5B and Mistral 7B, evaluated before and after fine-tuning. Results show that fine-tuning substantially improved the performance and run-to-run reliability of the open-weight models across both tasks relative to their base versions. The fine-tuned compact open-weight models became competitive with, and often outperformed, the proprietary prompt-only models. These findings suggest that compact open-weight LLMs can support scalable, locally controllable, and privacy-conscious AI-assisted measurement of students' metaphor responses in mathematics education.
toXiv_bot_toot
@johl@mastodon.xyzA declaration of 25 Field Medalists on AI and mathematics: “In recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. (…) Indeed, the mass production at faster and faster pace of "true/false" statements could destroy fertile ground instead of breathing life into new ideas.”
@dderigo@hostux.social1/
Commentaries by @… on #generativeAI use in #mathematics noting research mechanisms that may go beyond the specific field
[A]
@scott@carfree.cityI enjoy making claims that are technically true, but so overqualified as to sound ridiculous. For example, tuxedo cats have rarely been accepted to graduate programs in mathematics: less than 25 of them over the last decade.
@SmartmanApps@dotnet.socialRE: #Mathematics
@v_i_o_l_a@openbiblio.socialheute zufällig entdeckt:
"Einführung in die RSWK – Regeln für die Schlagwortkatalogisierung": 9 Video-Tutorials von Kolleginnen der @…
» https://doi.org/10.5446/s_1686
@Techmeme@techhub.socialOpenAI releases a range of new mathematical results produced by an internal model, with details like estimations of compute spent in terms of ChatGPT Pro usage (OpenAI)
https://openai.com/index/sharing-ai-progress-in-mathematics/
@Treppenwitz@sfba.social
@shriramk@mastodon.socialFor a while programming looked most under AI threat, but math has taken pole position. My theory for why is 2-fold:
1. Math has had 1000s of years to get to clean formulations.
2. Math is self-contained: no "network misconfigured", etc. to gum up the works.
The latter brings to mind Davis and Hersh's definition of mathematics in "The Experience of Mathematics": "the study of mental objects with reproducible properties". That makes it (like…
@cdarwin@c.imFrom the coauthor of Algorithms to Live By,
an exploration of the quest to use mathematics to describe the ways we think,
from its origins three hundred years ago
to the ideas behind modern AI systems
and the ways in which they still differ from human minds
https://us.macmillan.com/b…
@teledyn@mstdn.caPhysicists made a black hole out of light to test Stephen Hawking's elusive radiation theory | Live Science
https://www.livescience.com/physics-mathematics/quantum-physics/smaller-than-the-tiniest-scale-in-nature-physicists-made-a-black-hole-out-of-light-and-used-it-to-test-stephen-hawkings-elusive-radiation-theory
@arXiv_mathGM_bot@mastoxiv.pageAscertaining Learning: Generative AI, the Proxy Problem, and Cognitive Competence in University Mathematics
Bob Osano
https://arxiv.org/abs/2610.03844 https://arxiv.org/pdf/2610.03844 https://arxiv.org/html/2610.03844
arXiv:2610.03844v1 Announce Type: new
Abstract: For decades, university mathematics assessed executable procedure, computing and reproducing standard proofs, as a proxy for the understanding it cared about, because procedure was cheap to mark and understanding was not. Generative AI now executes much of this procedure. It does not merely let students bypass the proxy; it exposes how much of what was certified was a proxy. The crisis is not simply cheating but a proxy problem, and resolving it forces a question the discipline has long avoided: what is the irreducible human core of mathematical competence, and how can it be built when some of the executable work can be offloaded? We set out two futures: displacement-and-re-centering, in which AI takes over some execution and education moves toward judgment, formulation and verification; and atrophy, in which premature offloading may erode capacities that depend on prior construction. At the heart of the optimistic future is a verification instability: some forms of oversight are cheap and bounded, while others approach the competence required to construct the work. The outcome is a design choice, not a technological destiny. Rather than add a model, we state the response as two principles: construct before you delegate, and let verification set the ceiling: how far a student can independently verify AI output limits what they may safely delegate. We illustrate with a sequence and two worked problems, and close on the question: whether the construct-before-delegate dependency is a hard constraint or an artefact of how mathematics has been taught.
toXiv_bot_toot
@arXiv_mathGN_bot@mastoxiv.pageCompleteness properties of the space of quasicontinuous functions
\v{L}ubica Hol\'a
https://arxiv.org/abs/2608.12318 https://arxiv.org/pdf/2608.12318 https://arxiv.org/html/2608.12318
arXiv:2608.12318v1 Announce Type: new
Abstract: Quasicontinuous functions have found applications in many areas of mathematics. We study completeness properties of the space of quasicontinuous functions equipped with the topology of pointwise convergence. Let X be a Hausdorff topological space, Q(X) be the space of quasicontinuous real-valued functions and {\tau}_p be the topology of the pointwise convergence. For (Q(X), {\tau}_p) complete metrizability, Polishness and Cech-completeness are equivalent. If (Q(X), {\tau}_p) is completely metrizable, then X is countable and the set I(X) of isolated points of X is dense in X. If X is first countable, then (Q(X), {\tau}_p) is completely metrizable if and only if X is countable and I(X) is dense in X.
toXiv_bot_toot
@SmartmanApps@dotnet.socialRE: #Mathematics #Maths
@catsalad@infosec.exchangeDoki Doki Mathematics Club
@david_colquhoun@mstdn.socialGood grief. Trump not only interferes with football and the law. Now he has interfered with the University of Ghent's judgement about US "Philosopher" and alround ignoramus (about genetics and mathematics), Nathan Cofnas.
Shame on Ghent for succumbing to pressure.
https://www.
@Techmeme@techhub.socialThe Association for Human Mathematics says OpenAI's new math documents show power, not scholarship, and urges mathematicians to stop working with the company (AHM)
https://www.ahmath.org/statements
@fazalmajid@vivaldi.net@… Normaliens (ENS alums) pride themselves on their intellect (the school has almost as many Fields Medals as Cambridge, Harvard and Oxford combined, despite enrolling only about 15 students a year in Mathematics), so I'm not surprised they would steer away from dependency on AI.
@SmartmanApps@dotnet.socialRE: #Mathematics
@Techmeme@techhub.socialFields medalist Jacob Tsimerman, set to join OpenAI later this month, launches the Mathematical AI Safety Institute to apply higher math to AI safety problems (Siobhan Roberts/New York Times)
https://www.nytimes.com/2026/09/08/…
@cdarwin@c.imJoan Birman thought her major discoveries were behind her.
Then came an email from a young neighbor — a girl who knew little but wanted to learn.
It was a kind of note that Joan Birman had received many times: a plea from a high school student, asking for help learning mathematics.
After enjoying freshman geometry class, the student wrote, she had recently read her first real mathematical proof. It made her think there might be something more to math than what she was lear…
@tiago@social.skewed.deMathematicians: “Math isn't really about proofs, it's about understanding!”
Physicists: 👀
https://terrytao.wordpress.com/2026/09/18/if-math-is-more-than-proof-we-need-to-better-celebrate-the-rest-of-it/…
@Techmeme@techhub.socialOpenAI says an internal version of Astra, its next big model, produced results for 10 problems in math, quantum complexity, and theoretical computer science (OpenAI)
https://openai.com/index/ten-advances-in-mathematics
@UlrikeHeiss@eldritch.cafeFalls es noch eines Beweises bedurft hätte, dass Schlaf politisch ist, wie die @… sagen: https://beige.party/@MamaLake/117115542439540667
@cosmos4u@scicomm.xyzStudents’ reading and mathematics performance declined sharply across the OECD: #PISA study results for 2025 are abysmal.
@arXiv_mathGM_bot@mastoxiv.page[2026-10-07 Wed (UTC), no new articles found for math.GM General Mathematics]
toXiv_bot_toot
@Techmeme@techhub.socialOpenAI says its internal model produced 372 math results, nearly all from a single prompt handed to a single AI agent; some might have taken multiple attempts (Joseph Howlett/Scientific American)
https://www.scientificamerican.com/article
@barijaona@mastodon.mgDr. Joan Birman thought her major discoveries in mathematics were behind her.
Then came, in the summer of 2019, an email from a young neighbor — a girl who knew little but wanted to learn.
Dr. Birman was 92 years old, and had no interest in being a babysitter. Still, she messaged the student back and said that she’d think about it.
@ErikJonker@mastodon.social @arXiv_mathGN_bot@mastoxiv.pageSchool of Mathematics and Statistics, Guilin University of Technology, Guilin 541004, ChinaScott spaces of complete Boolean algebras need not be co-sober
Wei Ji, Xiaoquan Xu
https://arxiv.org/abs/2608.08484 https://arxiv.org/pdf/2608.08484 https://arxiv.org/html/2608.08484
arXiv:2608.08484v1 Announce Type: new
Abstract: In this paper, we first prove that for a complete Boolean algebra $L$, the complement graph of $L$ is a \emph{KC}-space (as a subspace) and each non-singleton compact irreducible subspace of that graph generates a non-principal $k$-irreducible compact saturated set in the Scott space of the square algebra $L\times L$. We then show that every compact sequential \emph{US}-space embeds into the complement graph of a suitable complete Boolean algebra. The embedding is built from a finite tail-constraint poset and its regular-open completion. Applying the construction to van Douwen's compact Fr\'echet anti-Hausdorff \emph{US}-space gives a complete Boolean algebra $B$ whose Scott space $\Sigma~\!\!B$ is not co-sober, thereby answering negatively a question on Scott spaces of complete Boolean algebras. The same Scott space $\Sigma~\!\!B$ is non-sober and, as a Scott space of a complete lattice, is well-filtered.
toXiv_bot_toot
@thomasfuchs@hachyderm.ioReasoning requires logic (which is the study of correct reasoning) and logic is a philosophical discipline. It requires understanding and a theory of mind.
You can’t statistics yourself into logic; despite some mathematicians claiming you can—it’s a categorical error to think this (indeed, a reasoning logic error).
Both from a perspective of mathematics (“it’s likely therefore it’s true” is not logically valid) and from a perspective of philosophy (which requires understanding what is actually talked about).
Therefore statistical algorithms such as LLMs can never reason.
@tomkalei@machteburch.socialThis is already two years ago, but I heard one mathematician say that they would not go to a conference if the homepage was vibe coded.
On the other side, the AI-open group is applying the old standards of what is good mathematics and trying to preserving those.
Hilbert said "in mathematics there is no ignorabimus“, meaning that we can answer our questions and we will do that.
@arXiv_mathHO_bot@mastoxiv.pageReplaced article(s) found for math.HO. https://arxiv.org/list/math.HO/new
[1/1]:
- Mathematics in the age of the reproduction of intelligence
Ali Enayat
https:/…
@Techmeme@techhub.socialAs AI automates parts of pure mathematics research, a look at formalization challenges and why human imagination remains key to deciding which questions to ask (Stephen Wolfram/Stephen Wolfram Writings)
https://writings.stephenwolfram.com/20
@SmartmanApps@dotnet.social1/9
#MathsMonday
#Mathematics #Maths #Math
I want to come back to Lennes' letter, which I&…
@arXiv_mathGM_bot@mastoxiv.page[2026-10-06 Tue (UTC), 9 new articles found for math.GM General Mathematics]
toXiv_bot_toot
@Techmeme@techhub.socialOpenAI says it's no longer sponsoring Caltech's math hackathon, where participants use AI to solve research problems, following criticism of "slop mathematics" (Truman Dickerson/Business Insider)
https://www.businessinsider.com/openai-cal
@SmartmanApps@dotnet.socialI was just reminded of a funny moment in my Year 7 #Mathematics class yesterday. We were covering ratioes, and I didn't hear it, but apparently one of the kids asked what "ratioed" meant. I heard some of the banter, so I explained, complete with board illustrations, what ratioed meant, upon which one of the kids said "OMG!
@kexpmusicbot@mastodonapp.uk @Techmeme@techhub.socialOpenAI says it is working with an independent advisory group of mathematicians to responsibly share math-related AI advances (OpenAI)
https://openai.com/index/advisory-group-on-mathematics-and-ai/
@arXiv_mathGM_bot@mastoxiv.page[2026-10-05 Mon (UTC), no new articles found for math.GM General Mathematics]
toXiv_bot_toot
@thomasfuchs@hachyderm.ioRE: https://hachyderm.io/@thomasfuchs/117236445086373612
fwiw
Statistics is a field of mathematics concerned with the analysis of data.
Logic is a field of philosophy concerned with reasoning correctly.
@arXiv_mathHO_bot@mastoxiv.pageCrosslisted article(s) found for math.HO. https://arxiv.org/list/math.HO/new
[1/1]:
- What is mathematics now, and what should it be?
Jeremy Avigad
https://
@cdarwin@c.imAccording to Xin Zhi Yuan reports,
the list of 2026 Fields Medal winners has been unexpectedly leaked.
Two Peking University alumni, Wang Hong and Deng Yu, are both on the list
— marking the first time Chinese mathematicians will claim the highest honor in mathematics in the same edition.
Someone discovered four Fields Medal laureate lecture fields marked “HIDDEN” in the front-end code of the ICM 2026 official schedule.
A single curl command generated by Codex c…
@arXiv_mathGM_bot@mastoxiv.page[2026-10-02 Fri (UTC), no new articles found for math.GM General Mathematics]
toXiv_bot_toot
@tomkalei@machteburch.socialRE: #Mathematics, what for?
@arXiv_csPL_bot@mastoxiv.pageDistributive Laws for Parallel Composition in Rely-Guarantee Concurrency
Ian J. Hayes, Larissa A. Meinicke
https://arxiv.org/abs/2607.17536 https://arxiv.org/pdf/2607.17536 https://arxiv.org/html/2607.17536
arXiv:2607.17536v1 Announce Type: new
Abstract: The rely/guarantee approach supports the stepwise development of concurrent programs. Our goal is to develop a theory for reasoning algebraically about concurrent programs in a rely/guarantee style, where rely and guarantee conditions are encoding as commands within our theory. As for mathematics, distributive laws are essential for algebraic manipulation of concurrent programs. In this paper we investigate distributive laws for parallel composition and show how these can be applied to rely/guarantee concurrency. The most general distributive laws are only refinements in a single direction, however, by restricting the form of the command being distributed, one can devise stronger equality laws, which are applicable to guarantee commands as well as to suitable combinations of rely and guarantee commands. Our approach is to develop the distributive laws in a more abstract synchronous atomic algebra, and then apply them to an instance of that algebra supporting rely and guarantee commands. The theory has been formalised in Isabelle/HOL along with proofs of the lemmas presented here.
toXiv_bot_toot
@Techmeme@techhub.socialFields Medalist Timothy Gowers says most famous mathematics problems solved by LLMs so far have almost all been with counterexamples rather than proofs (Timothy Gowers/Gowers's Weblog)
https://gowers.wordpress.com/2026/08/12/what-sort-of-maths-are-llms-good-a…
@thomasfuchs@hachyderm.ioI don’t buy the “AI will kill all jobs” argument, because you can (thoroughly and with high quality) automate only mechanical, repetitive and non-creative work.
For example you can’t automate fields of knowledge (e.g. mathematics), it doesn’t matter if it’s LLMs or some other yet to be invented machine doing it.
If we humans don’t know the knowledge (and understand it), it might as well not exist.
Some might claim that “AI-powered fully automated luxury abundance” is the future, and we don’t need to know anything.
First of all, “AI” doesn’t exist. It’s science fiction. LLMs aren’t intelligent and can’t think.
More importantly though, many people want to know and understand things.
What’s the point of a world that’s synthetically generated based on what past humans did and where no one knows anything or learns anything anymore?
@tomkalei@machteburch.socialWe are seeing a split of math into roughly two groups, let’s call them AI-open and AI-closed.
The AI-closed community does not want anything to do with this. They want to preserve mathematics as it always has been, an expression of human creativity, etc.
Consequently, everything with AI in it is tainted. They don’t referee papers with any AI contribution, don’t submit to journals who accept AI-infused papers, don’t work with grant agencies that are AI-open, etc.
@tomkalei@machteburch.socialTsimerman has posted an interesting opinion on X. I've screenshotted it for you so you don't need to visit the cesspool, but I'm seriously considering creating a new read only account.
So sad that all these smart people take their discussions there. 😔
On the content: The pessimistic side of me agrees with him. #Mathematics as we know it is over. Most of it exists because of problem solving. Many mathematicians are just in the base of a pyramid that exists to produce top problem solvers. 1/3
@thomasfuchs@hachyderm.io“... Every one knew how laborious the usual method is of attaining to arts and sciences; whereas, by his contrivance, the most ignorant person, at a reasonable charge, and with a little bodily labour, might write books in philosophy, poetry, politics, laws, mathematics, and theology, without the least assistance from genius or study.”
You never guess when this was written (solution in reply)
@cosmos4u@scicomm.xyzPlanetary shielding and surface precipitation of solar energetic particles during BepiColombo’s close Mercury flyby: #BepiColombo measured Mercury's particle bombardment up close: https://www.helsinki.fi/en/news/mathematics-and-science/bepicolombo-measured-mercurys-particle-bombardment-close - the results help assess the impact of space storms on Mercury's surface and on Earth's atmosphere.
@tomkalei@machteburch.socialIt's not even clear what these people even want from us? Academic recognition? Co-Authorship on some follow-up paper? A cookie?
I think behind all this is a gross misunderstanding of how mathematics works and what the day-to-day conjectures in our papers mean.
They are not huge prizes like Jacobian conjecture or similar but they would serve as a little prize for the humans (often students!) who do point 2.
What do we do now? Keep our conjectures for ourselves? 2/2
https://thomas-kahle.de/blog/2026/just-42-tells-us-nothing/
@BBC6MusicBot@mastodonapp.uk🇺🇦 #NowPlaying on #BBC6Music's #6MusicsForeverDark
Deftones:
🎵 The Spell of Mathematics
#Deftones
https://open.spotify.com/track/6tFjBPdrwXhIpdR6i59DVx
@tomkalei@machteburch.socialAfter all old mathematics has been put into the AI slot machine, we will have a clearer picture of what is hard and what is just a language game and that could be interesting too.
But I still wonder who will still put out conjectures in this future. So if you want to solve one yourself, better hurry up. We might run out of people who openly conjecture something.
End.
@tomkalei@machteburch.socialNew blog post with Mateusz Michalek!
Impressed by the recent multiplication of great mathematical results we ask what this means for the community, e.g. prize or hiring committees.
Before AI a breakthrough paper also testified that the authors are experts in a certain area. That is certainly gone and it will have possibly disastrous consequences for the merit system of mathematics.
We are very curious to hear your thoughts on how to assign academic credit nowadays!
https://thomas-kahle.de/blog/2026/just-42-tells-us-nothing/
@tomkalei@machteburch.socialI share Linus Torvalds perspective on AI and I raise from OSS projects to #math. Same principles apply in my opinion. We do math because in mathematics there is no ignorabimus as Hilbert said. There is no religion that dictates how math should be done.
https://lore.kernel.org/linux-media/CAHk-=wi4zC Ze8e p3tMv8TtG_80KzsZ1syL9anBtmEh5Z40vg@mail.gmail.com/
@tomkalei@machteburch.socialHere is another scenario how research #mathematics as we know it will die (or is dead already?): Balkanization!
Without speculating about the future, current agentic AI systems can produce very impressive research math, certainly on PhD level, sometimes on Fields medal level. It needs to be post processed, etc. but I think it is an established fact.
#llm #math #ai 🧵
