[This is a guest post by Raghu Meka. This blog post was initially written in a different file format and converted using AI. — T.] “This problem has been tried by several famous mathematicians.” “There is a heuristic argument for why these methods cannot work.” “Getting this algorithm would give new circuit lower bounds.” Observations […]
Brandon Yates, professional composer and amateur physicist Why is it that when a new and particularly powerful tool is brought into the world, one with which many subjects of research can be accelerated and studied with more scrutiny and attention than a person might ever be able to manage on their own, the first instinct […]
“As announced a few weeks ago, OpenAI has released a large collection of mathematical results generated by an internal model, reporting solutions to hundreds of open questions. This is an important event for mathematics, with consequences both for mathematics and for the mathematical community that extend far beyond the individual results. […]”
With Danny and Sharon Kleitman and Michel Goemans at the MIT Endicott house. Sharing AI progress on mathematics (OpenAI) A few hours ago, Open AI shared solution to a few hundred mathematical problems. Certainly this is an amazing milestone for … Continue reading →
[This is a guest post by Ben Antieau, cross-posted from his blog. — T.] There was no personal problem, no world problem, whose eloquent solution did not exist— somewhere in some hexagon. —Jorge Luis Borges, “The Library of Babel” [1] New repository I am writing to announce Hexagon, a new repository for research works in […]
Mathematics is beginning to face a turbulent age due to the rapid advancements of AI systems. A recent Summit on PhD Math Education in the Age of AI (CMSA) discussed recommendations on the adaptations for the Math PhD programs. While I agree with the main points, this post is an opinion on my major objection to the proposed direction of PhD in mathematics. I argue for a radical change in the defin…
[This is a guest post by Thomas Bloom, crossposted from the Erdős problems forum. This blog post was initially written in a different file format and converted using AI. — T.] AI is changing everything, for better and/or worse, and the rate of change is dizzying; in recent months this has been particularly evident in […]
“Large language models (LLMs) first appeared to the general public as a curiosity. Today, everyone uses them, and there is no doubt that their use is radically transforming the nature of our technical activities. This is particularly true in mathematics. […]”
“We are in an age in which artificial intelligence is no longer a technological curiosity or a tool used by specialists. Generative AI can now write, summarize, translate, code, solve mathematical problems, and assist with almost every stage of academic work. The opportunities are enormous. […]”
[This is a guest post by Jeremy Avigad. This blog post was initially written in a different file format and converted using AI. — T.] “Mathematics underwent, in the nineteenth century, a transformation so profound that it is not too much to call it a second birth of the subject—its first birth having occurred among […]
Before AI, writing papers and grant applications served as costly signals of a scientist’s ability. Today, they can no longer serve that function. The time has come to return to illegible, subjective human evaluations of scientific quality. Rate-limiting authors is a necessary first step.
Are mathematicians only bearers of truth? I argue not; I argue there is an element of “taste” and “value judgment” behind the scenes that does not appear in the discussion of AI math.
[This is a guest post by Diego Córdoba and Luis Martínez-Zoroa. This blog post was initially written in a different file format and converted using AI. — T.] Euler formulated the equations for an inviscid incompressible fluid more than 250 years ago. Published in his 1757 memoir, they belong to the earliest systems of partial […]
Some thoughts on what an old folk song can teach us about recent advances in artificial intelligence.
[This is a guest post by Jennifer Taback. This blog post was initially written in a different file format and converted using AI. — T.] Recently I have read a stream of articles questioning the future of mathematics: what constitutes a proof, what we value, how we retain the human enterprise of creating knowledge. Many […]
If we are not needed to produce maths, then we can spend our time learning. With the right incentive structure, that does not sound so bad.
I use large language models quite a lot in my research. I ask them to look for references, explain unfamiliar mathematics, write code, suggest approaches, find counterexamples, and try to prove things.
[This is a guest post by Matthew Colbrook. This blog post was initially written in a different file format and converted using AI. — T.] (Disclosure: ChatGPT helped me write and refine this post.) Inspired in part by the recent discussions on this blog, we have started a new project, AIM, an initiative to create […]
— 1. The Hardy-Littlewood maximal inequality — We work in Euclidean space with Lebesgue measure; we write instead of for the Lebesgue measure of a set . For any and let denote the open ball of radius centred at . Thus for instance . For any , we use to denote the dilate of around […]
“At the moment, the mathematics community is facing an unprecedented misalignment brought on by the advent of LLMs. According to the standard telling, the basic tension is between our traditional values (whatever those may be) and those of the corporations that make and market LLMs. […]”
In this personal essay, I reconstruct the reasons why I chose to become a professional mathematician. In particular, I want to find out whether I would still find these reasons convincing and motivating today, at a time when AI is becoming capable of conducting excellent and potentially superhuman mathematical research.
In response to an exponential growth of submissions, the arXiv just announced changes to its rate limiting policy, which among other things restricts submissions to at most two a month for each submitter.
About the possibility of new paper mills in mathematics.
Preprints are central to math research and immediately feed back into LLMs. Could the mainstream preprint workflow be adjusted in a way that gives individuals more choices to impact the balance between creation of novel papers and digestion of knowledge?
The EMS should establish a structure to shepherd the use of artificial intelligence in mathematics research. This could include developing in house AI models, regulating their use by the mathematical community in accordance with European law and establishing protocols for publication.
A brief post to note two reports that just came out: The Advisory Group on Mathematics and Artificial Intelligence (AGMAI) has posted its general recommendations to AI companies with regards to generation of solutions to mathematical problems. A working group report “AI and TCS: The Next Six Months” arising from a two-day event at the […]
“As more and more central problems are nuked into oblivion by generated proofs, against the spreading AI-gloom the voices rise, emphasizing the internal value of deep mathematical thought and advocating for measures ranging from exercising extreme discretion with generative tools to seizing railway stations and the telegraph (or was it departments and classes of mathematical problems?) from the ti…
[This is a guest post by Rachel Webb. This blog post was initially written in a different file format and converted using AI. — T.] The way I do math experienced a great upheaval once before, halfway through my PhD. I was in a seminar with a group of graduate students and faculty developing new […]
Stepan Nesterov, PhD student at Stanford University About a hundred years ago, David Hilbert gave a rigorous definition of a mathematical proof: Definition. A mathematical proof is a sequence of formal statements A1,…,AnA_1, \ldots, A_n such that every statement AiA_i in the sequence either belongs to a predefined set of axioms of logic or there […]
[This is a guest post by a coalition of Caltech mathematicians: the original organizers of Mathathon (Alvan Arulandu, Andrea Li, Avni Garg, Brian Zhao, Caiman Moreno-Earle, Sathvik Redrouthu), two coauthors of the Open Letter about the Mathathon (Dylan King, Tasmin Chu), and other members of the Caltech community (Mayla Ward, Merrick Hua, Robert Joseph George, […]
A coalition of Caltech Mathematicians. Mathathon is centered around one question: how can we use AI to augment human understanding of mathematics? This past week, the original organizers of Mathathon, two coauthors of Open Letter about the Mathathon, and other members of the Caltech community engaged in a conversation to redesign this event. We quickly […]
Why does AI worry applied mathematicians less? We have met the machine before: human computers moved up to designing algorithms, and a computer run led to the solution. Driven by problems rather than great conjectures, we expect AI, used with careful verification and validation, to make us better mathematicians.
This essay was, in some sense, written as a way to grapple with the questions raised by AI about my own value as a researcher. It is a reflection on the effects these changes were having on me, on my practice of mathematics, and on how I might learn to cope with them.
[This is a guest post by Jess Werk. This blog post was initially written in a different file format and converted using AI. — T.] Hello, I am Jess Werk, professor and chair of Astronomy at the University of Washington. Astronomy may interest mathematicians right now because our field has already been reshaped by supercomputers […]
We can use puzzles as a philosophical playground to think about the nature of insight, and compare human and artificial approaches. And we can explore what understanding means to us as human beings—both when we struggle toward it ourselves, and when we share it with each other.
Some Mathematician. Some mathematicians don’t use LLMs at all. Some others use LLMs and desire to state which models they use in their papers. But if you use LLMs and do not hold this desire, you may choose to state “I used some LLMs to do this and that” without specifying which models you used. […]
[This is a guest post by Ivan Corwin. This blog post was initially written in a different file format and converted using AI. — T.] Mathematics and those mathematicians who guide its development have been central to societal advancement since antiquity. AI, like many tools that were invented by mathematicians (e.g., the abacus, slide rule, […]
The very human story of the discovery of non-sofic, non-MF and non-hyperlinear groups over the past two months.
Just a quick post to note that the International Council for Industrial and Applied Mathematics (ICIAM) has released a statement on mathematics and artificial intelligence (as well as a longer version), which makes many points echoing several already made recently here and elsewhere. The longer statement also makes reference to a recent statement by the […]
[This is a guest post by Bryna Kra and Rachel Ward. -T.] The Summit on PhD Math Education in the Age of AI was held September 17–18, 2026, at Harvard’s Center of Mathematical Sciences and Applications (CMSA). It brought together twenty-four senior mathematicians from across the discipline, along with several current PhD students and postdocs, […]