Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems at the Paris conference of the International Congress of Mathematicians, speaking on August 8 at the Sorbonne. The complete list of 23 problems was published later, and translated into English in 1902 by Mary Frances Winston Newson in the Bulletin of the American Mathematical Society. Earlier publications appeared in Archiv der Mathematik und Physik.
Michael Truell on Twitter / X
We believe Cursor discovered a novel solution to Problem Six of the First Proof challenge, a set of math research problems that approximate the work of Stanford, MIT, Berkeley academics. Cursor's solution yields stronger results than the official, human-written solution.…— Michael Truell (@mntruell) March 3, 2026
Bartosz Naskręcki on Twitter / X
Congrats to @LechMazur for the solution and to Terence Tao for the digestion and storytelling. You see the trend. Mathematicians are still needed if we want to make any sense of the formal proofs. For now... Maybe the next gen LLMs will simply read allthe blogs of Terry and… https://t.co/yXiISCrNAF— Bartosz Naskręcki (@nasqret) August 13, 2026
Timothy Gowers @wtgowers on Twitter / X
AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried.https://t.co/SD1vVPkrHR— Timothy Gowers @wtgowers (@wtgowers) May 20, 2026
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in philosophy of mathematics. The theorems are interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
Przemek Chojecki | PC on Twitter / X
The Growing Map of Open Mathematical Problems.We mapped 15,000+ conjectures from UnsolvedMath to show potential links between concepts.It also shows how under formalized the frontier is (less than 10%). pic.twitter.com/nm0PCpXVPf— Przemek Chojecki | PC (@prz_chojecki) August 28, 2026
Tony Feng on Twitter / X
I am a mathematician but I avoided commenting on this because the problems are (far) outside my domain. Even if I sat down to read the technical details (which I have not), it would be hard to appreciate the context of prior work, etc. But I've gotten enough sense of things… https://t.co/VZzosBYFto— Tony Feng (@tonylfeng) August 5, 2026
Ten advances in mathematics and theoretical computer science
OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.
Has an AI discovered new maths?
What sort of maths are LLMs good at?
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten majo…
Terence Tao – Kepler, Newton, and the true nature of mathematical discovery
“And what those stories teach us about how AI will revolutionize math”
Collapse Theories
Quantum mechanics, with its revolutionary implications, has posedinnumerable problems to philosophers of science. In particular, it hassuggested reconsidering basic concepts such as the existence of aworld that is, at least to some extent, independent of the observer,the possibility of getting reliable and objective knowledge about it,and the possibility of taking (under appropriate circumstances) atleast some properties to be objectively possessed by physical systems.It has also raised many others questions which are well known to thoseinvolved in the debate on the interpretation of this pillar of modernscience. One can argue that most of the problems are not only due tothe intrinsic revolutionary nature of the phenomena which have led tothe development of the theory. They are also related to the fact that,in its standard formulation and interpretation, quantum mechanics is atheory which is excellent (in fact it has an unprecedented success inthe history of science) in telling us everything about what weobserve, but it meets with serious difficulties in telling uswhat there is. We are making here specific reference to thecentral problem of the theory, usually referred to as themeasurement problem, which is accompanying quantum theory sinceits birth. It is just one of the many attempts to overcome thedifficulties posed by this problem that has led to the development ofCollapse Theories, i.e., to the Dynamical ReductionProgram (DRP). As we shall see, this approach consists inaccepting that the dynamical equation of the standard theory should bemodified by the addition of stochastic and nonlinear terms. The nicefact is that the resulting theory is capable, on the basis of a singledynamics which is assumed to govern all natural processes, to accountat the same time for all well-established facts about microscopicsystems as described by the standard theory, as well as for theso-called postulate of wave packet reduction (WPR), which accompaniesthe interaction of a microscopic system with a measuring device. As iswell known, such a postulate is assumed in the standard scheme just inorder to guarantee that measurements have outcomes but, as weshall discuss below, it meets with insurmountable difficulties if onetries to derive it by assuming the measurement itself to be a processgoverned by the linear laws of the theory. Finally, the collapsetheories account in a completely satisfactory way for the classicalbehavior of macroscopic systems.
Itai Sher on Twitter / X
I think there should be a norm that when a set of AI solutions to mathematical problems is released, the set of all problems attempted be released alongside.When trying to understand AI capabilities, it is problematic to selectively report only positive results. https://t.co/ywcWCnFojS— Itai Sher (@itaisher) August 1, 2026
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
