An elaboration of the previous post mentioning the bounded gaps between primes problem as an illustration of the opportunity cost of converting a fruitful problem such as this solely into a competitive benchmark. [Indeed, as I point out below, this already came close to happening back in 2013.] As with most other problems worth studying in pure mathematics, the particular bound one gets on these gaps is not of much intrinsic importance. Improving Zhang's bound of 70 million, to 246, 188, or 6 would not, in itself, have significant impact on any other mathematical problem, let alone any real-world application, except for a small number of other analytic number theory problems in which a related numerical bound would also similarly improve. Even the twin prime conjecture, which asserts that the bound can be chosen to be 2, would only unlock a small number of immediate applications if the result is taken as a "black box", although the significantly more general and quantitative prime tuples conjecture of Hardy and Littlewood would be more useful in this regard. But again: the value of this problem lies not in the numerical bound _per se_, but rather in what the quest to study this problem and improve the bound reveals. Let me first quickly review some key moments in the timeline on this problem. The Quanta articles https://www.quantamagazine.org/mathematicians-team-up-on-twin-primes-conjecture-20131119/ and https://www.quantamagazine.org/a-new-generation-of-mathematicians-pushes-prime-number-barriers-20231026/ in 2013 and 2023 respectively also do a good job of covering these events. (1/8)
Learning more about Claude's mathematical capabilities
An unreleased version of Claude has made strides on a problem related to the Riemann hypothesis. It improved the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis, increasing it from 41.6% to 67.2%.
Terence Tao (@tao@mathstodon.xyz)
I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce. This may seem unintuitive at first, since the set of possible problems one could ask is infinite. Perhaps the following analogy can help: a country or region can suffer a critical shortage of drinking water while simultaneously being surrounded by a massive ocean. One can easily generate any number of open problems in mathematics at will, such as working out the 10^10^10th digit of pi. But the vast majority of such problems are not worth focusing attention on: they show no particular propensity to reveal any further insights or connections to other questions, or may either be too easy or too impossible relative to known techniques to learn anything from the exercise. (1/4)
Noam Brown on Twitter / X
And yes we did try other major problems without success. Sadly no Millennium Prize problems (yet).But also, we didn’t spend a lot on each problem. It’s possible to push test-time compute much further.— Noam Brown (@polynoamial) August 1, 2026
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
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.
OpenAI's Unreleased Model Astra Solves Ten Major Open Mathematics Problems
Math is hard.
An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
Deedy on Twitter / X
The International Math Olympiad (IMO) 2026, the hardest math contest for high schoolers, just ended.I ran Fable (high), Sol (xhigh), K3 (max) and Axiom against it and all got a perfect score of 42/42 (repo below if you want to check their solutions):— Claude Fable 5 was the… pic.twitter.com/6oH7FiAjEP— Deedy (@deedydas) July 21, 2026
A big lesson of my China visit: compute shortages are holding back Chinese AI
One estimate suggests that OpenAI has about as much compute as the entire Chinese AI industry.
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
More on whether useful quantum computing is “imminent”
These days, the most common question I get goes something like this: A decade ago, you told people that scalable quantum computing wasn’t imminent. Now, though, you claim it plausibly is immi…
DEF CON 33 - Post Quantum Panic: When Will the Cracking Begin, & Can We Detect it? - K Karagiannis
Mathematicians still don’t know the fastest way to multiply numbers
A 23-year-old student overturned an ancient conjecture about one of math’s simplest operations
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
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…
