So today Claude reverse-engineered the NIST seeds from 2000 for ECDSA up to 521 bits. https://www.anthropic.com/research/ecdsa-curve-origins This doesn’t break ECDSA, only confirms that the seed was RNG-derived from a timestamp. So it’s just a kawaii piece of crypto trivia. But it also highlights the suspicious fact that none of the 722 math breakthroughs recently published by OpenAI were about cryptography. That seems implausible. Survivor bias suggests that there were results there too, but they were kept undisclosed to the public.

1 reply

0 recast

16 reactions

Continuing on this monumental dump: the Association for Human Mathematics is now calling for the boycott of OpenAi within the mathematical community: https://www.ahmath.org/statements I have to wonder — if some Euler-level gigabrained flesh-and-bones mathematician had suddenly dumped hundreds of proofs and counter proofs to major unsolved conjectures, he or she would be universally lauded and deified for his or her unprecedented contribution to humankind. So are we being speciesist toward non-human intelligence already?

2 replies

0 recast

7 reactions

“It’s as if you were teleported to the peak of a tall mountain. Surrounded by fog, you have no idea where you are, or what’s around you. You do not know how your mountain connects to others, and you have no equipment to help you explore, no way to help someone else join you. If you had climbed the mountain yourself, you would have experienced how the human body adapts to altitude and changes in oxygen levels. You might have had to invent tools to navigate, to climb steep cliffs, or to make a shelter. You might have encountered a fellow explorer, gotten lost together in a hidden valley, and found a plant that could be turned into a life-saving medicine.” From https://www.quantamagazine.org/is-ai-the-end-of-math-as-we-know-it-20261005/

1 reply

1 recast

10 reactions

I just LLM-mined those 722 proofs for connections to the Riemann hypothesis. There's actually a shocking result in a paper dated Sept 30 (https://github.com/openai/math/tree/main/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026), which I expect to blow up in social & trad media over the coming days. OpenAI's frontier model successfully showed that the real part of all (non-trivial) zeta zeros must lie between 1/8 (=0.125) and 7/8 (=0.875), instead of the previous critical strip boundaries of 0 and 1. This is an ASTOUNDING result, and quite possibly the largest unconditional advance toward RH in decades. Not so much because it narrows the critical strip closer to 1/2 (still plenty of room left), but because for the first time, it establishes height-independent boundaries for zeros. Previously, all classical zero-free regions shrunk to zero with height along the imaginary axis. There's no path to proving RH here, but it's such a leap that I wouldn't be surprised if we got there in the next 36 months.

2 replies

1 recast

18 reactions

Wake up babe, OpenAI just dumped *checks notes* 722 proofs (and counter proofs) of significant unsolved conjectures https://github.com/openai/math/tree/main/preprints

1 reply

1 recast

12 reactions

So math socials are buzzing now with Tristan Buckmaster (math prof at NYU) claiming to have co-developed a proof of Navier-Stokes smoothness (one of six remaining Clay Institute “millennia problems” worth $1M), using OpenAI models to help him; and OpenAI’s scientist Sébastien Bubeck having potentially sniped the result. What’s at stake is the claim (completely unverified at this stage) that OpenAI may have used Tristan’s Codex history to leverage (spelled s-t-e-a-l) his interim results. Which would be a pretty serious privacy breach ofc. At a minimum, Sébastien appears to have attempted to negotiate with Tristan the removal of his co-author from the upcoming paper, who happens to work at Anthropic. Here’s the initial statement by Tristan: https://cims.nyu.edu/~tristanb/statement.pdf Sébastien has said he’ll issue his own in the next few hours. 🌶️

5 replies

1 recast

28 reactions

Claude: at least 67.2% of all Riemann zeros lie on the critical line (up from 41.6%) It’s getting nearer https://www.anthropic.com/research/riemann-zeta

0 reply

1 recast

9 reactions

New 3Blue1Brown series covering information theory, and how the math behind data compression is related to the math behind measuring the intelligence of an AI model. https://youtu.be/l6DKRf-fAAM

1 reply

1 recast

4 reactions

William Shank (1812–1882) was an amateur mathematician who spent decades of his life laboriously calculating by hand hundreds of digits of pi, and the decimal expansion of the reciprocal of prime numbers up to 110,000. Now imagine being William Shank and waking up one morning only to find out that somebody just invented the modern programmable calculator, effortlessly replicating from scratch years of your work (and then blowing past it) within seconds. This is how entire cohorts of math PhDs are going to feel as frontier models start publishing breakthrough proofs at the speed that it takes to type a prompt. Context: https://openai.com/index/model-disproves-discrete-geometry-conjecture/

1 reply

0 recast

15 reactions

Every math theorem is named after the second mathematician who discovered it, the first one being Euler

2 replies

0 recast

61 reactions

The Riemann hypothesis has long been an obsession of mine, as my cast history can attest. I have read many books and watched virtually every mainstream video about it. This new video is arguably the best explanation I have watched to date; it is satisfyingly complete while avoiding becoming impenetrable to non-mathematicians. Highly recommended if you are interested in the topic. https://youtu.be/pyEGbhwYOeo

0 reply

2 recasts

42 reactions

Terence Tao responding to a question on what advice he would give someone considering a career in math in 2026: 'Yeah, so we live in a time of change. It is, as I said, we live in a particularly unpredictable era. And I think things that we've taken for granted for centuries may not hold anymore. So, yeah, the way we... do everything, not just mathematics, will change. In many ways, I would prefer the much more boring, quiet era where things are much the same as they were 10 years ago, 20 years ago. But I think one just has to embrace that there's going to be a lot of change and that, you know, the things that you study, some of them may become obsolete or revolutionized, but some things will be retained. There'll be a lot of opportunities for things that you wouldn't be able to do before. So, I mean, in math, you previously had to basically go through years and years of education to be a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level or whatever, that you could get involved in a math project and actually make a real contribution because of all these AI tools and lean and everything else. So there'll be a lot of non-traditional opportunities to learn. So you need a very adaptable mindset. There'll be one for pursuing things just for curiosity, for playing around. And I mean, you still need to get your credentials. I mean, I think for a while it would still be important to sort of still go through traditional education and learn math and science and so forth the old-fashioned way for a while. Yeah, but you should also be open to very, very different ways of doing science, some of which don't exist yet. Yeah, so it's a scary time, but also very exciting.' More: https://www.dwarkesh.com/p/terence-tao

0 reply

0 recast

8 reactions

Trusting the math is a bit like trusting your instruments while flying in poor visibility: they don’t lie, even when your gut feels otherwise (sometimes literally — you could be flying upside down and, with the right acceleration, not know it). The quintessential example is Dirac’s equation. Around 1927, he set off to find a quantum equation for the electron that was fully relativistic and linear in time, unlike the Schrödinger equation. Problem was, his equation had two roots, one positive and one negative. Because a negative energy solution seemed nonsensical, it was ignored by most physicists, except Dirac, who stood by his result. He was vindicated in 1932 when the first positron was observed: same mass as the electron, just with an opposite charge. The negative energy solution pointed to the existence of antimatter. We “just” had to trust the math, even as they felt unintuitive. The thing is… this works until it doesn’t. In fact, Dirac’s equation is more exception than rule. We can’t have negative length or probabilities, or violate causality or energy conservation, and yet plenty of math results give exactly that. So what’s the difference? Dirac’s negative results met three conditions: they were unavoidable, they solved the system’s instability, and they mapped cleanly to a (at least predictably) observable particle with definite charge and mass. Most other negative solutions fail at least one of these. TL;DR: shit’s complicated, yo

1 reply

2 recasts

6 reactions

As it turns out, you mostly can't even achieve meaningful consistent upward mobility via taking EV+ risks as well, especially if EV is arithmetic but returns are geometric.

0 reply

0 recast

0 reaction

I can't believe nobody recommended Steve Brunton's channel on YouTube, absolutely goated https://youtube.com/@eigensteve?si=Y-KvK1wemUGmVUMD

0 reply

0 recast

1 reaction