Andrew Turner

@PlasmaAI

[Andrew Turner @_andrewturner]

@nicholas_diao and I had the chance to speak with Kathryn after the OpenAI results were published. The frontier of human knowledge has never been controlled by humans. It pushes itself!

https://t.co/wDSZx81mFr

[Elliot Glazer @ElliotGlazer]

“I don’t like set theory. I don’t think problems should be independent of the axioms” -Scott Aaronson’s 9-year old son

I wasn’t expecting such a tough crowd at the ice cream shop 😭😭😭😭😭

[Natalie Trono @Natalie_Trono]

@sama @PlasmaAI

[Andrew Turner @_andrewturner]

@sama @sama Mathematicians did not ask for this shirt to be made

[Andrew Turner @_andrewturner]

@PlasmaAI @OpenAI @SebastienBubeck the people want a lower theta

[Andrew Turner @_andrewturner]

Don't let them sweep this under the rug. What happened to the goblins @sama? Where did you put them?

[Andrew Turner @_andrewturner]

New SOTA benchmark

[Plasma AI @PlasmaAI]

@OpenAI recently released a proof of the quasi-Riemann Hypothesis, which says there is some fixed θ < 1 such that no zero of the Riemann zeta function has real part greater than θ. They prove it with θ = 7/8. The paper hasn't been peer reviewed yet, but its main theorem has a computer-checked proof in Lean.

This improves the bound on the root-mean-square error of the prime count against li(N). In general, that error is bounded by roughly N^θ if and only if no zero has real part greater than θ. The Riemann Hypothesis is the case θ = 1/2. So the best proven bound has dropped from almost N to roughly N^(7/8).

That's real progress, but the bound is still far above a random set's √(N/ln(N)) error, by a factor of about N^(3/8). It's worth noting that proving that the primes are merely as steady as random is sufficient to prove the full Riemann Hypothesis.

[will brown @willcb]

should’ve been obvious that neurosymbolic would win in hindsight

[Merriam-Webster @MerriamWebster]

@SKress7514 what

[Andrew Turner @_andrewturner]

Refreshing

[Eric Weinstein @ericweinstein]

Feel free to give up on heroic and romantic mathematics, Sir.

We don’t know each other, but I have admired your work. Yet I offer an alternate interpretation, respectfully. We have simply forgotten what it is like to live among true giants. True heroes.

von Neumann, Einstein, Grothendieck, Weyl, Turing, Gödel, Cartan, Shannon, Weil, Kolmogorov, Serre, Gelfand, Feynman, Dyson, Chern, Leray, Kodaira, Milnor, Atiyah, Singer, Thom, Bott, Borel, Harish-Chandra, Wiener, Courant, Pontryagin, Bohr, Heisenberg, Dirac, Schrödinger, Fermi, Pauli, Landau, Schwinger, Tomonaga, Yang, Oppenheimer, Wigner, Wheeler, Bethe, Bose, de Broglie, Yukawa, Gell-Mann, Salam, Weinberg, Dyson, Chandrasekhar

etc., etc.

were all alive on New Years Day 1954. That’s not nostalgia. That is how far we have fallen in this preposterous era you have celebrated.

This is absolutely categorically *NOT* the romantic era of individual heroism. This has been the era of mostly modest, professional, institutional incrementalism…with an occasional Grisha Perelman or Witten.

PREDICTION: AI is going to break this stranglehold that our leadership has had on credit assignment, how fast we are allowed to go, and who lives and dies within this community. And you are absolutely free to take the other side of that. But you might stop trying to speak as the leader of mathematics and mathematicians who do not agree with many of your mysterious recent statements.

Respectfully.

[Andrew Turner @_andrewturner]

Claude, draw a self-portrait.

[Nick Diao @nicholas_diao]

Our team built on @OpenAI's recent mathematical breakthroughs to resolve Erdős problem 408. Exciting to see how quickly progress in this field is compounding.

[Andrew Turner @_andrewturner]

More to come.

[Plasma AI @PlasmaAI]

More than 50 years after Erdős posed it, we have resolved Erdős problem 408: for almost all n, totient iteration takes ∼α log n steps to reach 1, for some constant α. The proof builds on @OpenAI's recent results (including their proof of the quasi-Riemann hypothesis), along with classical methods of Erdős, Granville, Pomerance, and Spiro. It is formally verified in Lean.

This is the second Erdős problem that we've fully resolved using Fractal (coming soon). We will be releasing results on more problems in the coming weeks.

https://t.co/I9AmJy1c0x

[Natalie Trono @Natalie_Trono]

Thanks @khulick for including @PlasmaAI!

https://t.co/UdycUv3OKd

[Andrew Turner @_andrewturner]

@Jon_Hartley_ Congratulations @Jon_Hartley_ !

[Jon Hartley @Jon_Hartley_]

My college classmate Matt and I just used AI to create a Erdos #374 solution w/ a Lean-verified proof. We used a reciprocal-prime equidistribution estimate, Harman’s almost-all short-interval theorem, Weil’s bound, and the analytic large sieve. Full proof: https://t.co/CFmmbzfTVX

[Plasma AI @PlasmaAI]

Fedir Yudin and Hartley &amp; Olson independently completed the problem: an asymptotic for D₃ and linear growth for D₅ and D₆. Together with the known result for D₄, this settles every k from 3 to 6. Both claims are now accepted on https://t.co/RsUEtUckh1.

[Plasma AI @PlasmaAI]

Erdős Problem #374 is solved! Jonathan Hartley and Matthew Olson proved the Erdős–Graham conjecture that D₆, the set of numbers needing six factorials to form a square, has positive density. They formalized the complete solution in Lean, and we verified it.

https://t.co/Ha91ph2Am6

[Andrew Turner @_andrewturner]

Tom deciphered Linear A, an ancient Minoan language from 1800 BC.

[🔥 Tom di Mino💧 @IdaeanDaktyl]

While OpenAI merely waived a wand from behind the curtain, we took an agentic approach to math that will stand the test of time.

We envision a future in which research methodology means more than pointing AI models at a problem.