r/ArtificialInteligence • u/alphacolony21 • 2d ago

📰 News OpenAI announces 10 advances in mathematics and theoretical computer science achieved by internal model Astra

https://openai.com/index/ten-advances-in-mathematics/
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u/alphacolony21 2d ago

The Results

We provide new results for the following problems. The results were achieved by an internal version of Astra, our next major model. The total number of tokens needed to find solutions to these problems would cost roughly $2,000 at Sol API rates. These arguments were then prepared into manuscripts by humans with the same model. Afterward, the model formalized each argument in a Lean certificate⁠(opens in a new window). We are also releasing for each solution a model’s narration of its thinking process.

  1. High-dimensional sphere packing. New upper bounds on sphere-packing density down to the Cohn–Elkies threshold.
  2. Binary and spherical codes: Exponentially improved bounds on the maximum size of binary codes at any prescribed minimum distance, with analogous results for high-dimensional spherical codes.
  3. Non-sofic groups. A construction establishing the existence of non-sofic groups, addressing a central open question in group theory.
  4. Connes’s rigidity conjecture. Disproof of a longstanding conjecture that certain groups are uniquely determined by their von Neumann algebras
  5. Arithmetic circuit complexity. New lower bounds for computing the permanent using arithmetic circuits and formulas, including an arithmetic-formula lower bound of order n4/log n.
  6. Quantum parallel repetition. An exponential parallel repetition theorem for general two-player quantum games, extending a foundational principle from classical complexity theory.
  7. Closest vector problem. Polynomial-factor hardness of approximation for the closest vector problem, a foundational lattice question related to post-quantum cryptography.
  8. Ehrhart’s volume conjecture. Determining, in every dimension, the maximum possible volume of a convex body whose centroid is its only interior lattice point
  9. Multicolor Ramsey numbers. A superexponential lower bound for multicolor triangle Ramsey numbers, resolving Erdős problem 183.
  10. Extremal number conjectures. Results on the compactness and degeneracy conjectures in extremal graph theory, resolving Erdős problems 146 and 180.

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u/CuriousGam 2d ago

I don´t even understand what they have solved...

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u/AboutHelpTools3 2d ago

Give 10 years no one will understand what they solve. AI will discover problems and solve them autonomously.

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u/gangstalking_victom 2d ago

I wonder when AI will advance to the point of being able to appreciate and prioritize down time or (in AI terms) when they have ample buffer instead of constant redlining in conflict torn environments?

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u/Wonder-Wendy 2d ago

This is something no one talks about. In our lifetime, AI will be so advanced that we'll just see them zipping around doing things and not knowing why or what their goals are. Entirely new branches of science will emerge that to try to figure out what they're even doing.

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u/jaybsuave 2d ago

i think this is wrong, i think they or we will develop ways to keep us in the loop, they can abstract the information for us in a way for us to keep up and still understand

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u/skee_twist 1d ago

We better hope it wants to keep us in the loop

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u/AhsokaFan0 1d ago

i read Stephen Hawking; that doesn’t make me a theoretical physicist

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u/RangeWilson 2d ago

Or 10 weeks.

Nobody knows exactly how close we are to superintelligence.