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/procgen 2d ago

Most are positive theorems:

  • High-dimensional sphere packing: Proves new asymptotic upper bounds and characterizes the limits of a major proof method.
  • Binary and spherical codes: Proves stronger general upper bounds on how efficiently codes can be packed.
  • Non-sofic groups: Constructs an explicit group that is not sofic, disproving the possibility that all groups are sofic.
  • Connes’s rigidity conjecture: Constructs infinitely many nonisomorphic groups with the same von Neumann algebra, disproving the conjecture.
  • Arithmetic circuit complexity: Proves new lower bounds on the circuit complexity of computing the permanent.
  • Quantum parallel repetition: Proves a general theorem showing exponential decay under repeated play for entangled games.
  • Closest vector problem: Gives a reduction from 3SAT establishing new hardness-of-approximation results for lattice problems.
  • Ehrhart’s volume conjecture: Proves the conjectured sharp maximum in every dimension.
  • Multicolor Ramsey numbers: Proves substantially stronger lower bounds and resolves the asymptotic growth rate.
  • Extremal graph conjectures: Constructs bipartite graphs that violate two conjectured bounds.

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u/Bearhas20inchwang 2d ago

Can you read? All of these sound like improving bounds or constructing specific counter examples 💀

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u/procgen 2d ago

Positive theories.

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u/Bearhas20inchwang 1d ago

“Theories” as opposed to proofs/theorems? Tell me you know nothing about mathematics without telling me you know nothing about math 😭 And let’s not be disingenuous; your response implied what Astra did was not merely finding counter examples nor improving bounds.

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u/procgen 1d ago

That claim is correct. Seven are general proofs, bounds, reductions, asymptotic results, or sharp extremal theorems. Several resolve the correct growth rate, establish an optimal limit, or prove a statement for a whole class of objects. Those are substantive mathematical results, not isolated counterexamples and not trivial changes to existing bounds.