AI has solved 10 long-standing open problems in mathematics — all verified with machine-checked Lean 4 proofs. Title: Ten advances in mathematics and theoretical computer science URL: ❓ What problems were solved? 💡 Ten results spanning eight fields: high-dimensional sphere packing, existence of non-sofic groups, disproving Connes's rigidity conjecture, exponential parallel repetition for quantum games, polynomial-factor hardness for the closest vector problem (with post-quantum cryptography implications), Ehrhart's volume conjecture, multicolor Ramsey numbers, and extremal number conjectures (Erdős problems 146, 180, 183). Each problem had seen no progress on its main result for at least a decade. ❓ Which AI solved them? 💡 An internal evaluation version of Astra, OpenAI's next major unreleased model. Astra found the core proof structures; humans then prepared manuscripts and formalized the arguments using the same model. The total compute cost: roughly $2,000 at standard API rates — "theorem proving as a routine batch job any lab can run." ❓ Are these proofs actually correct? 💡 Every result ships with a machine-checkable Lean 4 certificate (mathlib + Lake, Apache-2.0, on GitHub). Running `lake exe cache get && lake build All` either compiles or it doesn't — correctness is resolved in minutes, not months of peer review. This is the strongest verification bar AI-produced mathematics has cleared at this scale. ❓ What does this mean for the future of math research? 💡 The significance is breadth, not a single lucky strike: eight fields, ten results. The bottleneck is no longer compute budget — it shifts to prompt design and result vetting. The rate-limiting step in mathematical discovery may soon be a human's ability to pose the right question and formalize the answer, not AI's ability to find it. #AIMath# #OpenAI#

.@littmath calls OpenAI's autonomous solution to the unit distance conjecture the most important AI math result: "The solution to the unit distance conjecture might be that. That was the first of these substantial results produced by a model fully autonomously. And it had the feature of some amount of creativity that we hadn't seen from the models before. It was taking some idea in one field and applying it to another field." "One reason I liked this solution to the unit distance problem more than some of the more recent results is we've seen actually people taking some of the ideas that appeared in that argument and applying them, so we know the ideas are generative." "The main idea of the construction was to use a classical construction from number theory called class field towers, to construct a counterexample to this question of Erdős." "Shortly afterwards, we saw a number of mathematicians take that idea and use it to construct counterexamples to some other questions in additive combinatorics, the sum-product conjecture over the real numbers."

Your startup intuitions were trained on a world that no longer exists. Steven Sinofsky and Martin Casado have watched computing flip from an engineering-bound field to a capital-bound industry. Twenty people can now put a billion dollars to work productively, AI solves the distribution problem that kept startups small, and challengers sit on a level playing field with Microsoft and Meta for the first time. With Erik Torenberg, they get into why some mathematicians are cheering on their own automation, every AI panic that already happened in past eras of computing, and why nobody can predict the capabilities of a model built with $20 billion. 00:55 Why mathematicians love being automated 02:45 Is AI math worth any money? 08:50 The first proof humans couldn't check 14:35 Computing before electricity 19:50 How IBM explained computers in 1953 26:00 The failed computer that birthed the web 27:50 When Harvard banned computers from exams 30:20 Is AI just another abstraction layer? 38:15 When 20 people can spend $1B productively 42:50 The zero-sum VC myth 46:25 Disruption is physics, not business school 53:25 The chip Intel called a printer part 55:05 What a $20B model can do 59:45 What Martin got wrong about AI risk YouTube: @stevesi @martin_casado @eriktorenberg

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