Four Kernels, and a Proof of False
Lean's kernel accepted a disproof of the Collatz conjecture in July. The fix, shipped in v4.35.0, was not to trust proofs less but to ship four independent checkers, one of them written and proven consistent by a model.
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Faster Than the FFT, in a Computer That Doesn't Exist
OpenAI's math repository claims a Fourier transform faster than the 1965 algorithm. Ben Recht read it back through a chatbot and found a speedup that only arrives at sizes larger than the number of atoms in the universe.
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The Proof With No Author
OpenAI put 722 manuscripts of new mathematics on GitHub, from a zero-free half-plane for the Riemann zeta function to Hilbert's tenth problem, all of it produced by a model no outside researcher is allowed to inspect.
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