OpenAI's matrix multiplication ω≤9/4 proof extended to all fields, verified in Lean with GPT-6 assistance
thomasahle · x · 2026-10-07
A new open-source effort extends OpenAI's Lean formalization of the fast matrix multiplication exponent bound ω≤9/4 from the complex numbers to every field. Found and formalized by consumer-grade GPT-6 Astra and GPT-6.1 Sol under Sela Navot's direction, the proof passed Lean verification and is released under Apache-2.0.
- Why it's notable: the new FMM paper takes a strikingly different approach from prior work—instead of powering the CW tensor and trimming it, it defines a potential function on tensors and proves the result by contradiction via the simple convolution tensor.
- Implication: the generalization strengthens the result's universality, and the author speculates n^{9/4} may actually be the right exponent for matrix multiplication.
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