Raphael Steiner
Mathematician, ETH Zurich · as of 2026-10-06 · source
Graph theorist; with Sergey Norin proved the linear Hadwiger conjecture with a proof found by GPT-6 Astra (Oct 2026); earlier extended a Ramsey construction from OpenAI Astra.
News mentioning Raphael Steiner (2)
- Linear Hadwiger conjecture proved: K_t-minor-free graphs are O(t)-colourable; proof found by GPT-6 Astra (Norin & Steiner), Lean-verified by Codex ★★★★★
On Oct 4, 2026 Sergey Norin (McGill) and Raphael Steiner (ETH Zurich) posted arXiv 2610.05291, proving the linear Hadwiger conjecture: there is a constant C such that every graph with no K_t minor is Ct-colourable. The authors say the proof "was found by GPT-6 Astra, following the directions by…
- OpenAI's unreleased 'Astra' model claims ten advances in maths and theoretical CS, with Lean proofs ★★★★★
On 1 Aug 2026 OpenAI published 'Ten advances in mathematics and theoretical computer science' by an internal model, Astra (released as GPT-6 Astra on 3 Sep). It came with a 249-page manuscript and Lean 4 proofs. The claims include the first explicit non-sofic group, a disproof of Connes's rigidity…
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