English(EN) W(2;3,21) = 416 - a van der Waerden number conjectured by Kullmann in 2010, now proved with a Lean 4 kernel-checked proof [R]

数学家通过Lean 4内核验证的证明证实W(2;3,21) = 416

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-29 20:46

一个重要的数学猜想W(2;3,21) = 416已通过名为Lean 4的形式验证系统得到证明。该证明经过内核验证，解决了Kullmann于2010年提出的问题，此前该问题列在DeepMind的形式猜想列表中。证明涉及超过209个案例和数百万个公式，由LRAT检查器cake_pr执行验证。 AI

影响展示了形式验证系统在证明复杂数学定理方面日益增长的能力。

排序理由使用形式验证工具证明数学猜想。[lever_c_demoted from research: ic=1 ai=0.7]

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r/MachineLearning TIER_1 English(EN) · /u/Rodriguez909 · 2026-10-29 20:46

W(2;3,21) = 416 - 2010年Kullmann推测的van der Waerden数，现已通过Lean 4内核验证的证明得到证实 [R]

<div class="md">w(2;3,21) = 416 - today proved with a Lean 4 kernel- checked proof (preprint + 13.6 GB evidence package). Every red-blue colouring of {1, ..., 416} contains a red 3-term or a blue 21-term arithmetic …