Math & science · July 2026

Cycle double cover proof

A 1970s graph theory conjecture reportedly proved in under an hour.

GPT-5.6 Sol Ultra, running 64 parallel subagents, produced a proof of the Szekeres-Seymour cycle double cover conjecture in under an hour. Thomas Bloom described it as short and elementary; full community review was still under way.

See it in the living tree Wikipedia Source

Arcs above join it to what it stood on, arcs below to what it led to. The bar places this stretch on the tree's whole timeline.

What it built on 2

GPT-5.6 2026
AI starts solving Erdős problems 2026

Related measurements

The dashed line marks when it first worked.

Best AI score on GPQA Diamond Latest: 95.8 % correct (2026) Source: Epoch AI, Capabilities & benchmarking (benchmark_data.zip, gpqa_diamond.csv); Anthropic: Claude 3 public launch (March 4, 2024)

Training compute of notable AI models Source: Epoch AI, Notable AI Models (CC BY 4.0)