the beginning of the math singularity: jul 2024: alphaproof + alphageometry 2 reach imo silver jul 2025: openai + gemini reach imo gold late 2025: gpt-5 contributes to unsolved math problems feb 2026: gemini solves several open erdős problems may 2026: openai model disproves an 80-year-old erdős conjecture aug 2026: anthropic improves a riemann bound from 41.6% to 67.2% aug 2026: astra produces 10 advances on longstanding open problems sep 2026: openai internal model beyond astra produces a claimed navier–stokes solution