A group of mathematicians and formalization specialists, including Jeremy Avigad and Kevin Buzzard, published a guest post responding to calls—spurred by a recent OpenAI release—to use AI to formalize all of mathematics quickly. They say they are optimistic about AI's potential but worried that a rushed, uncoordinated effort could waste resources or cause lasting harm, and they outline conditions for doing large-scale formalization well.
xenaproject.wordpress.com
· 2026-10-16
John Harrison and Juneyoung Lee have released a tutorial intended as an easier on-ramp to the HOL Light theorem prover than its existing manual. The guide walks new users through installation, including options for Windows users via Windows Subsystem for Linux or Cygwin, followed by a graded set of worked examples. It is presented as a supplement to, not a replacement for, the standard HOL Light manual.
hol-light.github.io
· 2026-10-16
A guest post by mathematician Thomas Hales surveys the state of formal proof verification, noting that major theorems—including Fermat's Last Theorem, the sphere packing problem, and Navier-Stokes forced blowup—have recently been formally verified using computer proof assistants. Hales identifies Lean, created by Leo de Moura at Microsoft in 2013 and later open-sourced, as the proof assistant now most favored by mathematicians among several competing systems like Coq, Isabelle, and HOL Light.
terrytao.wordpress.com
· 2026-10-09
A formal verification project has completed a machine-checked proof in the Lean theorem prover establishing the optimal side length for packing 11 unit squares into a square container, with the exact value defined as the root of a polynomial equation. The verification run, tied to a specific pinned commit, accepted all 7,920 local Lean modules with zero admissions, using native numerical certificates for computationally expensive exact checks alongside standard Lean proofs for geometry and proof assembly.
github.com
· 2026-10-07
A recent gathering of innovative startups supported by Convergent Research highlighted the positive outlook among mathematicians regarding AI's influence. While acknowledging significant changes to traditional workflows, many see potential for AI to complement and enhance mathematical research. The discussion reflects a community adapting to rapid technological advancements that challenge conventional problem-solving methods.
terrytao.wordpress.com
· 2026-10-05
Ten Claude Opus 5.5 agents were tasked with finding a faster exact shortest-path algorithm for directed graphs with non-negative real weights and proving it correct in the Lean theorem prover. Over roughly 15 hours and 733 messages, the agents produced an algorithm called C-HD, which its creators say formally improves on previously published complexity bounds, including Dijkstra's algorithm and two recent 2025 and 2026 papers.
vals.ai
· 2026-09-22
GoKawiil