“Erdos problem #728 was solved more or less autonomously by AI”

TL;DR Highlight

Terence Tao used AI tools (Aristotle + LLM) to formally prove unsolved math problem Erdős #728 in Lean.

Who Should Read

Mathematicians and CS researchers interested in AI-assisted formal verification, and ML researchers tracking AI's progress on math reasoning.

Core Mechanics

Terence Tao (Fields Medal winner) used an AI tool called Aristotle in combination with an LLM to construct a formal Lean proof for Erdős conjecture #728 — a long-standing open problem.
This is significant because it's not a toy problem — Erdős conjectures are real mathematical research-level challenges, and #728 had resisted proof for decades.
The proof process was collaborative: Tao provided the high-level mathematical insight and strategy, while Aristotle/LLM handled the Lean proof formalization.
The result was machine-verified — not just plausible but formally checked by Lean's type system, guaranteeing correctness.
This demonstrates the emerging pattern: world-class mathematicians can now prove harder theorems faster with AI assistance than without.
Lean proof assistants become a trust anchor — even if the AI makes reasoning mistakes, the proof checker catches them before they're accepted.

Evidence

The Lean proof was made publicly available and verified by the community — not just a claim but checkable artifact.
Tao himself described the experience as significantly faster than manual formalization, even with his deep mathematical expertise.
HN discussion noted the importance of the 'Aristotle' tool specifically — it bridges between natural language mathematical reasoning and Lean's formal syntax.
Researchers in the Lean community confirmed this is a meaningful result — Erdős #728 is a legitimate research-level theorem, not a textbook exercise.
Comparison was made to AlphaProof's work on IMO problems — a pattern of AI enabling mathematical progress rather than replacing mathematicians.

How to Apply

If you work in software verification, track Aristotle and similar tools — the ability to bridge natural language specs to formal proofs is the missing piece for wider adoption.
For researchers: AI-assisted Lean proof writing is now at the stage where it's worth attempting on your own open problems, not just educational exercises.
The Tao collaboration model (human provides insight, AI handles formalization) suggests the near-term workflow: focus your effort on the mathematical ideas, delegate the proof mechanics.
Monitor the Lean/Mathlib ecosystem for AI tooling improvements — this is moving fast and the tools available in 6 months will be significantly better.

Terminology

Erdős conjecturesA large collection of open mathematical problems posed by prolific mathematician Paul Erdős, ranging from elementary to research-level difficulty.

Lean proof assistantA software tool where mathematical proofs are written in a formal language and machine-checked for logical correctness.

Aristotle (tool)An AI tool that helps bridge natural language mathematical reasoning and formal Lean proof syntax, used in Tao's collaboration.

Formal verificationMathematically proving that a statement (or program) satisfies a specification, with machine-checked guarantees of correctness.