Ten-Minute Breakthrough: Terence Tao Uses Gemini Deepthink to Help Mathematicians Solve Erdős Problem Proof
Machine Heart Report
Introduction
There is a dedicated website for mathematical research and problem-solving, focusing on challenges posed by the legendary mathematician Paul Erdős.
This site — the Erdős Problems website — contains a curated collection of problems across fields such as number theory, combinatorics, and graph theory.
Researchers, academics, and enthusiasts can pose, discuss, and solve these problems collaboratively.
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AI Assistance in Problem Solving
Case Study: Erdős Problem #367
Source: https://www.erdosproblems.com/367
On November 20, independent researcher Wouter van Doorn presented a human-generated counterexample to part two of the problem, based on a congruence identity he believed to be true.
He remarked:
> “I’m sure someone could verify it… and it’s indeed correct.”
Source: forum thread
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AI Proof Generation
A few hours later, mathematician Terence Tao tested the problem using Gemini 2.5 Deep Think.
Result:
- AI returned a complete proof in ~10 minutes.
- The proof applied p-adic algebraic number theory — more advanced than strictly necessary.
Source: Gemini proof
Tao spent half an hour rewriting the proof into a more elementary form, publishing it on the site.
The cleaned-up proof appeared suitable for Lean formalization (“vibe formalizing”).
Following review, Wouter van Doorn thanked Tao for the confirmation and assistance.
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Lean Formalization
Two days later, mathematician Boris Alexeev used Harmonic’s Aristotle tool to create a Lean formalization.
He additionally manually formalized the final statement to guard against AI misuse.
This process took 2–3 hours.
Source: Erdos367.lean
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Terence Tao’s Ongoing AI Experiments
Recent AI-related mathematical projects Tao has participated in include:
- Google AlphaEvolve inspires new mathematical constructions — Tao publishes a paper
- GPT-5 Pro: small-scale and macro-scale performance excellent; mid-scale results “somewhat lacking”
- Thanks to Lean, Tao rewrote a 20-year-old textbook
- DeepMind’s AlphaEvolve breaks mathematical limits in collaboration with Tao
- Using ChatGPT, Tao completed an open-source project in 4 hours
Original post: https://mathstodon.xyz/@tao/115591487350860999
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The Bigger Picture: AI + Mathematics
The rapid rise of AI in mathematics demonstrates how human insight and machine reasoning now complement each other — from solving complex identities to formal verification in Lean.
Creators, researchers, and educators can now leverage AI to produce and share cross-platform knowledge efficiently.
An Example Platform: AiToEarn
AiToEarn官网 offers tools to:
- Create AI-powered content
- Publish across multiple channels (Douyin, Kwai, WeChat, Bilibili, Rednote, Facebook, Instagram, LinkedIn, Threads, YouTube, Pinterest, X)
- Integrate analytics, AI model rankings, and monetization features
Such ecosystems simplify publishing, enable global-scale sharing, and allow efficient knowledge monetization — crucial for modern researchers and creators.
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Summary:
From Gemini-generated p-adic proofs to Lean formalizations and multi-platform AI publishing, advanced tools are accelerating research workflows. Leading mathematicians like Terence Tao are blending AI systems with deep mathematical thinking — forging a future where collaboration between human and machine is integral to discovery and dissemination.
