I Solved an 'Impossible' Math Problem with AI

Siraj Raval · Advanced ·🧠 Large Language Models ·6mo ago

Key Takeaways

The video demonstrates the use of AI models, specifically Claude, GPT, and Gemini, to solve decades-old math problems, including one with a $1,000 cash bounty, and showcases the potential of AI in mathematical research, using tools like Lean 4, a compiler for truth, and GitHub for code sharing.

Original Description

Math just hit a tipping point. In the last 21 days, AI has helped solve decades-old math problems, and even Fields Medalists like Terence Tao are now using AI to check their own proofs. The barrier to entry for serious mathematical research is collapsing. So I decided to push it further. I gave myself 24 hours, 3 AI models (Claude, GPT, Gemini), and a folder of unsolved problems left behind by the legendary Paul Erdős. One problem has a $1,000 cash bounty. One completely broke my code. But one resulted in a green checkmark: a machine-verified proof of a new mathematical theorem, written entirely by AI. This is not just ChatGPT doing homework. This is a glimpse into the future of scientific discovery. 🔗 Resources 📄 Lean Code (GitHub): https://github.com/llSourcell/Solving_Erdos_Problems_with_AI/ 🧠 Erdős Problems List: https://www.erdosproblems.com/lists 📘 Learn Lean 4: https://leanprover-community.github.io/learn.html ⏱️ Chapters 00:00 — The Tipping Point 01:22 — Lean 4: A Compiler for Truth 02:08 — Level 1: Erdős Problem 379 03:48 — Level 2: The $1,000 Abyss 05:30 — The Next Industrial Revolution 09:18 — Level 3: The “Impossible” Proof 11:50 — Why Math Just Changed 🚀 Sponsor: The Infrastructure of the Future This video is sponsored by Humanoid Global Holdings (OTC: $RBOHF). We are at the zero-mile marker of the most profound productivity shift in human history: humanoid robotics. To gain exposure to private companies building this future (including Agility Robotics and Apptronik), learn more about Humanoid Global Holdings. Disclaimer: This is for informational purposes only and not financial advice. 📬 CONTACT Business: hello@sirajraval.com 📲 FOLLOW X: https://x.com/sirajraval Instagram: https://instagram.com/sirajraval LinkedIn: https://linkedin.com/in/sirajraval 🔔 Subscribe for more AI videos! Keywords: #AI #Mathematics #Lean4 #DeepSeek #TerenceTao #MachineLearning #Erdos #Coding #Python #FutureTech
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The video showcases the potential of AI in mathematical research, demonstrating how AI models can be used to solve decades-old math problems, and providing a glimpse into the future of scientific discovery. Viewers can learn how to apply AI models to solve complex math problems and use Lean 4 to verify mathematical proofs. The video also highlights the importance of collaboration and sharing code on platforms like GitHub.

Key Takeaways
  1. Choose a mathematical problem to solve
  2. Select and train an AI model
  3. Use Lean 4 to verify the mathematical proof
  4. Share and collaborate on the code using GitHub
  5. Refine and iterate on the solution
💡 The use of AI models can significantly accelerate mathematical research and solve problems that were previously considered unsolvable, and collaboration and code sharing are crucial for advancing scientific discovery.

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Chapters (7)

The Tipping Point
1:22 Lean 4: A Compiler for Truth
2:08 Level 1: Erdős Problem 379
3:48 Level 2: The $1,000 Abyss
5:30 The Next Industrial Revolution
9:18 Level 3: The “Impossible” Proof
11:50 Why Math Just Changed
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