New AI Model Solves 10 Long-Standing Math Problems

@OpenAI· August 3, 2026 View original

Key takeaways

  • AI is demonstrating significant capabilities in solving complex mathematical problems.
  • This advancement could accelerate scientific discovery across various fields.
  • The transparency of releasing proofs and reasoning is crucial for validation.
  • AI's role in foundational research is expanding beyond mere data analysis.

Who benefits

AcademiaR&DTechnologyPharmaceuticalsEngineering

Summary

An internal version of a major AI model generated 10 new solutions to open problems in mathematics and theoretical computer science, costing approximately $2,000 in tokens. The results, spanning various advanced mathematical fields, are being released with formal certificates and reasoning walkthroughs for examination.

A new, unreleased AI model has achieved a significant breakthrough by solving ten long-standing open problems in advanced mathematics and theoretical computer science. These solutions were generated with a relatively modest computational cost. The problems addressed cover diverse areas such as sphere packing, coding theory, and quantum complexity, including establishing the existence of non-sofic groups and improving bounds on high-dimensional sphere packing. The developers are making the manuscripts, formal Lean certificates, and detailed reasoning walkthroughs publicly available. This initiative aims to allow mathematicians to thoroughly review the findings and build upon these AI-generated insights, potentially accelerating progress in foundational research that underpins many modern technologies.

Why it matters

This demonstrates AI's potential to accelerate fundamental scientific discovery, offering new tools for researchers to tackle complex problems previously thought intractable.

How to implement this in your domain

  1. 1Monitor advancements in AI for scientific discovery and problem-solving.
  2. 2Explore integrating AI tools into research workflows for hypothesis generation or proof verification.
  3. 3Collaborate with AI researchers to apply advanced models to specific industry challenges.
  4. 4Invest in R&D to leverage AI for foundational scientific breakthroughs relevant to your domain.

Original post by @OpenAI

"An internal version of our next major model produced 10 new results on long-standing open problems in mathematics and theoretical computer science, using roughly $2,000 worth of tokens at GPT-5.6 Sol API rates. The results span sphere packing, coding theory, group theory, quantum…"

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