Terence Tao Uses GPT-5 Pro to Solve Math Problem in 11 Minutes
AI Revolutionizes Mathematical Research Through Collaboration
Renowned mathematician Terence Tao has achieved a breakthrough by collaborating with GPT-5 Pro, solving a differential geometry problem that had puzzled researchers for three years. This landmark achievement demonstrates AI's potential to transform mathematical research and opens new possibilities for human-AI collaboration.
The Challenge: A Complex Geometry Problem
The problem involved analyzing smooth topological spheres in three-dimensional space where the absolute value of principal curvature doesn't exceed 1. Researchers sought to determine whether such surfaces enclose volumes at least equal to unit spheres.
While Tao has made significant contributions across multiple mathematical fields, differential geometry isn't his primary specialty. After initial attempts, he recognized gaps in his knowledge and turned to AI assistance.
The AI Breakthrough: Proof Completed in Minutes
Tao provided GPT-5 Pro with the problem's general direction. Within just 11 minutes, the AI completed complex calculations and delivered a complete proof process. This astonishing speed showcased:
- Rapid computational capabilities
- Ability to identify key logical pathways
- Capacity to challenge human intuition
The collaboration yielded multiple proof approaches, including familiar tools like Stokes theorem and Willmore inequality, plus novel concepts such as the first Minkowski integral formula.
Human-AI Synergy: Strengths and Limitations
The project revealed important insights about collaborative mathematics:
- Small-scale problems: AI excels at rapid calculations and derivations
- Medium-scale strategy: May reinforce incorrect intuitions without human oversight
- Large-scale understanding: Provides valuable insights but requires expert interpretation
Tao emphasized that while AI offers powerful tools, human mathematicians remain essential for critical thinking and verification.
Implications for Future Research
This collaboration represents more than solving one problem—it establishes a new research paradigm:
- Dramatically accelerates proof processes (from months/years to minutes)
- Allows mathematicians to focus on creative thinking rather than computation
- Demonstrates how AI can expand human capabilities rather than replace them Tao predicts deeper integration between AI and mathematics will lead to more breakthroughs.
Key Points:
- GPT-5 Pro completed proof in 11 minutes
- Collaboration revealed both strengths and limitations of mathematical AI
- Human oversight remains crucial despite AI capabilities
- Establishes new model combining human insight with machine computation
- Potential to fundamentally change mathematical research methodology
