Interview
Why Vlad Tenev and Tudor Achim of Harmonic Think AI Is About to Change Math—and Why It Matters
- A 43% probability is assigned to an AI or human-AI team solving the next Millennium Prize, a figure considered an underestimate, with a specific prediction that a hybrid team could solve an easy prize by 2026 and a fully AI-assisted or unassisted win on a tough prize by 2028.
- Specific timelines for mathematical milestones include solving the Riemann hypothesis by 2029 and Larry Guth potentially solving the same hypothesis in the near future.
- Mathematical reasoning capabilities are expected to reach the 99.99th percentile of human reasoning within the next year, with general human or superhuman reasoning broadly defined to be achieved within a couple of years.
- The primary training methodology is projected to shift to synthetic data generation due to the scarcity of human-written mathematical data.
- Auto-formalization of real-world situations and new mathematical theories is anticipated to become operational within the next several years.
- The role of mathematicians is expected to fundamentally evolve from direct problem-solving to guiding algorithms, directing massive compute resources, and posing questions, ensuring humans remain in the loop even if AI solves the problems.
- AI systems are predicted to progress through recursive intelligence levels, eventually creating their own data via an "AlphaGo to AlphaZero" approach to synthesize information and develop new, complex theories.
- Future AI capabilities include solving problems significantly harder than the Riemann hypothesis that humans have not yet conceived and auto-formalizing scenarios like a baseball team throwing balls into Lean code.
- Software verification is forecast to become the norm with costs approaching zero, with the expectation that the vast majority of software will be provably correct and verified within five to 10 years.
- Uncertainty exists regarding when AI will reach a point where human assistance in chess degrades results, though surpassing human capability is viewed as inevitable.
- The ultimate trajectory suggests a hybrid human-AI tool could solve all Millennium Prize problems and extend into fundamental physics research and history reasoning.