Terence Tao Proposes 'Math 2.0' Framework to Shift Mathematics from Proof Scarcity to Proof Abundance

The Shift to Proof Abundance

Terence Tao outlines a transition from Math 1.0, characterized by proof scarcity and the difficulty of finding solutions, to Math 2.0, an era of proof abundance driven by modern AI. This shift is enabled by three unique properties of mathematics: objective verifiability (proofs can be checked by computers using tools like Lean), digitizability (no physical instantiation required), and the availability of high-quality data from digital research literature.

Risks of Indiscriminate AI Use

While AI can solve many open problems, Tao warns that blind optimization of problem-solving is now actively harmful to the field. In the past, the struggle to solve problems generated valuable insights and human understanding. Now, reaching solutions prematurely via automated tools can sterilize the surrounding field by skipping the exploration of "paths not taken." He distinguishes between aligned solutions that enhance human understanding and misaligned ones that may exploit weaknesses in verification processes without providing mechanistic insight.

New Frontiers and Experimental Mathematics

Tao advocates for using AI to expand the research frontier through experimental mathematics rather than just solving isolated problems. Key examples include:

• Equational Theories Project (2024–2025): Crowdsourced human and automated arguments to settle over 22 million true/false statements in universal algebra.
• Inverse Galois Problem challenge (2026): A competition to locate degree 24 polynomials with each of the 25,000 possible Galois groups, with a second stage extending to degree 31.
• Mathathon (Nov 13-15): A student-run event using open-source AI to find improved proofs for existing results with unsatisfactory current proofs.
• Integrated Explicit Analytic Number Theory Network (IEANTN): A living "spreadsheet" of interconnected results in explicit analytic number theory.

The Path Forward

The primary bottleneck to achieving Math 2.0 is not technology but imagination. Tao suggests focusing on open exposition problems (finding motivated explanations for opaque proofs), creating large formal mathematics libraries like Mathlib, and developing tailored, open-source math models for interpretability and safety. He emphasizes that the lessons learned while attempting to solve problems are often more valuable than the final solution itself.