Terence Tao – How the world’s top mathematician uses AI

Kepler's discovery process as a historical data science model

• Kepler initially proposed a "beautiful" theory based on inscribing the five Platonic solids between planetary orbits, which fit observational data from Brahe to within approximately 10%.
• When the data from Tycho Brahe's high-precision naked-eye observations (10x more accurate than previous records) contradicted his geometric model, Kepler spent years experimenting with various "fudges" before accepting that planetary orbits were ellipses, not circles.
• Kepler's third law (orbit time proportional to distance raised to a power) was derived via regression on only six data points (planets), a method he treated tentatively due to the small sample size, unlike his first two laws.
• Johannes Bode later attempted a similar regression on planetary distances to predict a missing planet, which successfully predicted Uranus and Ceres but failed with Neptune, illustrating the risk of statistical flukes in low-data regimes.
• Terence Tao frames Kepler's career as a "high-temperature LLM" scenario: a system generating random hypotheses (Platonic solids, musical harmonics, geometric ratios) against a verified, high-quality data bank until a true empirical regularity is found.

Shift in scientific paradigms and the bottleneck of verification

• The classical scientific method (hypothesis first, then data collection) is being inverted in modern science toward "big data" approaches where massive datasets are analyzed first to induce patterns and laws.
• AI has driven the cost of idea generation to near zero, analogous to the internet's impact on communication, shifting the scientific bottleneck from hypothesis generation to the verification, evaluation, and sorting of ideas.
• Current peer-review and publication systems are overwhelmed by AI-generated submissions, necessitating new scalable structures to distinguish high-signal progress from "AI slop" or dead ends.
• Future scientific evaluation may require assessing the "unifying potential" of ideas (like the concept of the "bit" or the "transformer" architecture) rather than just immediate correctness, as true progress often takes decades to be recognized.
• Scientific progress is historically non-linear and context-dependent; for instance, Copernicus's heliocentric model was initially less accurate than Ptolemy's geocentric model but was valued for conceptual simplicity and the deletion of erroneous assumptions (Aristotelian physics).

AI performance in mathematics and the "breadth vs. depth" distinction

• AI systems have solved approximately 50 of the 1,100 Erdős problems, a pace that slowed significantly after the "low-hanging fruit" of easily solvable problems was exhausted.
• Current AI excels at breadth (testing thousands of standard techniques or solving problems with no prior literature) but struggles with depth (human-level intuition for identifying partial progress, creating new intermediate concepts, or navigating complex, multi-step proofs).
• The success rate of AI on individual math problems is estimated at only 1–2%, but this is amplified by the ability to run massive parallel trials, a capability humans lack.
• Future math may rely on a hybrid model where AI handles broad exploration and data synthesis, while human experts focus on deep, difficult problems and the development of new conceptual frameworks.
• Terence Tao predicts that within a decade, AI will handle most routine mathematical tasks (similar to how computers replaced log-table calculators), allowing mathematicians to shift focus to higher-level theory and novel problem classes.

Challenges in formalization and the nature of mathematical understanding

• A major concern is the potential for AI to generate "gobble-de-gook" proofs (like the brute-force four-color theorem proof) that are correct but lack conceptual insight or new mathematical understanding.
• Tao distinguishes between "artificial cleverness" (brute-force trial and error) and "artificial intelligence" (adaptive, cumulative building of partial understanding through interaction, which current models lack).
• There is a proposed need for a "semi-formal language" for mathematical strategies and conjectures, moving beyond the strict axiomatic formalism of Lean to capture the heuristic, probabilistic, and narrative aspects of how mathematicians assess plausibility.
• Formal proofs in systems like Lean facilitate "ablation" studies, allowing researchers to strip away boilerplate steps to identify the core, innovative lemmas within a proof.

The role of serendipity and education in the AI era

• Highly optimized digital workflows (search engines, scheduled meetings) may inadvertently reduce serendipitous discovery, such as stumbling upon relevant articles while physically browsing a library or encountering unexpected collaborators in casual settings.
• Tao advises aspiring mathematicians to embrace an adaptable mindset, as traditional educational paths and problem sets may become obsolete; AI lowers the barrier to entry, allowing high school students to contribute to frontier research.
• Learning new fields remains a "hedgehog" (depth) and "fox" (breadth) trade-off, where Tao describes his own process as an "obsessive completionist" who collaborates with experts and documents learnings to prevent knowledge decay.
• While AI accelerates discovery, Tao warns that the "test of time" remains the ultimate validator for truly groundbreaking ideas, as initial consensus can be wrong and paradigm shifts often look worse than existing, albeit incorrect, theories before they succeed.