Terence Tao – Kepler, Newton, and the true nature of mathematical discovery

Kepler spent years proposing theories about planetary motion—from Platonic solids nested between planetary orbits to musical harmonies explaining cosmic order. Most were wrong. His famous third law, relating orbital period to distance from the Sun, appeared almost as an aside in a book about astrology and planetary harmonics. Yet this empirical regularity, verified against Tycho Brahe's unprecedented dataset, became the foundation for Newton's inverse-square law of gravity a century later.

The analogy to modern AI is striking. Like a large language model sampling at high temperature, Kepler generated countless hypotheses—some geometrical, some mystical—and tested them against data. Success required two ingredients: a massive, high-quality dataset (Brahe's observations, ten times more precise than any predecessor) and a verification mechanism. The process was inefficient but transformative: one correct empirical pattern, extracted from decades of failed attempts, catalyzed genuine scientific progress.

This raises a provocative question about AI's future role in science. If we can deploy millions of AI systems to hunt for empirical regularities across every domain—each one trying random relationships for the equivalent of twenty subjective years—we might discover thousands of «Kepler's third laws» waiting to be explained. The bottleneck would shift from discovery to interpretation: identifying which patterns matter and constructing the theories that unify them.

Modern society has become remarkably efficient at scheduling and optimization, but Tao warns we may be optimizing ourselves into intellectual stagnation. During COVID-19, academia maintained its meeting schedules through remote work, yet lost the casual hallway conversations and accidental discoveries that emerged from physical proximity. When Tao worked at the library searching for journal articles, he would stumble upon adjacent papers that sparked new ideas—serendipity now eliminated by targeted digital searches.

The danger extends to AI-driven research. While AI can instantly retrieve exactly the paper you need, it cannot replicate the experience of browsing adjacent ideas or encountering unexpected connections. Tao spent a year at the Institute for Advanced Study with no distractions, producing papers efficiently for weeks—then running out of inspiration. «You actually do need a certain level of distraction in your life,» he reflects. «It adds enough randomness and high temperature.»

This tension between efficiency and creativity may be fundamental. If we build AI systems that perfectly optimize research trajectories, eliminating «wasted» time on tangential explorations, we risk losing the accidents that produce revolutionary insights. The question is not just whether AI can replicate human mathematical ability, but whether it can replicate the productive randomness that makes discovery possible.