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

Kepler's Discovery of Planetary Motion00:00

Terence Tao retells the story of Kepler discovering the laws of planetary motion. Kepler built on Copernicus, who proposed the heliocentric model with the Sun at the center and planets orbiting in perfect circles. This fit observations from Greeks, Arabs, and Indians. Kepler noted ratios of Copernicus's predicted orbit sizes had geometric meaning, proposing enclosing Earth's orbit in a cube where the outer sphere matched Mars's orbit, and so forth. With six known planets and five gaps, matching five Platonic solids: cube, tetrahedron, icosahedron, octahedron, dodecahedron. Kepler theorized inscribing these solids between planetary spheres, seeing it as God's mathematical design.

He needed data from Tycho Brahe, a wealthy eccentric Danish astronomer who funded an observatory on an entire island. Brahe took decades of naked-eye observations of planets like Mars and Jupiter on clear nights, the last naked-eye astronomer. Kepler worked with Tycho, who jealously gave data in bits. Kepler stole/copied it, fighting Brahe's descendants to use it. His Platonic solid theory failed, off by 10%. After years of fudges, he analyzed data to find actual orbits were ellipses, not circles—shocking. He derived two laws: orbits are ellipses; equal areas sweep equal times. Ten years later, with more data (Saturn and Jupiter hardest), third law: orbital period proportional to some power of Sun distance. No explanation; all empirical. Newton explained all three a century later.