Henri Poincare worked only four hours a day and produced more original mathematics than almost anyone in history. His breakthroughs came not through grinding labor but through sudden flashes of insight — stepping onto a bus, walking along a cliff, lying in bed unable to sleep. He was the last mathematician who could work across every branch of the field, and his discoveries in topology, chaos theory, and relativity anticipated ideas that would take decades to fully develop.

This episode traces Poincare from his childhood in Nancy through the three-body problem that launched chaos theory, the near-miss with special relativity, and the conjecture that took a century to prove.

• Poincare’s famous four-hour workdays and the psychology of mathematical creativity he described
• The three-body problem and the accidental discovery of chaos theory
• How Poincare came within reach of special relativity before Einstein published
• The Poincare Conjecture and the hundred-year quest that ended with Perelman’s reclusive proof