A Union in Service of Truth

Paris had worn him down. Weeks of proofs that refused to budge, nights of ink-stained failure. So Henri Poincaré did the only sensible thing a desperate mathematician can do. He stopped thinking about the problem.

He boarded a bus in Coutances. Coins clinked, boots shuffled, morning light spilled across the aisle. As the horses started forward, something in him slipped the leash. The insight arrived whole. Fuchsian groups. The structure he’d been groping for stood suddenly before him. Intact, inevitable. He didn’t have a notebook. And he didn’t need one. By the time he stepped off the bus, he knew.

Later, walking by the sea, another flash linked curved geometry to number theory. Back in his study, logic did its work. Line after line, the proofs held. The invention had come first; the demonstration followed.