If you have read Cixin Liu’s The Three Body Problem, the name Henri Poincaré might ring a bell. Poincaré was an early twentieth century mathematical master. One of his feats was an analysis of how three masses in mutual orbit behave. This analysis provides the foundation for chaos theory. In Liu’s science fiction book, the main character becomes obsessed with an online game that hinges on a world orbiting three suns — a cosmic version of Poincaré’s problem.

Poincaré is also the central figure in modern topology. He made an educated guess — a conjecture — that any 3 dimensional manifold ( I promise that you’ll get the feels for what a manifold is if you follow the link) that is finite in size and without boundary can be described by a 3 dimensional sphere. Basically if you have a shape that has no holes and can be fit into a box, then you can mush the shape into a sphere. Ok, just watch this video or try these games.

It took about a hundred years to prove Poincaré’s guess — Grigori Perelman did so in 2002 and was awarded (but refused) a Fields Medal and won (but refused) the $1 million Millenium Challenge. Poincaré accomplished intellectual gold in his short lifetime, giving us the formalization for gravitational waves and chaos theory among many other thins. He championed human rights and the Poincaré Institut actively continues his work.

On a whim I visited Montparnasse Cemetery where he rests with other family. The groundskeeper was so excited to point me to the location. I took some photos during a brief lull in the rain as the day’s national strike unfolded.

Robbert Dijkgraaf gives a great and concise discussion of what makes a good mathematical conjecture in this post https://www.quantamagazine.org/the-subtle-art-of-the-mathematical-conjecture-20190507/