Henri Poincaré, a French mathematician and philosopher, spent his life trying to untangle some of the most complex problems in mathematics. In the 1880s, he had been struggling to make sense of Fuchsian functions — a problem that eluded every attempt at concentrated thought.

So he set aside his work and joined a geological excursion through the French countryside with the School of Mines. Days of walking, fresh air, and unhurried conversation put his mind at ease. It was then, far from the world of equations and proofs, that he made his breakthrough.

Poincaré later recalled:

“The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus, and at the moment I put my foot on the step, the idea came to me, without anything in my former thoughts paving the way for it, that the transformations I had been studying were identical with those of non-Euclidean geometry. I did not verify the idea; I went on with a conversation already begun, but I felt a perfect certainty. On my return to Caen, I verified the result at my leisure.”