Descartes on the Lost Simplicity of Mathematics

Exploration
Published

August 15, 2025

René Descartes, while reading the mathematical works of his time, found himself disappointed. The methods were overly complex, and the problems addressed seemed trivial or irrelevant. He knew that in Ancient Greece, mathematics was held in high regard—so much so that, according to legend, the entrance to Plato’s Academy bore the inscription: “Let no one ignorant of geometry enter”. Reflecting on this, Descartes wrote:

“I have come to think that these writers themselves, with a kind of pernicious cunning, later suppressed this mathematics as, notoriously, many inventors are known to have done where their own discoveries were concerned. They may have feared that their method, just because it was so easy and simple, would be depreciated if it were divulged; so to gain our admiration, they may have shown us, as the fruits of their method, some barren truths proved by clever arguments, instead of teaching us the method itself, which might have dispelled our admiration.”

I came across this story in Mathematica: A Secret World of Intuition and Curiosity.