Fertile errors
Mathematics is the discipline where errors are most feared and stigmatized. And yet, Fermat was able to make a mistake in a division and deduce a false theorem! Euler, with somewhat shaky reasoning, opened the way to a revolution in arithmetic. Legendre believed he had proved Euclid's fifth postulate by using circular reasoning. These errors, and some others that you will discover, nevertheless had a very positive impact on the history of mathematics: they were the driving force behind many works whose developments continue to fuel scientific thought.
All articles in this folder
PodcastFermat's false theorem
Fermat formulated many theorems, but one of them proved false: he conjectured that all "Fermat numbers" were prime, an error exposed by Euler. This notably illustrates how induction can lead us astray.
PodcastA shaky proof revolutionizes arithmetic
Euler rescued from oblivion Fermat's proposition that it is impossible for the sum of two cubes to be a cube. Though the explanation he provided for it was shaky, it opened up a new framework for arithmetic.
PodcastMisunderstanding Indian numerals | Tangente
Indian numerals passed through Islamic lands as early as the eighth century (see Tangente special issue 93), then naturally made their way to Spain. There was just one problem: in the medieval West, zero was systematically left out! This failure to grasp the decimal positional system would cause a delay of a good century and a half…
PodcastWhen Legendre believes he has proved the fifth postulate
For two millennia, mathematicians sought to prove Euclid's fifth postulate. Adrien-Marie Legendre believed he had found a proof, before realizing that his proof implicitly assumed the truth of that same postulate. A circular argument…
PodcastMisleading graphical proofs: the missing square paradox and more
Discover how seemingly rigorous diagrams can fool us: the missing square paradox, the astonishing proof that every triangle is equilateral, and more.