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.
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Fermat'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.
A 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.
Misunderstanding 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…
When 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…
Misleading 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.