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A formidable book of mathematical stories.
What was the fatal instant in which men discovered that there are magnitudes like the diagonal and the side of a square, and that these are not commensurable with each other? From zero to irrational numbers, from alephs to Cantor's transfinite numbers, from infinitesimal numbers to surreal numbers. A great mathematician identifies the fatal moments that have marked the affirmation of mathematical numbers and concepts, providing us with the key to deciphering the world and revealing its mysteries. The fatal instant is the instant in which a long chain of causes and effects precipitates and overturns the course of things. As Stefan Zweig wrote: "It is necessary for people to generate millions of humans so that a genius can be born, and millions of amorphous hours must always flow before a truly historic hour appears, a stellar hour for humanity".
This book is a story of a multiplication of "instants", each of which is the outcome of stories that intertwine and separate to then find each other and define fundamental elements of our culture. What was the fatal instant in which men discovered that there are magnitudes like the diagonal and the side of a square, and that these are not commensurable with each other? Was it when the Babylonian scribes engraved the figure on a tablet 1750 years BC? Or when Hippasus of Metaponto revealed the secret of the Pythagoreans? Or when a brahmin entrusted the approximation of that inexpressible relationship for the first time to a sulvasutra to be able to build the altars of Agni, the god of fire? And what is the instant in which we discovered that the ratio between a circumference and its diameter is also an irrational number? Was it in the Babylonian tablets or in the Egyptian papyrus of two thousand years before Christ? Or was it in the approximations of Archimedes' pi or those of the moderns who struggle to always find new decimal digits?