Main post link -> The Discovery of Irrational Numbers: Death at Sea?

The discovery that not all numbers are rational was devastating to the ancients.

The first man to recognize the existence of irrational numbers might have died for his discovery. Hippassus of Metapontum was an Ancient Greek philosopher of the Pythagorean school of thought. Supposedly, he tried to use his teacher’s most famous theorem \(a^{2}+b^{2}=c^{2}\) to find the length of the diagonal of a unit square. This revealed that a square’s sides are incommensurable with its diagonal, and that this length cannot be expressed as the ratio of two integers. The other Pythagoreans believed dogmatically, that only positive rational numbers could exist. They were so horrified by the idea of incommensurability, that they threw Hippassus overboard on a sea voyage, and vowed to keep the existence of irrational numbers an official secret of their sect....

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