Mathematics

Euclid

Greek geometer · ~300 BC, Alexandria

The axiomatic method - building all of geometry from a handful of self-evident truths.

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Lessons

The Elements and the Axiomatic Method

Euclid’s Elements - how a handful of definitions, postulates, and common notions become the foundation from which the whole of geometry is logically deduced, the model of rigorous reasoning for two thousand years.

The Pythagorean Theorem

Euclid’s proof of the most famous theorem in mathematics - that the square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides - and how he proves it by pure geometry, without meas…

The Fifth Postulate and the Shape of Space

Euclid’s troublesome fifth postulate about parallel lines - why mathematicians tried for two thousand years to prove it, and how their failure led to the discovery of non-Euclidean geometries and a revolution in our und…

The Infinitude of the Primes

Euclid’s proof that there are infinitely many prime numbers (Book IX, Proposition 20) - one of the most beautiful and durable arguments ever devised, and a window into the number theory hidden inside the Elements .

Proof, Rigour, and the Geometric Spirit

The deepest legacy of Euclid - not any single theorem but the idea of proof itself, the ‘geometric method’ that became the model of rigorous reasoning across mathematics, science, and philosophy for two thou…

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