Euclid Quotes

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.

The once-surprising existence of non-Euclidean models of Euclid’s first four axioms can be seen as a sort of mathematical joke.

The early study of Euclid made me a hater of geometry.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

The primes are the raw material out of which we have to build arithmetic, and Euclid’s theorem assures us that we have plenty of material for the task.

Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament.

I have in later years taken to Euclid, Whitehead, Bertrand Russell, in an elemental way.

Euclid alone has looked on Beauty bare. Let all who prate of Beauty hold their peace, And lay them prone upon the earth and cease To ponder on themselves, the while they stare At nothing, intricately drawn nowhere.

From Euclid to Newton there were straight lines. The modern age analyzes the wavers.

If Euclid’s point, though incapable of being drawn by any human agency, has an imperishable value, my picture has its own for mankind to live.

The sacred writings excepted, no Greek has been so much read and so variously translated as Euclid.