Euclid Quotes

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.

Euclid for children is barbarous.

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.

I have given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid; and I find myself much the happier.

Euclid ‘s manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

We think of Euclid as of fine ice; we admire Newton as we admire the peak of Teneriffe. Even the intensest labors, the most remote triumphs of the abstract intellect, seem to carry us into a region different from our own-to be in a terra incognita of pure reasoning, to cast a chill on human glory.

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

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.

Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.
Having himself spent a lifetime unsuccessfully trying to prove Euclid’s postulate that parallel lines do not meet, Farkas discouraged his son JГЎnos from any further attempt.

Euclid Alone Has Looked on Beauty Bare.

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.

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.

I was interviewed on the Israeli radio for five minutes and I said that more than 2000 years ago, Euclid proved that there are infinitely many primes.В  Immediately the host interrupted me and asked, ‘Are there still infinitely many primes?’