Views of Euclid

We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable—I refer to Euclid’s geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements. If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.

Albert Einstein

He was (vide his life) 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentlemans library in …, Euclid’s Elements lay open, and ‘twas the 47 El. libri I. He read the proposition. ‘By G–,’ (he would now and then sweare an emphaticall Oath by way of emphasis) sayd he, ‘this is impossible!’ So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps that at last he was demonstratively convinced of that trueth. This made him in love with geometry.

John Aubrey, life of Thomas Hobbes, ca. 1690.

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.

Walter Bagehot, Estimates of Some Englishmen and Scotchmen, 1856.

If you have ever studied geometry, you remember that by a course of reasoning, Euclid proves that all the angles in a triangle are equal to two right angles. Euclid has shown you how to work it out. Now, if you undertake to disprove that proposition, and to show that it is erroneous, would you prove it to be false by calling Euclid a liar?

Abraham Lincoln, in the fourth Lincoln-Douglas debate at Charleston, 1858.