In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the door of his academy, mathematics has been the standard of exact truth against which other philosophical discourse is measured. Descartes’ Discourse on Method grew out of his Geometry. Spinoza wrote his Ethics in the style of Euclid’s Elements. And Leibniz dreamed of a Characteristica Universalis by means of which ‘we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis’.
Mathematics is not only supremely logical, it is also astonishingly powerful. Here is how it struck Thomas Hobbes, according to Aubrey’s Brief Lives:
He was 40 yeares old before he looked on Geometry; which happened accidentally. Being in a Gentleman’s Library, Euclid’s Elements lay open, and ‘twas the 47 El. libri I. He read the Proposition. By G——, sayd he (he would now and then sweare an emphaticall Oath by way of emphasis) 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…that at last he was demonstratively convinced of that trueth. This made him in love with Geometry.