A couple of weeks ago, John Armstrong posted an interesting story about Abraham Lincoln. Lincoln carried three books with him when he traveled: the Bible, the works of Shakespeare, and Euclid’s Elements. For Lincoln, the Elements represented proof beyond the possibility of doubt.
The Elements once loomed large in the imagination a way no mathematical work does today. The influence can be seen from Newton’s Principia to Spinoza’s Ethics. The popular experience of mathematics and the experience of the practitioners of pure mathematics have diverged since Lincoln’s day. The difference between the Elements and a modern monograph is only one of style and sophistication (and accessibility). Pure mathematicians follow the same axiomatic method as Euclid. But the modern high school and early college curriculum concentrates on subjects useful in the sciences, which are mostly computational rather than deductive. (I had plane geometry in high school, but it was an elective.) It’s an interesting development.