A Concise History of Mathematics; Pages 151-200

Summary: This section on the book is still on 19th century mathematics. It mentions a few great minds which contributed to the study of mathematics, such as: Riemann, Weirstrass, Cantor, Steiner, Cayley, Lobscevkii, Sylvester, and Hamilton. It was because of these men that democratic ideas invaded academic life. With it, criticism rose against antiquated forms of thinking. Then, schools and universities had to be reformed and rejuvenated.

Quotation: "The mathematicians of the nineteenth century were no longer at royal courts or in the salons of the aristocracy" (Struik 165).

Reaction: The chief occupation of the mathematicians no longer consisted in membership in learned academy; they were usually employed by universities or technical schools and were teachers as well as investigators. This is important because now the mathematicians will not only know how to compute complex things, but they will have the chance to teach others what they have learned at the universities.