Welcome to the Nature of Mathematics. This blog is a set of notes for a First Year Seminar course that I’m teaching at the University of Richmond. This course will be a selective historical view of what is mathematics and what do mathematicians really care about. We will consider questions such as
- Why is the concept of proof so important to mathematics?
- Is mathematics invented or discovered?
- Who has the burden of proof in a mathematical argument, the author or the reader?
- Are some proofs better than others?
- Do computer calculations give satisfying mathematical arguments?
- Does mathematics need to be practical?
- Is mathematics really standing on firm ground?