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 ask questions like

- Why is 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 logical ground?

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