ABSTRACT
The idea of proof dates back to the ancient Greeks, and has kept mathematics rigorous and reliable for 2500 years. When a chemist asserts that a substance that is subjected to heat will tend to expand, he/she verifies the assertion through experiment. It is a consequence of the definition of heat that heat will excite the atomic particles in the substance; it is plausible that this in turn will necessitate expansion of the substance. Mathematics is a less ambitious subject. In particular, it is closed. It does not reach outside itself for verification of its assertions. This chapter considers the notion of mathematical proof and concentrates on the three principal types of proof: direct proof, proof by contradiction, and proof by induction. It will make one conversant with the most basic methods of proof. But he or she should understand that there are literally hundreds of proof techniques. A professional mathematician spends his/her life learning new proof techniques.
