Euler, Godel, Cantor and Gauss: The Cool Math You Never Learned in School
Many of the greatest results in mathematics are easy to explain and the theorems they are based on are easy to prove. Unfortunately, most high school and college math courses do not teach them. In this seminar, you will learn about some of the greatest of these ideas and results, from Cantor’s calculus of infinities to Euler’s proof that there are only five perfect solids to Godel’s incompleteness theorem. The topics will introduce ideas from diverse areas of mathematics and the way they can be applied to solve problems of practical importance, such as how properties of prime numbers are used in encryption, the connection between graph theory and the four color problem, the theory of games and the emergence of cooperation, etc. Topics will be chosen from Topology, Logic, Number Theory, Game Theory and Analysis. Each lecture will be self-contained and accessible to anyone who can add, subtract, divide and multiply.