Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Mathematical Gems

This page contains a number of mathematical problems, concepts, and arguments that I find intriguing. A number of them roused or reinforced my interest in mathematics when I was a high school student.
  1. Why is the square root of 2 irrational?
  2. How do we know that there are infinitely many prime numbers?
  3. The Four Color Map Problem
  4. Fermat's Last Theorem
  5. Transfinite Numbers, Set Theory.
  6. The Mandelbrot Set, and some modifications.
  7. The Platonic Solids.

Fine print, your comments, more links, Peter Alfeld, PA1UM