I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on attempting to prove theorems by looking at special cases.

Famous propositions that are true for the first few cases (or many cases) before failing.

Part 1: The proposition “Is always a prime number?” is true for the first 40 cases but fails with .

Part 2: The Polya conjecture is true for over 900 million cases before failing.

Part 3: A conjecture about the distribution of prime numbers is true for the first cases before failing.

Mathematical induction

Part 4: Pedagogical thoughts on mathematical induction.

Part 5: More pedagogical thoughts on mathematical induction.

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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