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.

**Famous unsolved problems in mathematics**

Part 6: The Goldbach conjecture.

Part 7: The twin prime conjecture.

Part 8: The Collatz conjecture.

Part 9: The Riemann hypothesis.

**Theorems in secondary mathematics that can be proven using special cases**

Part 10: The sum of the angles in a convex polygon with sides is degrees.

Part 11: The Law of Cosines.

Part 12: Trig identities for and .

Part 13: Uniqueness of logarithms.

Part 14: The Power Law for derivatives, or .

Part 15: The Mean Value Theorem.

Part 16: An old calculus problem of mine.

Part 17: Ending thoughts.

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