This is a random selection of mathematical facts, ideas or related observations. They have nothing in common except that they all appeal to me. The occasional bit may be original. If you spot any errors please do let me know.

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- What is the probability that a random walk returns to the origin? And how does this vary with the spatial dimension? Polya's Theorem.
- The Great Triangle Theorems: Part 1
- The Last Great Triangle Theorem: Morley's Theorem
- A Quaternion Cauchy's Theorem
- How to derive the Solution to the Cubic Equation via a non-existent number system
- The Amazing Matijasevic Polynomial which generates All The Prime Numbers
- Less Room in N-Dimensions? Volume of a Sphere in N Dimensions
- Euler's method for Summing the Reciprocal Squares
- Tarski-Banach :the Mathematical Reason Why Matter is Atomic
- Chaitin's Number: It's not as uncomputable as you thought
- Monstrous Moonshine and the Entropy of a Minimal Black Hole
- Mathematical Ways to Catch a Lion
- Mathematical One-Liners (almost)
- Never mix Intuition and Probability: Monty Hall and that guy with the two kids
- Analysis of the AV Voting System and various related rigorous voting theorems

All the roots of all polynomials of degree less than or equal to 5 with integer coefficients ranging from -4 to 4 (Dan Christensen, 2006)