Mathematics (like programming) is often called an art form. This makes
mathematics the art of *argument* in the sense that the beauty of a proof lies
in its method. An aesthetic proof is an elegant, inspired, concise, and
beautiful expression. Here I present a collection of aesthetic proofs I’ve come
across over the years.

## No Background Needed

- Area of a triangle within a rectangle Number of games in a tournament
- Computing percentages easier
- The party problem
- Tiling chessboards with dominoes
- A rook game
- The handshake lemma (with double counting)

## Number Theory & Combinatorics

- Sums of k powers
- Sum of the first n numbers, sum of the first n squares
- An arithmetic expression for $\binom{n}{2}$
- There are infinitely many primes (a lower bound on $\pi(n)$)
- Ramsey number lower bound $R(m, m)$
- Learning a single variable polynomial
- A parlor trick for SET

## Linear Algebra

## Geometry

- Double Angle Trigonometric Formulas
- Geometric series with geometric proofs
- Three circles and collinear centers of dilation
- Mobius transformations are isometries of a sphere
- The square root of two is irrational (geometric proof)

## Logic

## Analysis

## Abstract Algebra

## Complexity Theory

## Topology

## The Fundamental Theorem of Algebra

- With Liouville’s Theorem (complex analysis)
- With fundamental groups (algebraic topology)
- With Galois theory (group theory & field theory)
- With Picard’s Little Theorem (complex analysis)