• 1: The Irrationality of the Square Root of 2
• 2: Fundamental Theorem of Algebra
• 3: The Denumerability of the Rational Numbers
• 4: Pythagorean Theorem
• 5: Gödel's Incompleteness Theorem
• 11: The Infinitude of Primes
• 13: Polyhedron Formula
• 15: Fundamental Theorem of Integral Calculus
• 17: De Moivre's Theorem
• 18: Liouville's Theorem and the Construction of Transcendental Numbers
• 20: All Primes Equal the Sum of Two Squares
• 23: Formula for Pythagorean Triples
• 25: Schroeder-Bernstein Theorem
• 26: Leibnitz's Series for Pi
• 27: Sum of the Angles of a Triangle
• 29: Feuerbach's Theorem
• 32: The Four Color Problem
• 35: Taylor's Theorem
• 44: Binomial Theorem
• 49: Cayley-Hamilton Theorem
• 51: Wilson's Theorem
• 52: The Number of Subsets of a Set
• 55: Product of Segments of Chords
• 60: Bezout's Theorem
• 57: Heron formula
• 61: Theorem of Ceva
• 65: Isosceles Triangle Theorem
• 66: Sum of a Geometric Series
• 69: Greatest Common Divisor Algorithm
• 71: Order of a Subgroup
• 72: Sylow Theorem
• 74: The Principle of Mathematical Induction
• 75: The Mean Value Theorem
• 79: The Intermediate Value Theorem
• 80: The Fundamental Theorem of Arithmetic
• 87: Desargues's Theorem
• 89: The Factor and Remainder Theorems
• 94: The Law of Cosines
• 95: Ptolemy's theorem
• 97: Cramer's rule
• 98: Bertrand’s Postulate
• Notes