Pizza Seminar Topic ideas:
Neat topics:
Fun detours in mathematics.
Surreal numbers
Hyperreal numbers
Nonstandard Analysis (infinitesmals, etc.)
Benford's Law
Fuzzy logic
Non-transitive dice (Sicherman dice)
Black-Scholes Formula
Perfect numbers
Hadwiger-Nelson problem
Cellular automata
Sphere eversion ("Smale's paradox")
Cayley-Dickson construction & algebraic properties
Ways to calculate π
Hardy-Ramanujan asymptotic for the partition numbers
Uses of guess-and-check in mathematics
Connections between conservation laws and symmetry (Noether's Theorem)
Classic theorems:
Many old theorems are well-known. For some, offering multiple proofs could be interesting.
Four Squares Theorem
Law of Quadratic Reciprocity (multiple proofs?)
The Infinitude of Primes (multiple proofs)
Fundamental Theorem of Algebra (multiple proofs)
The Number of Platonic Solids - prove in multiple ways - generalize to higher dimension (regular polytopes)
Jordan Curve Theorem
More recent theorems:
Some of these could be quite advanced. You may have to just sketch the proof, while demonstrating some tools used in the proof.
Kepler Conjecture
Prime Number Theorem
Four color theorem
Classification of Finite Simple Groups
Green-Tao Theorem
Poincaré Conjecture
Atiyah-Singer Index Theorem
Fermat's Last Theorem
Borsuk-Ulam theorem
Bertrand's Postulate
Past Pizza Seminar Coordinators:
