Pizza Seminar Topic ideas:
Neat topics:
Fun detours in mathematics.
Hyperreal/surreal numbers, nonstandard analysis
Banach-Tarski paradox (or the lack thereof in dimension 2)
Connections between conservation laws and symmetry (Noether's Theorem)
Improbability of Gravitational Collision
Sphere eversion ("Smale's paradox")
Non-transitive dice (Sicherman dice)
Hadwiger-Nelson problem
Cayley-Dickson construction & algebraic properties
Ways to calculate π
Hardy-Ramanujan asymptotic for the partition numbers
Benford's Law
Black-Scholes Formula
Voting theory (e.g. Arrow's impossibility theorem)
Uses of guess-and-check in mathematics
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
Spectral 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:
