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: