The Story of Mathematical Proof - From Ancient Greece to Modern Logic

John Stillwell traces the history of mathematical proof and its changing role across mathematics. The talk connects Greek geometry, algebra, calculus, logic, set theory, and computation, including Cantor’s diagonal argument.

Syllabus

Intro
My Favourite Proof
My Favourite Response to a Proof
Why Did the Greeks Insist on Proof?
What About Algebra?
Geometric Algebra
Algebra Becomes Efficient
Algebra and Geometry Switch Places
Calculus
Infinitesimals
The Story So Far
The Nature of Logic: Propositions
The Nature of Logic: Predicates
Set Theory- the Theory of Infinity
Uncountability
Cantor's Diagonal Argument
Logic and Computation
Conclusions