Great Ideas in Theoretical Computer Science - On Proofs

Explore the foundations of theoretical computer science in this lecture from CMU's "Great Ideas in Theoretical Computer Science" course. Delve into the concept of proofs, tracing their evolution from prehistory to modern computer-assisted and formalized methods. Examine landmark theorems like Banach-Tarski and the Four Color Theorem, and gain insights into the classification of finite simple groups and the Kepler Conjecture. Learn 10 practical tips for constructing proofs, understand common induction mistakes, and consider alternative perspectives on mathematical reasoning. Engage with open notebook mathematics and tackle a challenging problem on proving inequalities using induction.

15-251: Great Theoretical ideas in Computer Science Spring 2016, Lecture 1.5
Proposition
Banach-Tarski Theorem
What is a proof?
Proofs — prehistory
Proofs — 19th century
Principia Mathematica, ca. 1912
Classification of Finite Simple Groups
More anecdotes
Kepler Conjecture
Computer-assisted proof
Computer-formalized proofs
Proof of the Four Color Theorem
10 tips for finding proofs
Open notebook mathematics
Alternate Perspective
Possible complaints/points off from your TA
Some common induction mistakes
Problem: Prove 2n n for all integers n 2 1.