Different Problems, Common Threads - Computing the Difficulty of Mathematical Problems

Explore the intricacies of mathematical problem-solving and computational complexity in this 56-minute AMS-MAA Invited Address delivered by Karen Lange from Wellesley College at the Joint Mathematics Meetings 2020 in Denver, CO. Delve into the fascinating world of "Different Problems, Common Threads" as Lange examines the difficulty of computing mathematical problems. Journey through key concepts such as mathematical theorems, computability, the Halting Problem, and the Tree Theorem. Investigate the Prime Ideal Theorem and its algorithmic handling, and gain insights into the foundational crisis of mathematics and reverse mathematics. Conclude with a thought-provoking exploration of "The Big Five" and engage in a stimulating Q&A session.

Introduction
Mathematical Theorems
Theorems vs Problems
Shorthand
Oracle Approach
Computability
The Halting Problem
The Tree Theorem
Whats a Tree
Is it computable
Building the tree
Using the halting problem
Prime Ideal Theorem
Algorithmic Handing
Oracle Example
The foundational crisis of mathematics
What is reverse mathematics
The Big Five
Proof
Conclusion
Questions