Why Are Proof Complexity Lower Bounds Hard?

Explore the challenges of proving lower bounds in proof complexity through this 23-minute IEEE conference talk by Jan Pich and Rahul Santhanam. Delve into the fundamentals of proof complexity, its applications, and current knowledge about proof compression. Examine hard candidates and conditional results before diving into formalization techniques, including standard and more precise statements. Gain insights into the proofs, perspectives, and barriers in this field. Conclude with thought-provoking questions that highlight the complexities and open problems in proof complexity research.

Introduction
What is Proof Complexity
What is Proof Complexity good for
What is known about Proof Compression
Hard Candidates
Conditional Results
Rootage
Formalization
Standard Formalization
More Precise Statements
Proofs
Perspective
Barriers
Questions