ESP Biography

In this class, we will begin with the rigorous foundations of modern mathematics. What are "axioms"? What does it mean to "prove" something formally? Ultimately, we will be answering a question that plagued mathematicians of the early 20th century -- is every problem solvable? The answer, by Godel's Incompleteness Theorem, is no. There are certain statements which can be neither proven nor disproven, regardless of what axioms you start with. This incompleteness theorem is actually intricately connected to another foundational result in theoretical Computer Science -- the halting problem. We will explore the deep connection between the logical underpinnings of mathematics and, what at first glance, seems to be an unrelated problem in another field.