Olivetti Club

Malte HasslerCornell University
Hilbert’s Tenth Problem and unexpected applications of Diophantine equations

Tuesday, October 26, 2021 - 4:35pm
Malott 406

Before the Second International Congress of Mathematicians in 1900, David Hilbert presented 23 problems left to be solved in the upcoming century. The tenth problem asked to devise a process according to which it can be determined whether a Diophantine equation has a solution in the integers. Seventy years later, it was proven that no such general algorithm exists. The reason behind it is that a surprisingly large collection of sets can be expressed as the solution set of a Diophantine equation. For example, there exists a polynomial in 26 variables whose positive values are exactly the prime numbers. In this talk I will go through the proof of H10 and, if time permits, mention some related work of myself. No prior knowledge of logic or number theory is required.