Math Colloquium: Reasoning with irrationality: factorization with 19^(1/5)
Wednesday, November 9, 2022
3:00 PM-4:00 PM
Abstract:
The ancient Greek philosopher Hippasus is often
credited with discovering irrational numbers.
These numbers that cannot be expressed as a ratio of whole numbers have
fascinated and troubled mathematicians for centuries. In the 19th century, amidst great
consternation about the foundations of mathematics, people started to work with
certain irrational numbers as if they were integers. This led to number systems with strange
properties including failure of unique factorization — a key property used to
prove that the square root of 2 is irrational.
We will introduce some of these number systems and the fundamental open
questions that surround them to this day.
Finally, we will end with a sample of the limited progress modern number
theorists have made on these questions
Contact Information
Darij Grinberg
dg899@drexel.edu