Infinity

Course Description

The legend has it that around 520 BC, the Greek philosopher Hippasus was drowned at the sea after suggesting that some numbers are irrational. The Greek's rejection of irrational numbers was just part of a general rejection of infinite processes, and the concept of infinity was forced upon them from the physical world. Mathematicians have long followed philosophers in avoiding the concept of infinity, because of its paradoxical nature and the inconsistencies it introduces. It was only until the late 1800s, that the German mathematician Georg Cantor finally created a consistent theory of the actual infinite. Before being largely accepted, Cantor's unorthodox ideas and monumental work were first controversial among mathematicians and philosophers. Cantor's mentor, Leopold Kronecker, claimed: ‘I don't know what predominates in Cantor's theory – philosophy or theology, but I am sure that there is no mathematics there’, whereas David Hilbert, another famous German mathematician, said: ‘No one shall expel us from the paradise which Cantor has created for us.’ In this course, we will explore the evolution of the concept of infinity from ancient civilizations to the modern era, shedding light on its influence on philosophy, art and mathematics. Throughout readings and short videos, paradoxes and rather counterintuitive statements will be discussed, inviting students to rethink infinity in an attempt to tackle the question: (how) does the infinite exist? Prerequisites: Must be at least Sophomore Standing.

Code

CCOL-UH 1108

Credits

4

Subject

Core: Colloquium