The Abstract Mathematical Universe

About the lecture

In this mini-lecture, we explore the motivations behind studying the abstract nature of mathematics. In particular, we consider: (i) what ‘2 + 2 = 4’ really means by looking at adding together familiar objects such as pens and elephants; (ii) the abstract noun ‘four’ and how mathematicians seek to explain the abstract nature of something being ‘four’; (iii) how adding one to four, and so on, produces an infinite collection of numbers; (iv) the Universe, which physicists can show to be finite, and how this is different from the abstract ‘Mathematical Universe’; (v) the number line, which is infinite and lives in the abstract Mathematical Universe of pure mathematics; and (vi) how working in the abstract Mathematical Universe can be used to model the real Universe, for example, in the work done by applied mathematicians studying sound waves, statisticians modelling viruses, and computer scientists creating unbreakable codes.

About the lecturer

Kevin Buzzard is a Professor of Pure Mathematics at Imperial College London, where he specialises in algebraic number theory. Recently, he has become interested in formal proof verification, specifically through the aid of computers. He is helping to build a database of modern mathematical theorems and definitions, and is passionate about teaching undergraduates how to use this software. In 2002, Professor Buzzard was awarded the Whitehead Prize by the London Mathematical Society for his working in number theory. In 2008, he was awarded the Senior Berwick Prize, which recognises outstanding mathematical research.