Aesthetics, Intuition/Insight and the feelings associated with mathematics

Abstract

In this chapter, I explore the role the mathematicians perceived for aesthetics in their coming to know but also look more closely at intuition (which some mathematicians preferred to call insight) and the connections the mathematicians made between intuition and aesthetics, intuition and beauty are related. The mathematicians discussed aesthetics and intuition/insight in terms that were emotive, full of expressed feelings. Both appeared to contribute, sometimes severally, sometimes together, to the ways in which the mathematicians came to know. Their role is, therefore, very interesting, spanning and linking the domains of feeling and knowing. Unlike most of the mathematicians, including the one whose quote opens this chapter, the aesthetic described by the next participant lies not in the product, that is the proof, but in the chosen strategy to reach that end:

How you choose to make the decisions about the route you are going to follow constitutes the aesthetics of mathematics. I make these decisions by guessing — that is the intuition part — it feels good.

I am not talking about the fact that the diagrams looked pretty on the board. I am talking about the sort of excitement that you might get from looking at something structurally beautiful such as a beautiful picture or hearing a particular piece of music that was rendered particularly beautifully by a certain artist. It is the chain of logic, the structure connecting the beginning to the end, the completeness, the structure of the proof appealed to me aesthetically. When I chose a branch of mathematics it had to appeal to me in that particular kind of way.

A first version of part of this chapter originally appeared as the article Why is Intuition so Important to Mathematicians but Missing from Mathematics Education? in For the Learning of Mathematics, 19(3) November 1999, 27–32.