Mathematicians are storytellers. Our characters are numbers and geometries. Our narratives are the proofs we create about these characters.
Many people believe that doing maths is a question of documenting all the true statements about numbers and geometry – the irrationality of the square root of two, the formula for the volume of the sphere, a list of the finite simple groups. According to one of my mathematical heroes, Henri Poincaré, doing maths is something very different:
“To create consists precisely in not making useless combinations. Creation is discernment, choice. …The sterile combinations do not even present themselves to the mind of the creator.”
Mathematics, just like literature, is about making choices. What then are the criteria for a piece of mathematics making it into the journals that occupy our mathematical library? Why is Fermat’s Last Theorem regarded as one of the great mathematical opuses of the last century while an equally complicated numerical calculation is regarded as mundane and uninteresting. After all, what is so interesting about knowing that an equation like xn+yn=zn has no whole number solutions when n>2.
What I want to propose is that it is the nature of the proof of this Theorem that elevates this true statement about numbers to the status of something deserving its place in the pantheon of mathematics. And that the quality of a good proof is one that has many things in common with act of great storytelling.