I had the idea to do something funny with integrals when I remembered that a lot of people are terrified of integrals. On page 1 of his 1910 classic Calculus Made Easy, Silvanus P. Thompson called the integral a “preliminary terror” that “chokes off most high school students from even attempting to learn how to calculate.”

I must admit that when you first see the integral it is intimidating. But it is also a little exhilarating. You start thinking that maybe you can do more than long division, that it’s perhaps time to skip tenth grade and apply to NASA. The integral is an operation like addition or subtraction or square rooting. In fact it is actually addition — just a more sophisticated version of it.

Given its reputation — and the fact that there is a huge chunk of the world that has no idea what it is — I thought it was time to make the integral the star of a ridiculous prompt.

“Integral” means “the whole.” So the integral of a thing is the whole thing. One way to use the integral is to find the area between curves.

But why would we do anything like this.

A (Possible) Fields Medalist

For context, in case nobody follows me on Instagram, I have been wanting a Fields Medalist to have a chat with a regular person that hates math and knows nothing about it. A Fields Medalist I have in mind is Cédric Villani. I will shamelessly say that the main reason for this is that I’ve read his book and it contains lots of integrals. Cédric Villani also loves spiders, and wears a spider brooch, but he gets asked about spiders relentlessly. How many times does Cédric Villani get asked about cotton candy?

As you can see, Cédric Villani is not afraid of integrals.

My version of integration looks about as sophisticated as his.

Why cotton candy? The integral is intimidating. Cotton candy is pink and light as a feather and reminds us all of theme parks and county fairs. Plus we can do other fun things, like perhaps take the double integral of cotton candy. Or the triple!

I am sure a world-renowned Fields Medalist will be thrilled to discuss this. Though, if we were to get Cédric Villani, should we also examine the integral of crème brûlée?

The integral of cotton candy

Hamilton the Poet

The point