Adam Kucharski

But what happened was some mathematicians came along and showed that when you have things that can be infinitely small,

that intuition didn't necessarily hold in the same way.

They came up with these examples that broke a lot of these theorems.

A lot of the establishment at the time called these things monsters.

They called them these aberrations against common sense and this idea that if Newton had known about them, he never would have done all of his discovery because they're just nuisances and we just need to get rid of them.

There's this real tension at the core of mathematics in the late 1800s where

Some people just wanted to disregard this and say, look, it works for most of the time.

That's kind of good enough.

And then others really weren't happy with this quite vague logic.

They wanted to put it on a much sturdier ground.

And what was remarkable, actually, is if you trace this then into the 20th century, a lot of these monsters and these, particularly in some cases, functions which...

you know, could almost kind of move constantly, this kind of constant motion, rather than our intuitive concept of movement as something that's smooth.

You know, if you drop an apple, it kind of accelerates a very smooth rate, would become foundational in our understanding of things like probability, Einstein's work on atomic theory.

A lot of these concepts where geometry breaks down would be really important in relativity.

So actually,

These things that we thought were monsters actually were all around us all the time and science couldn't advance without them.

So I think it's just this remarkable example of this tension within a field that's supposedly concrete and the things that were going to be shunned actually turned out to be quite important.

science was the thing that got us where we are today.

You know, the reason that so much normality could resume and so much risk was reduced was development of vaccines and the understanding of treatments and the understanding of variants as they came to the next characteristic.

So it was kind of this amazing opportunity to see this happen faster than it ever happened in history.