By 1876, we had a pretty good idea that matter is made up of chemical elements and that

there's a basic form of those elements that we call atoms. What atoms are, however, wasn't so clear

then. Many scientists at the time still believed in this idea of the ether or some mysterious substance that filled space.

And it was against this backdrop that William Thompson, later known as Lord Kelvin,

came up with what is called the vortex theory of the atom.

In this idea, atoms are made up of vortices like tornadoes, connected at the ends like a smoke ring.

Building on the work of others, Kelvin posited that the atoms of different elements were the result of different kinds of knots in the vortex rings that are spinning in the ether.

It was a popular theory, but not for long, since it wasn't able to explain very much,

but it did inspire another mathematician and physicist, Peter Guthrie Tate, to think about

and classify these imaginary knots.

The result, eventually, was an entire field of math that we now call knot theory.

It's turned out to have wide application across

the sciences, and it's also remained a subject of fascination for mathematicians, because trying

to understand these knots can be just as befuddling as untying a badly tangled shoelace.

Welcome to the Quanta podcast, where we Welcome to the Quantum Podcast, where we explore the frontiers of fundamental science and math.

I'm Samir Patel, editor-in-chief of Quantum Magazine.

Knot theory is one of these areas of math that has a simple, basic element.

You can create any one of these knots with a length

of string and some tape and a ton of patience, but it conceals endless complexity. And that's exactly

the theme of a recent story on Quanta called A Simple Way to Measure Knots has come unraveled. The author

of that piece, frequent quantum contributor

Layla Sloman, is here with us today to talk about knot theory and why just when things

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