Count Socrates and Isaac Newton, among the great thinkers who had doubts about new ideas and new technologies,

Socrates thought writing would sap our mental abilities to remember and think and reason.

And Newton, he thought that algebra was too abstract

and didn't have the same intuitive power that geometry did.

But ideas in mathematics have evolved,

like calculators came along, made it easy to do arithmetic,

computers made certain kinds of problems almost trivial to solve.

Math seems to be, at another inflection point, just as impactful as when writing upended the Socratic approach.

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

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

In this episode, we're going to explore the landscape of modern mathematics

to attempt to get a handle on how AI and other technologies,

which are already being used in writing proofs and solving problems,

stands to change research mathematics as we know it.

We recently explored this idea as part of our special issue, science, promise, and peril in

the age of AI. One of the stories in it was written by our math editor, Jordana Sapelowitz, and she joins us today

to talk about her piece that tackles how mathematicians are seeing this coming shift

and what it means for the grand project of math in the coming decades.

Jordana, welcome.

Thanks for having me.

We like to, before we jump into these conversations, get a sense of where we're going.

So what's the big idea that we're exploring here?

...