Every time you enter a password or.

Buy something online or send any kind of encrypted WhatsApp message, you're betting your security on a pattern in prime numbers. A pattern no mathematician on earth has.

Ever been able to prove.

There are the atoms of multiplication. They're supposed to be random, unpredictable, and our entire digital security infrastructure assumes that they are. But here's the thing, we don't actually know that. We've tested it with supercomputers on trillions of cases. But mathematical proof, it's still elusive. Today, the man sitting across from me has solved more legendary math problems than almost any human alive. Terence Tao won the Fields Medal, that Nobel Prize of math, and he's tackled questions that have stumped the greatest minds for centuries. And he just told me there could be an undiscovered pattern hiding in prime numbers.

A pattern that, if it exists, could break the encryption protecting every financial transaction you'll ever do.

We're going to talk about the beauty of numbers, why AI keeps getting the math wrong, what it was like to.

Meet the legendary Paul erdos as a 10 year old, and whether or not mathematics is invented or discovered. Let's go deep into the impossible with the Mozart of math.

First question I always ask a mathematician is, how do you like your coffee?

I actually don't drink coffee much, except on social occasions. Actually black, no sugar. Okay.

So the reason I asked that maybe you'll recognize as Erdos, I believe said. What did he say about mathematicians in coffee?

He said that mathematicians are a means for turning coffee into theorems. There's a very nerdy follow up joke to that, which is that a co mathematician is a way of turning co theorems into feet.

Into feet.

Yeah, it's a very inside joke.

That's right, that's a dad joke. Plus a mathematician joke that's really, really bad but really good at the same time. Well, the reason I bring up Erdos, of course, you actually met him when you were a kid, didn't you?

Yes, I think I was 10 at the time. So he had a collaborator in Adelaide, which is the city where I grew up, George Zegeres. So he would visit every now and then at the time. I think one of the math professors at the local university introduced me to him and Erdos was always very good at, he was known for meeting bright young kids and so we had a nice conversation. I wish I'd remembered more of it actually. I was too young at the time to realize just sort of how much of an honor it was really the one Thing I remember was that he really treated me like an equal, like he didn't condescend as a kid. And he later sent me a postcard that it just said, thank you for your nice hospitality. Here's a math problem which I didn't solve actually, but it did get soul plated by someone else.

Oh, that's amazing. Yeah. He was one of the most prolific mathematicians in at least modern history, maybe in all time history. And famously there's a relationship between the number of authors you have to go through before you're related to him. Right. What is your Erds number?

Yeah, so there's this concept called the Erds number. So Erds worked a lot in graph theory, and so this concept is inspired by graph theory. So Erds himself has an erds number of 0. If you've written a paper with Erds, you get an erdish number of 1. If you've written a paper of someone who's written a paper with Erds, you have an Erds number two. So I have an Erdish number two, for instance. And I think nowadays people, it's common to have Erdish numbers of four or five. People have made similar numbers in other fields.

There's a Bacon number. So if you've starred in a film with Kevin Bacon, you have a Kevin Bacon number of one and so forth. And then there's something called the Erds Bacon number, which is the sum of your Erds number and Bacon number, which is usually infinite because you either don't have a chain of papers going to Erds or you don't have a chain of movies going to Bacon. But there are a half dozen people who have like the combinable, like seven or eight.

Yes, yes, I've heard of random things like that, but yeah, he was known in many ways. I remember hearing from Jim Simons, who is my late great mentor, and obviously you knew him well, that he had. He was incredibly productive, but part of his productivity relied on the use of amphetamines. He used to take some. Is that true?

That's what I've heard. Apparently one of his friends convinced him to give up amphetamines for a month for a bet or something. And Erdos grudgingly did it. And then at the end he just went back and just said, you just set mathematics back by one month. So he was, I guess, hardcore. You don't see that so often nowadays. I think back then maybe there was less of a stress on work, life balance than you are today now.

You had work related to ERDs, right, the ERDs discrepancy theorem or something.

Yeah.

What is that? Can you explain that for my audience?