How to pronounce “number theory” in English

All of number theory could be done that way.

So something like number theory-- every day, when we conduct a transaction using HTTPS, uses number theory in the most essential way.

So what is number theory?

The big change in number theory in the last 40 years or so is that suddenly you got these applications, right?

They show up in number theory all the time.

There was a book on number theory, elementary number theory, "The Book of Squares" about Pythagorean triples.

And the Pythagoreans especially were interested in number theory from that point of view.

Another interesting thing about the history of number theory is that it went to sleep after Diophantus pretty much.

Hardy was famous for saying that number theory had no applications at all.

I'm working on this number theory.

There is a lot of number theory involved in the right ways to compute pi.

where he spent the next 10 years working on problems in number theory, including Goldbach's conjecture.

Lehmer had used the machine for some interesting number theory stuff and had really taken a lot of advantage of its parallelism.

One of the nice things about working in number theory is you feel you're connected to a long intellectual history going back to at least the ancient Greeks and probably

A kind of very pure vision of what number theory was.

It was just the most amazing thing that has happened in number theory.

And this is an example of a statement in number theory.

That's really important if you want to go further in number theory.

My major was number theory.

Do any of you know like cake-cutting problems and number theory?

We'll be speaking about "Summing It Up From 1 plus 1 To Modern Number Theory."

I'm going to speak for about 10 minutes and try to explain what is number theory.

And finally, the security that protects your data online is based on number theory, which for a long time was truly considered the most pure

He was working on a new way to attack one of the hardest unsolved problems in number theory, the twin prime conjecture.

To do it, they started with one of the crowning achievements of number theory, the prime number theorem, which tells you that the odds

- The two quickly became friends, bonding over a shared obsession with number theory.

To do it, they relied on one of the most important results from number theory, the prime number theorem.

And then, Rob is going to give a worked out example of number theory.

Well, that was the history of number theory.

And I'm going to give you the example of Fermat's Last Theorem of something in number theory.

So I was going to ask you, how far back were you interested in math and number theory?

The concept of calculating things using Boolean number theory existed before, but around 1937,

And that's all of analysis, in general analytic number theory in particular is the fight between the main term that you think is the truth, if it actually is the truth,

Yet, while doing all of that in his spare time, he would drive down to the local library to read books and journals on number theory.

- Meanwhile, there's a young postdoc named James Maynard, who just got his PhD at Oxford with Roger Heath-Brown and other one of these analytic number theory world experts.

Around 1917, they invented what's known as the circle method, and used it to tackle different problems in number theory.

So it turns out to be surprisingly connected to a lot of problems in partial differential equations, in number theory, in geometry, combinatorics.

And he hoped that all of mathematics-- well, certainly, it was beginning with number theory.

And now, because of coding, actually, number theory's at the very center of cyber security, et cetera.

In Plato's dialogues, there are a lot of-- very simple number theory is often used as an example of something

So anyway, I think I'll let Rob discuss now just one topic, so you can see in great detail what a typical number theory

And closest in spirit to what we would call number theory today.

Now Ambrose realizes that as computing gravitates toward the center of our universe and cryptography spreads, the whole Pythagorean idea of prowess in number theory, of secrecy and so forth,