Terence Tao
π€ SpeakerAppearances Over Time
Podcast Appearances
Those are so far out of reach.
You think so?
Yeah.
There's no even viable strategy.
Like even if I,
activate all the cheats that I know of in this problem.
There's just still no way to get me to be.
I think it needs a breakthrough in another area of mathematics to happen first, and for someone to recognize that it would be a useful thing to transport into this problem.
So the natural numbers have two basic operations attached to them, addition and multiplication.
So if you want to generate the natural numbers, you can do one of two things.
You can just start with one and add one to itself over and over again.
And that generates you the natural numbers.
So additively, they're very easy to generate.
One, two, three, four, five.
Or you can take the prime number, if you want to generate multiplicatively, you can take all the prime numbers, two, three, five, seven, and multiply them all together.
And together, that gives you all the natural numbers, except maybe for one.
So there are these two separate ways of thinking about the natural numbers from an additive point of view and a multiplicative point of view.
And separately, they're not so bad.
So any question about the natural numbers that only involves addition is relatively easy to solve.
And any question that only involves multiplication is relatively easy to solve.