How to be a Mathematician

**N:**
What's the daily life like for a mathematician?

**C:**
What's the daily life like for a mathematician!
Oh my God, I don't know how to answer that one!
Well, it's marvelous when one has a good idea.
Because then you can throw your whole personality
at it.---And I can just speak personally.---I can
throw my whole personality at it, and then I'm
completely wrapped up in it, and since I live alone,
that means that I can just exist just for the idea, until I develop it.
And when I'm in this state, I feel I see things
much more clearly, I'm much more alive.
I feel sort of like one feels when one hikes up a mountain.
You know, you don't have a clear view---maybe you're going through cloud
layers---and then you get to the top, and there you are
with a marvelous view, maybe you've gone above the clouds,
there's bright sunshine, and it's a wonderful experience!
Then of course it's a bit of a let-down when you come out of that!
So the problem is the holes, when you don't have an idea
that you can run with.

**N:** And this interest in Gödel's incompleteness theorem came at what age?

**C:** Well, I don't know, 11, 12, 13, 14, ...

**N:** Alan Turing, the English mathematician?

**N:** And what happened to you when you were starting to understand it?

**N:** And you did certainly discover something very, very significant, but you were...

And so, I guess that my friend Walter Meyerstein...

**N:** ...the Spanish philosopher...

There's also a remark, by the way, of Gödel's which I think also goes in the same direction that I'm talking about. Now Gödel has a completely different view than Einstein. Einstein is an empiricist, he's a scientist, he believes in the physical world, right, that mathematics is all invented. Gödel believes that mathematics exists, that mathematical reality is just as real as physical reality. And he believes we observe, we discover mathematical truths, we don't invent them. We don't invent mathematics, we just discover it, we just observe it. And that's a very different philosophical position from Einstein. But the funny thing is that it leads Gödel to the same conclusion, to the same point that Einstein said. Because if mathematical reality is just as real, it's different, but it's just as real as physical reality, if 1, 2, 3, 4, 5, ... are just as real as an electron or an electromagnetic wave, then why can't we sort of use the scientific method, and if we find a new mathematical principle that helps us to organize our mathematical experience, maybe we should just add it to mathematics as a new axiom, the same way that physicists would!

Here's an interesting fact. I've gotten old enough that I'm not even sure that I believe in mathematics at all any more! I mean, not just because, you know, maybe I prefer to have a family and a more normal life. But also because I don't really believe in real numbers anymore and I don't even think I believe in positive integers anymore.

**N:**
So there is no, sort of,
full and perfect theory?