Stephen Wolfram

And he did.

It took a little while to iterate, but he had a proof.

Unfortunately, the proof is very... It's a lot of micro details.

It's not like you look at it and you say, aha, there's a big new principle.

The big new principle is...

The simplest Turing machine that might have been universal actually is universal, and it's incredibly much simpler than the Turing machines that people already knew were universal before that.

And so that, intuitionally, is important because it says computation universality is closer at hand than you might have thought.

But the actual methods are not, in that particular case, were not terribly illuminated.

It would be nice if the methods would also be elegant.

That's true.

Yeah, no, I mean, I think it's one of these things where, I mean, it's like a lot of we've talked about earlier, kind of, you know, opening up AIs and machine learning and things of what's going on inside.

And is it just step by step?

Or can you sort of see the bigger picture more abstractly?

It's unfortunate.

That's true.

But you know, one of the things is that's another consequence of computational irreducibility.

This fact that there are even quite short

results in mathematics whose proofs are arbitrarily long.

That's a consequence of all this stuff.

And it makes one wonder, you know, how come mathematics is possible at all?