Yes, it's why I love math. You can't buy fluency.

There are subtleties to mathematics that aren't easy to understand from the written page alone. It's why it's a living medium.

For example, as we're talking about LLMs... why not, there are ways to reason about vector spaces that weren't intuitive for me to understand. It's something that required talking things out with a friend who is a practising mathematician (albeit in training).

I am not smart enough to reconstruct all of mathematics on my own from scratches on paper alone. That back and forth is necessary. And it's something that you couldn't have "bought" for cutting edge math at any price a few months before this point in time. Because it exists in the minds of people and it needs lots of back and forths with those people.

It's why LLM proofs can be slop on paper. A proof that no one can check or understand is not but scratches on paper. BUT LLMs are also the solution to the problem they create. The machines that can generate proofs are also machines that can help us understand them.

The living medium can now be represented and scaled inside of a machine. I can now sit down at an airport and have that discussion. I think that's transformative for our species.