Perhaps he and other true geniuses can understand things transcendently. Not so for me. My thoughts are serialized and obviously countable.
And in any case: any kind of theorem or idea communicated to another mathematician needs to be serialized into language which would make it computable. So I’m not convinced I could be convinced without a computable proof.
And finally just like computable numbers are dense in the reals, maybe computable thoughts are dense in transcendence.
You needn't be a genius. Go on a few vipassana meditation retreats and your perception of all this may shift a bit.
> any kind of theorem or idea communicated to another mathematician needs to be serialized into language which would make it computable
Hence the suggestion by all mystical traditions that truth can only be experienced, not explained.
It may be possible for an AI to have access to the same experiences of consciousness that humans have (around thought, that make human expressions of thought what they are) - but we will first need to understand the parts of the mind / body that facilitate this and replicate them (or a sufficient subset of them) such that AI can use them as part of its computational substrate.
Typing isn't the fun part of it for me. It's a necessary evil to realize a solution.
The fun part of being an engineer for me is figuring out how it all should work and fit together. Once that's done - I already basically have all of the code for the solution in my head - I've just got to get it out through my fingers and slog through all the little ways it isn't quite right, doesn't satisfy x or y best practice, needs to be reshaped to accommodate some legacy thing it has to integrate that is utterly uninteresting to me, etc.
In the old model, I'd enjoy the first few hours or days of working on something as I was designing it in my mind, figuring out how it was all going to work. Then would come the boring part. Toiling for days or weeks to actually get all the code just so and closing that long-tail gap from 90% done (and all interesting problems solved) to 100% done (and all frustrating minutia resolved).
AI has dramatically reduced the amount of time the unsatisfying latter part of a given effort lasts for me. As someone with high-functioning ADD, I'm able to stay in the "stimulation zone" of _thinking_ about the hard / enjoyable part of the problem and let AI do (50-70%, depending on domain / accuracy) of the "typing toil".
Really good prompts that specify _exactly_ what I want (in technical terms) are important and I still have to re-shape, clean up, correct things - but it's vastly different than it was before AI.
I'm seeing on the horizon an ability to materialize solutions as quickly as I can think / articulate - and that to me is very exciting.
I will say that I am ruthlessly pragmatic in my approach to development, focusing on the most direct solution to meet the need. For those that obsesses over beautiful, elegant code - personalizing their work as a reflection of their soul / identity or whatever, I can see how AI would suck all the joy from the process. Engineering vs. art, basically. AI art sucks and I expect that's as true for code as it is for anything else.