[VladVladikoff]

A lot of this math is beyond my comprehension, but it often seems to talk of proofs of theorems. What I want to know is if we continue on this accelerated AI mathematics trajectory, will we eventually be discovering new forms of math that will in turn have some applications down the line in engineering or biomedicine etc? I guess what I’m asking is are we on the cusp of a huge breakthrough for humanity, or largely just proving what was already known?

[fatcatsbestcats]

It’s possible. Compressed sensing is one example of what I suppose you could call a new form of math with applications in biomedicine. It can be used to significantly shorten the time required to obtain a MRI scan, which can improve the patient experience and enable more patients to access MRIs.

https://en.wikipedia.org/wiki/Compressed_sensing

[koolba]

> will we eventually be discovering new forms of math that will in turn have some applications down the line in engineering or biomedicine etc?

If we do it probably won’t be for a long while. We’re barely using math from a couple hundred years ago for most applied usage.

[hgoel]

Engineering and biomedicine, probably in the long term (if at all). But accelerated development of new mathematical methods has a possibility of proving to be relevant for fundamental physics research.

Occasionally large improvements in our models of the universe have been associated with the development of mathematical tools that allow those models to be expressed and/or tested.

[gabriel666smith]

You can personally work out how apply this one in engineering today!

If you have a spare hour or two, I'd encourage you to have a go at learning (however you learn best - I like just asking smarter people or robots stupid questions) what the maths means and why it's important.

And then once you feel like you have a vague grip on the principles, think about a problem in a domain you know a lot about. Try to see if the maths - and how it's changed our perception - could be used as a tool to solve that problem, or if the solution is analogous to a solution you could try in your own domain of expertise.

LLMs are good at speeding up, I think, the journey an idea has to take between "theoretical academic stuff for academics" and "a usable idea for regular people", because they increasingly allow you to ask an infinite number of stupid questions and give you (hopefully) reasonably good responses.

I've had loads of fun doing this today - specifically seeing if the idea this counter (from what I understand: a many-to-one conversion that kind of does and kind of does not preserve meaning) can tell me anything about the relationship between language and meaning.

I'm sure everything I've done today while mucking around has been the equivalent of a monkey with a typewriter (and Codex), but I think the huge breakthrough(s) you ask whether we're on the cusp of are relatively dependent on how many monkeys are throwing typewriters at problems they know a little bit about, after learning a bit about new ideas like this one. Historically, that's a really good way for broad cultural innovation to happen - distributed information applied across multiple domains by experts in them.

[inigyou]

Most of maths is remarkably abstract and impractical, but sometimes real-world scenarios turn out to be related to some obscure branch of math. Internet security is based on elliptic curves in finite fields, and why would you ever study that if it wasn't powering internet security? Well some people did study it before, for no good reason, and that's how we knew about it.