People talk about research mathematics being a science or an art, but it's also a sport. AI will kill the sport aspect of it. The art will survive. The science will thrive.
With sufficient automation, there shouldn't really be a trade-off between rigor and anything else. The goal should be to automate as much as possible so that whatever well-defined useful thing can come out theory can come out faster and more easily. Formal proofs make sense as part of this goal.
This is very impressive. I once built an educational Haskell programming + math. + art web site (mathvas.com). Something like this would have simplified that a lot.
As a former professional mathematician: the benefits mentioned in the article (click-through definitions and statements, analyzing meta trends, version control, ...) do not seem particularly valuable.
The reason to formalize mathematics is to automate mathematical proofs and the production of mathematical theory.
He should add “Economists confidently making wishful-thinking based proclamations without a shred of evidence or even a plausible logical path.“ to the list!
It does make me uneasy that founding companies is becoming another tracked thing that people feel they can apply high-IQ pattern-matching to. Especially when startups are where first-principles thinking is the most valuable.
That being said, I can see this being useful to a lot of kids. Certainly beats going to grad school for someone who wants to start a company. Keep in mind that a 500K SAFE doesn't force a founder to go big or zero-out.
If data did live on a manifold contained, e.g. images in R^{n^2}, then it wouldn't have thickness or branching, which it does. It's an imperfect approximation to help think about it. The use of mathematical language is not the same as an application of mathematics (and the use of the word 'space' there is not about topology).
Data doesn't actually live on a manifold. It's an approximation used for thinking about data. Near total majority, if not 100%, of the useful things done in deep learning have come from not thinking about topology in any way. Deep learning is not applied anything, it's an empirical field advanced mostly by trial and error and, sure, a few intuitions coming from theory (that was not topology).
Make the cost of operating data centers reflect the damage to the environment and see how quickly people optimize. I don’t know how damaging storage is, but that’s the only way to make a difference.
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When considering a candidate on an F-1 + OPT, what should be our expectation of their need for H1B sponsorship?
What are O-1 and National Interest Waiver success rates for recent PhD grads (in computer science)?
If AI can prove major theorems, it will likely by employing similar heuristics as the mathematical community employs when searching for proofs and understanding. Studying AI-generated proofs, with the help of AI to decipher contents will help humans build that 'understanding' if that is desired.
An issue in these discussions is that mathematics is both an art, a sport, and a science. And the development of AI that can build 'useful' libraries of proven theorems means different things for each. The sport of mathematics will be basically over. The art of mathematics will thrive as it becomes easier to explore the mathematical world. For the science of mathematics, it's hard to say, it's been kind of shaky for ~50 years anyway, but it can only help.
Incept AI | Remote (US) | Full-time | Software Engineers and Deep Learning Scientists | https://www.incept.ai
Incept AI is solving the last mile problem in Voice AI. Our team of PhD applied scientists and software engineers builds neural audio processing systems, audio-processing foundation models, and agentic AI workflows that make Voice AI reliable and truly useful in the real world.
Our first application is the lucrative drive-thru and phone automation market for restaurants. We have built the most accurate order-taking restaurant Voice AI assistant in the world, and are working with major restaurant chains to help elevate their customer service while providing major automation-led savings.
We are well-funded are looking to grow our team with Software Engineers (generalists or back-end, previous work experience required) and Applied Scientists (PhD in a technical field like CS, Math, Physics, ... or equivalent deep learning experience required).
What is going to benefit the customers the most? You staying in your specialty where things are already in good shape, or you improving the area where the company has been underperforming? Perhaps, if the latter is better for the customers, you can find the motivation in yourself to seize the opportunity to deliver there.
Great observation. I have observed the same thing in my own life.
The solution: do things that you really believe people need. Then you owe it to them to find out if you actually are “good enough”, and you don’t care what others think because all you care about is whether the people who need it are happy with it.
- If you just run the previous generation of games on the newer graphics, it's only a tiny bit better. But games designed for this generation will have more of a difference. Ultimately, it's all about giving the creators more freedom in making the game. Amazing games have been made with much less capability than today.
- You're going to get another big jump in graphics and immersiveness once the current neural rendering techniques are productionized. (though PS5 Pro probably isn't going to be important for that.)