umutisik

Customers / users are the judge.

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.

The number of resume submissions from here is not a lot. It's not at all like on LinkedIn.

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.

You still need the other 80% of the folks to get the remaining 20% of the work done :)

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.

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).

https://www.incept.ai/careers

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).

https://www.incept.ai/careers

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.

Tablets and phones could be calm tech too if they adjusted their brightness and white-point correctly based on ambient lighting.

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.)

Real life use cases for theorem proving I am aware of: - Formal verification of implementations for applications that require extreme security and reliability. (banking, aerospace, ...) - Automated theorem proving would increase the pace of theoretical work. In some cases, that helps guide useful work. There are better examples, but a simple one: nobody is looking for faster (worst-case) sorting algorithms because there is a proven theoretical limit. Don't believe in theory, but don't be without theory! It definitely won't hurt if theory-building is cheaper and faster.

Also, it's the most complicated pure reasoning task you can build. So working on theorem-proving AI may help in reasoning and reliability.

It's called Acoustic Echo Cancellation. An implementation is included in WebRTC included in Chrome. A FIR filter (1D convolution) is applied to what the browser knows is coming out of the speakers; and this filter is continually optimized to to cancel out as much as possible of what's coming into the microphone (this is a first approximation, the actual algorithm is more involved).

Can the right LED panels make up for the lack of daylight in the interior areas?

I agree that it's hard to imagine an alternate history when things happened through a mixture of pure and application-motivated work. In each example, I can see how people arrive at these notions through an application-driven mind-set (transformation groups, GCD through simplifying fractions during calculations, solving polynomial equations that come up in physics calculations). Computability and complexity, in the flavor of Turing's and subsequent work, I already see as application-driven work, as they were building computing machines at the time and wanted to understand what the machines could do.

Related to this topic. I highly recommend this speech / article by Von Neumann: https://www.zhangzk.net/docs/quotation/TheMathematician.pdf

What specific, useful things in cryptography would never have happened if we had not been studying number theory for thousands of years? Even if there are some examples, would we be significantly behind in useful capability if we didn't have those specific results?

It's more efficient to work backwards from the problems you have and build out the math. That's what they did with a lot of linear algebra and functional analysis when quantum mechanics came about. I am not saying discovery-based exploration would never work; I am saying it's inefficient if the goal is technological progress.

This assumes that the parts of number theory that ended up being useful could not have been developed after people realized you could do public key cryptography with primes.

If the work is undertaken for its own sake, there should not be a need to argue about how it will be useful in the future.

As a former mathematician, I completely agree. Academic math is good stuff but you end up making too many assumptions that end up being hard to reconcile with a working system.

Personally, I stopped caring much about beauty because doing work guided by some beauty heuristics didn't make me happy. Doing work that is useful to many people does make me happy; and there ends up being beauty in it somehow.

Not my experience at Amazon. If an employee is performing but not growing, then their manager has some explaining to do as it is usually the case that the employee wants to grow but manager is not developing them the way they should be. I have seen plenty of cases where an employee just does not want to get promoted, the manager explains, and it’s fine.

+1 on Asianometry. It's more in depth than Chip War; in a much shorter amount of time.

This agrees with my experience when I was a young mathematician looking for math that is useful.