> understands it thoroughly, and uses it to develop interesting further questions or directions

He phrases it like these criteria are requirements, but they really aren't for every problem. They make sense for those theoretical problems whose solutions' main values lie in their understandability and further development, but not every problem is like that. Some problems' solutions are just revolutionary on their own even if you contribute or understand absolutely nothing else. AI technology itself is an example of this!

To give a trivial hypothetical counterexample: if you came up with a solution for the traveling salesman problem that is both empirically sufficiently faster than the state of the art, that is an immense contribution and you absolutely deserve the credit for it regardless of whether you or anyone else understands how/why it works. It could literally even produce wrong results 50% of the time and still revolutionize humanity if it's efficient enough when it's correct. Denying them credit because they didn't understand the algorithm would be ludicrous - the results stand & speak for themselves.

Statisticians, traditional-AI researchers, etc. had to learn this the hard way when (basically black-box) neural nets became so good that their otherwise-elegant & explainable classical algorithms just stopped being able to compete in more and more applications, and got left behind. Are mathematicians looking to repeat that history?

This echoes SICP's admonition that "Programs must be written for people to read, and only incidentally for machines to execute."

Which is absurd on it's face for most day to day programmers, but a critical distinction for theoretical computer scientists.

The fact that this wouldn't have been considered a contribution before, or that this is a novel idea, suggests that there was something wrong with mathematics culture all along. I'm glad they're figuring it out now, but it seems "too little too late" after decades of devaluing all expository and exploratory work other than writing difficult proofs.

Understanding is what takes the time. Understanding what someone else wrote is harder than understanding something you wrote.

The time saved using AI comes from reducing understanding.

I feel like the hyper-competitiveness of academia generally is the elephant in the room.

The disaster for a problem-solution-oriented mathematician isn't that once problem-solution is easy they'll just switch to theory-explanation and machinery-building. It is that they will have to compete (and won't be able to compete) with students and post-docs who've been doing theory-explanation and machinery-building for their entire career - and there are lots of these 'cause academic pipeline produces more people who can fill a job than jobs in every imaginable category and subcategory.

One of the best comments I read this month and in October

> Mathematics has become a field where results themselves matter less

Results are the only things that truly matter. Everything else is a position advocating for someone’s quality of life.

> writing code can sometimes be delegated to AI, and is arguably less important than understanding what the customer really wants from this software.

It’s still early days and the LLM can already ask the customer what they want directly.

> Mathematics has become a field where results themselves matter less

"Results" in mathematics has always been the proof. (Preferably a beautiful and succinct one.)

Math is supposed to expose the workings of the epistemological foundations of the universe. The result itself (number or formula or whatever) is absolutely irrelevant to math.

(It may be important to physics, chemistry or engineering, but it isn't to math.)

fewer mathematicians means fewer problems to solve. All problems have human origin, right? Can AI create a problem on its own and what would be the point? Closer to can god create a stone he can't lift.

The quote reads to me like “as long as you can analyze the solution after the machine solves it and make it suggest new ideas based on that, you’re almost the same as a discoverer yourself.” I’m deliberately avoiding “mathematician” here because I think Tao probably didn’t intend to take it that far. But, for many people that difference will be indistinguishable, especially because there will very likely be “math bros” just like “ai bros” and “crypto bros” before them who want to pretend they’re mathematicians just as we see people pretending to be engineers and financial experts based on how fast they got on the hype train.

I’m no mathematician, though I do have an undergrad degree in math, and unless I had a graduate degree or made substantial contributions at that level, I would never consider myself anything but a “student of mathematics,” and that too not just because I have a degree in the subject, but because I still have a great interest in certain branches of math and I keep learning in my spare time from books or from adjacent applied fields I continue to formally study. As a kid, I grew up hating math but I became interested in it later in life because of coding, computer science and formal logic, pushing myself a lot through my college years to get some foundational understanding of the subject at a deeper level than the general population, just to get my foot in the door, so to speak.

Even if I’m an outsider from the circle of mathematicians, this whole AI takeover of mathematics leaves such a bad taste in my mouth because I’ve long felt that math was one of those things that everyone could agree is a useful and beneficial thing for humanity in general, and it was one of the least divisive fields, where people from different parts of world, from different stations in life could participate, and very few points, especially today, caused any controversy (unlike just about every other subject). It feels like a great loss for humanity to lose a brunt of our engagement with it to the machines, like a whole wing of a gigantic library starting to be closed off from us indefinitely because some people decided that we don’t _need_ to access it anymore, except on an even grander scale possibly than my imaginary library metaphor.

Sure, but given the approximate tens of millions of dollars in API costs of solving these major math problems currently, we will also have to acknowledge that getting credit for major mathematical contributions is likely now to be far less about meritocracy and far more about access to capital to kickstart the original proof.

Less capable (but good enough) mathematicians with more capital will have a huge advantage over great mathematicians who are broke.

I'm not a mathematician, but that situation rubs everyone (except those with the most capital) the wrong way.

It's still confusing to call that a "change". Apart from the way the media covers the topic, I've never known mathematics to be about proofs.

[dead]

I'm so glad that sanity ulitmately won in his mind.

>> where writing code can sometimes be delegated to AI, and is arguably less important than understanding what the customer really wants from this software.

This statement is a monstrosity, and the reason why real software engineers know vibe coding will fail. It is fundamental misunderstanding of thinking that that the intellectual work consists of knowing what you want, and coding is merely the mechanical labor of making it happen.

The coding is the intellectual work!

Its where the actual problems are discovered, where the difficult decisions are made, where vague ideas become precise, and where solutions are invented. There is not such thing as a fully formed solution waiting to be translated into code. :-)

Again just the modern variation of the idea guy who goes around saying I have a genius idea for a new startup...I just need some Developers to implement it ....