AI Is Producing Beautiful New Math—and We Can't Keep Up

There is a failure to understand that the process is the result. You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind. The output of an LLM is useless without a human mind to comprehend it. We can have Super Intelligence, but if humans are incapable of comprehending it, it is just another useless dead artifact. Practice, applied over a lifetime, is what creates the capability for comprehension. Asking an LLM to give you an answer creates an artifact. Humans being humans, most of their requests boil down to "make me rich without having to work for it," so the request itself is paradoxical and impossible to satisfy. Philosophers have only been saying this for all of human history, so don't hold your breath for any breakthroughs.

I know many programmers for whom "developing domain understanding" is an abstract concept (if indeed, it is a concept for them at all). But in the age of big AI, I see more need for this, not less.

At least this is my observation: when my colleagues have been wholesale chucking stuff over to Claude, they've then been confronted with classic XY-Problem shit, poor user experiences, and over-complex solutions (which will mount future problems regardless of whether a person or an agent iterates on that code). Much of this can be solved by actually sitting down and thinking about it, and I mean at a code design level, not just a speccing level.

Many people don't realize that there are more useful outputs to solving a problem than just a mere solution. Obviously if one has a contractor mindset (you don't care about the after effects of a system) then this is of no relevance to you. Some companies promote that mindset, certainly ones that have no broader aspirations then getting acquired soon. That's fine - but many companies actually are about sustainability, and understanding in these places is paramount.

I feel like “giving up understanding” is inevitable.

There’s some hubris in thinking we can understand everything. For truly difficult problems, it’s entirely possible that humans are simply incapable of comprehending why a solution is true. But ultimately the practical value of applying that solution to the real world is going to eclipse our need to understand it.

Math is just the beginning. I see it happening in other fields too, like physics and biology. Many of us software devs have already given up on understanding parts of our own systems for the exact same reason.

Seems like a losing battle.

Like most of us I go back and forth between sheer optimism and fear for the future that AI may usher in. Recently I started vibe coding a fun video game with my ten year old. The experience is different than my work because it’s been such a joy to basically have a personal genie in a bottle help me make some personal art with a loved one regardless of either of our skill sets. The concept the author of this post is arguing now resonates with me more than it would have a few weeks ago. The sheer surface area that AI can create in our intellectual life is limitless and needs humans to explore. There can never be enough of us in that sense. Whether it’s as validators or creators.

"We’re gonna need a lot more mathematicians."

What the article really says is that we're going to need much smarter mathematicians.

That is not possible for puny meat-brain humans. Humans are close to their ceiling. AIs are just getting started.

In practice, we're probably going to hit that limit first in IC design. I once went to a talk by the Intel engineering manager who headed the Pentium Pro effort. That was the first superscalar x86 CPU, and it took about 5,000 engineers at peak to design it.

Getting that many people coordinated on one thing was a real achievement.

Then Intel stayed with minor tweaks on that design for years.

We're soon going to be seeing designs of even greater complexity cranked out by AIs. No human will understand them at the gate level. Reading AI-written programming language code is bad enough. Reading AI-written Verilog may be beyond human comprehension, except in small sections.

A lot of the conversations around AI in the past years have been “we will delegate almost all work to AI, but the most decisions will be left to humans.”

I’m fairly confident that the opposite will be true. The most important decisions will be made by AI, and humans will only be left to guide decisions as a matter of taste. AI has the ability to be impartial, and immutable. You can endlessly probe and reason its decisions.

This isn’t true of our current human decisions. Where we see red tape, bureaucracy, rent seeking, status quo. AI will see through these human constructs.

I do like the idea that we will need more mathematicians, physicists, and scientists to understand the discoveries of AI. That might be the best possible outcome of AI, but I fear the opposite and we are painting ourselves into a corner of which we no longer have the knowledge to sustain ourselves and society itself collapses.

> To take on this responsibility, we may need to broaden our view of what a mathematician can contribute. I have in mind something like a “deployable intellectual reserve”: communities of mathematically sophisticated people that humanity can call upon to help understand consequential AI-enabled breakthroughs.

> Our ability to understand difficult and unfamiliar ideas may become one of the most important contributions we can offer to society. We should be willing to bring that skill to problems far beyond our usual research interests. [3] Doing so asks us to expand our sense of our vocation.

Am I reading this wrong, or is he talking about what (mathematitian) Data Scientists have been doing for years? So he is basically saying that former Data Scientist that have turned into prompt/software engineers should go back to being data scientists.

In any case, people should stop trying to fit AI in the previous status quo. What we need is curious people, that is what we have always needed.

A few centuries ago there were no "mathematitians", there were mathematitians/philosophers/artists/physicists all in one person. So its not like "mathematitias" is something that has existed for millenia.

We need curious and ethical people.

Maybe AI brings back the age of a well rounded scientist/philosopher. I know this sounds counter intuitive because the article is saying that we cannot keep up with the AI.

The main reason to learn something is actually being able to communicate in the language of that subject. There are complex ideas in math that cannot be easily captured by the language of other fields. Pepole who don't study math cannot even understand what a worthwhile goal in math even is or how it could be useful to other fields.

You can't simply prompt a model to be "better" when "better" isnt even properly defined

> This is a guest post by Amit Sahai

Not Terrence Tao post. Beware.