We're gonna need a lot more mathematicians

siavosh

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.

atleastoptimal

It would be nice to have more mathematicians, but we don't need more. Once AI math goes so far beyond human abilities, any human involvement is like an ant trying to understand quantum physics

inopinatus

> Imagine that a future AI system proposes a radically new design for a one terawatt nuclear fusion power plant This is an unfortunate example to choose, being as it is entirely confounded by the canonical illustration of the https://en.wikipedia.org/wiki/Law_of_triviality .

macrolocal

Russell once remarked that all of mathematics would be trivial to a sufficiently intelligent being. It builds conceptual tools for limited minds, that lets them understand far beyond their natural reach. In a world with ASI, having that capacity is vital.

algorithm314

Life is all about tradeoffs. Mathematics have no tradeoffs. We need more engineers.

bluejay2387

"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. " -- I can't be the only one who thought about the scene where the scientists ask Deep Thought the ultimate question...

pyridines

> Before approving construction, I would want communities of humans to understand why the design works and what justifies confidence in its safety. I would hope that we all would. Until very recently, I pored over every single line of code Claude generated with razor sharp scrutiny. I would usually catch issues with every response. I'm catching fewer problems these days. Maybe the model is just getting better, and maybe I'm being less careful while under pressure to ship more and more often. But model capability is obviously growing. Even back in March, you could tell it "give me a function that adds two numbers" and you could be 100% confident that it would write the correct function. There was almost no point in looking at the code. Since then, the complexity floor of problems in the category "this is so simple that the model couldn't possibly get it wrong" is rising, and with it, my cognitive surrender to the model is increasing too. Why check it? It's obviously going to be correct. If AI designs a terawatt fusion plant, then of course we're going to meticulously pore over every detail to ensure safety, reliability, efficiency, whatever. If we find no flaws in the design whatsoever, will we be less careful about the second one? The third one? What about the ten thousandth one? Will "a nuclear fusion plant" become something that models couldn't possibly get wrong? Terence Tao is arguing that the human involvement in research is crucial, but doesn't convincingly justify why, in my opinion. He says that "human agency is a value of fundamental importance" and that we will need to build "thriving human communities that can understand [AI ideas] together" - not for the sake of correctness , which AI may surpass us on, but for, I guess, the possibility of reclaiming human meaning and purpose. I don't disagree with this at all, but it's not an argument, it's a statement of values. Unfortunately, the stark reality is that if AI does surpass humans, it will become the economically dominant strategy to not verify them and not double check them, but to just do whatever they say. This seems like a great way to raise p(doom). But as the models get better and better, and as I'm scrutinizing Claude's output less and less... I just hope that there are more Terence Taos out there than people like me.

imranq

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

cjfd

If we accept that AI is going to do all of these things humans will be superfluous and will just be optimized away. It looks a lot like we see the birth of silicon based life by the efforts of carbon based life. Carbon based life will die and it will not even be because AI decided to kill it, it will be because feeding and watering it was less important than other concerns. Bacteria may continue to exist, though.

metalspot

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.

calf

I think this is the most beautiful letter on the subject I've read all year, it brought a tear to my eye. It's like reading those famous STEM letters/essays from history.

maniksaraf

If we assume that trusting a model to execute an action is an ongoing exercise, since its trustworthiness is often discovered by the user organically as models develop, should trustworthiness be measured at the level of the model, or at the level of the human intent behind triggering it, whether explicitly or implicitly?

Animats

"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.