>And now that AI has solved all our problems, we can devote ourselves to more important work: going into quantitative finance, vibecoding sports-betting apps, consuming AI-generated TikTok shorts, and arguing with political bots on Twitter.

Grim but this is exactly where society is heading.

This is so well written, deep, funny, and sad.

> Looking up at the stars in wonderment, or enjoying a complex puzzle game, or being inspired by an encouraging teacher, and dreaming that one day an unfeeling corporate robot[1] will burn a rainforest to compile a list of 700 highly obscure barely-readable facts that might be true that nobody can understand as part of a marketing gimmick to raise hype for an IPO[2].

But if I am going to critique it's main point it would be this part:

> in the pursuit of advancing humanity’s knowledge as quickly as possible, many academics will recoil in anger at the suggestion that it is worth spending any time making results understandable to humans. It is inefficient to explain or check a result when those resources can be spent generating another.

While obviously ridiculous, I think this does not go far enough. The problem isn't that people don't care and resources should not be spent to explain AI results to human minds, the problem is that AI will soon be better at explaining itself than humans. The puzzle then changes from can AI formally verify and explain a proof to: do human minds trust the proof. Do we believe that the proof is correct and not an elaborate AI hallucination using tricks that are beyond our understanding. In order to trust it a formal verification is not enough unless it is human understandable. In fact human understandability is the only thing that matters. That is something that AI can never do on its own.

I think the author is hiding the ball a bit. The problem is that, for a long time, humans have attributed meaning, value, and social status to great cognitive insights. Taking physics as an example, it has almost always been the theorists who develop new ideas, not the experimentalists that test and validate them, who have won praise and acclaim. The name Arthur Eddington doesn’t have the same cachet as that of Albert Einstein. But now that the creation of those insights can be automated, there is a great wrenching as esteem shifts away from the former.

Well, maybe it’s a good thing that we are seeing this shift. Maybe it is good and right that we begin valuing your ability to exist in the real world, rather than play math puzzles on a sheet of paper. Because, while the AI labs are receiving a lot of attention and excitement now, that’s a short run phenomenon. Ultimately, people aren’t impressed for long by a machine doing something novel. Once it’s up and running, it fades into the background just like the combustion engine, or the dishwasher, or electric lighting.

Not a huge fan of the sentiment in this article, and the very cynical way it was communicated, but the references to the library of babel reminded me of this fun site.

https://libraryofbabel.info

The question is the right one. "Why are we even doing all this?"

Why, indeed, is society funding pure mathematics? Many mathematicians are complaining that they do not like AI and their jobs are less fun when AI is involved. But does that matter? Should that matter to the institutions who fund mathematics research?

To me it seems that we fund pure mathematics because we believe that some pure mathematics will end up being useful. Turing was doing "pure mathematics" when he invented the Turing machine, because we didn't have another word for it, yet.

So, which is going to be more useful - the sort of pure mathematics that AI does in 2026, or the sort of pure mathematics that humans do in 2026? That is the debate I would like to see.

I sympathize with some feelings the author is trying to communicate, but the cynical and sarcastic style really detract from the authors points in my view.

Man, mathematicians and scientists are going through it! I think one thing that makes things different for software engineers is there was always a belief that you were building for a specific use. It was rarely just for your own intellectual satisfaction. I think math and some of the sciences will now have to shift given that no one will be impressed by their intellectual achievements any longer.

What I’m most curious about is how this impacts our perception of who/what is smart.

Great satire, it is nice to see people with a human spirit left. The NYT should ask to republish this.

> From what I know about the academic community (mostly from Twitter and LinkedIn, which I assume are representative), there seems to be near-unanimous agreement that the purpose of math and science research is to gather a large quantity of potentially true factoids in a repository that nobody will actually ever read, in a ritual called “advancing humanity’s[3] knowledge”. That these results are well-written, understandable, pleasant to read or look at, or even completely correct is a secondary concern — in fact, in the pursuit of advancing humanity’s knowledge as quickly as possible, many academics will recoil in anger at the suggestion that it is worth spending any time making results understandable to humans.

Am I the only who thinks this is rhetorical? Modern mathematics is so far removed from the base average knowledge (lets just assume high school instead of going to axioms) that the only people who understand most (if not all new) mathematical achievement are the mathematicians themselves, heck not even all mathematicians, it needs to be spread and developed from "hot spots"?

Your math results are not "well-written, understandable, pleasant to read or look at" unless you literally operate with two or three levels within the proof paper compared to the average person who probably starts at an order of magnitude levels higher.

To the average person, asking a mathematician to explain something is the same as asking the AI/LLM. Both are asking an oracle to dumb it down to their level of abstraction.

To the person who are not career mathematicians, both LLMs and mathematicians do the same thing, pump out garbled output that they themselves understand, and to mathematicians, the difference is one probably explains using axioms rather than theorems.

> (that’s philosophy, which I would never be a doctor of)

I'm in the office and was trying to contain my laughter next to my colleagues, but this tipped me over the edge

> No rational person, least of all us masters of rationality in STEM, pursues these for the joy of creation, learning, or beauty

well yeah the purpose of STEM education is to be a factory to produce the correct worker for another factory

I work in construction now. Commercial Millwork/cabinets as a project manager.

It is so much harder and more stressful than my php/jquery mini saas coding days.

Often at work I start thinking "why are we doing all this? Why does anyone want this fancy reception desk?? This desk is not worth the human aggravation that it's causing."

I genuinely start thinking we should go back to concrete eastern European communist type buildings just for the simplicity and efficiency. Why all this fancy stuff that causes every project engineer, superintendent, and subcontractor Engineering department to get grey hair.

But I guess it makes the economy grow. I don't know.

> AI has solved all our problems

What about the Collatz conjecture? AFAIK, it requires some novel approaches to mathematics, which would be a real testament to AI creative skills.

I don't doubt it will be solved some day, but as of now it's too early to say that all our problems are solved.

I don’t accept this framing. If tools allow us to pursue ever more deeply into the mystery of being, and get to both questions and answers we never thought we’d see, that’s a good thing. I think the genuinely curious should have no problem redoubling their “freed up time” into further exploration. The library Borges describes is infinite. I won’t mind getting to read a few books I wouldn’t have otherwise.

We must secure the future of humanity and preserve dignity, freedom, purpose and agency.

This is not a very upbeat post. It does not say much about the AI Library of Babel but I have been wondering about the same thing.

So we have the Fields medal, awarded for making "progress" in math.

Now we are told explaining, understanding things, asking new questions is more important than proving things. So where is the math community medals/awards for this job?

> First, they came for the artists, and I did not speak out, because I was not an artist.

// actually FIRST they came for the programmers. and many of us were ultimately ULTIMATELY pretty tickled to get such a massive productivity boost. this anti-AI sentiment as seen here and in Jon Stewart's rant that all AI is good for is optimizing shopping carts or something... it's so upsetting see good folks buying into this and not realizing how much benefit it will bring. If anything, I've seen how much amazing power it has now given programmers such as myself... I can do what would take me years in an afternoon.

// Btw, can we retire the "first they came for the..." template, it's a little tired.

Such a weird take.

There's a library of babel simulator here: https://libraryofbabel.info/

Just hit "random." It's always gibberish. The odds of getting something that isn't gibberish are astronomically low, like winning the lottery.

The actual library Borges describes has 25^1312000 books, the very vast majority of which are utter nonsense. (As the simulator makes clear.)

Yet with AI, we're getting an abundance of very credible -- and, as Tao himself notes, frequently correct -- mathematical proofs. In these new AI math results, the ratio of signal to noise is high, which makes our current situation the exact opposite of the library, which is pure noise where signal emerges only by random necessity.

    Failure to detect and appreciate irony and metaphor

    Failure to engage with core critique

  > Fortunately, OpenAI has brought us one step closer to realizing Borges’s vision. Rather than generating every possible mathematical paper, they’ve found a way to probabilistically generate things that look correct.

> dreaming that one day an unfeeling corporate robot[1] will burn a rainforest to compile a list of 700 highly obscure barely-readable facts that might be true that nobody can understand as part of a marketing gimmick to raise hype for an IPO

The climate effect argument against AI is so intellectually dishonest. It’s the same as saying that Tao is on the side of stopping the advancement of Cancer research.

I thought the people clowning him were dumb, but the people arguing for either side are really fighting on a mud pit.

> This is a guest post by Rikab Gambhir.

Very much worth nothing for those about to read this! haha I got a couple of paragraphs in and shook my head.

oh stop it

I’m not doing it. Why are you?

>In order to trust it a formal verification is not enough unless it is human understandable.

The whole point of formal verification is to remove the necessity of understanding most of the work. We only need to trust the formalization of the problem statement, the proof verifier, and the formalization of the result. We already have proof verifiers that humans understand to a high level, and the formalizations of the problem statement and the result are much simpler than the full proof.

I'm confident that the Navier-Stokes equations can blow up because I'm confident that Lean works correctly, and I'm confident that the mathematicians verified the problem statement and result correctly. This is despite the actual proof not being human verified yet (as far as I know), and despite the "human-readable" version not actually corresponding to the formal proof. The formal method still worked.

I find it shallow.

Beneath the sarcasm it's making a rather simplistic argument that OpenAI cares little about human understanding of the results or their correctness.

The author appears to argue that this in service of a pointless goal, that no one will even care to read the results, and that all this is taking away from human creativity and removing the fun in scientific discovery.

I don't see a convincing argument here that OpenAI does not in fact aim to further humanity's understanding of mathematics, or that using AI for scientific discovery is comparable to automating away the fun parts of life.

The sarcasm is rhetorically strong, but profound? I don't think so.

There are plenty of things we use and found useful before we understood them. We knew how to make it, how it works was for the most part inconsequential.

I'm all for advancing human understanding, even if it might lag behind machine understanding, but there is a way to have machines prove they understand something we don't: ask them to build something functional that we can't. If your hypothetical future comes to pass, and we ask the machine to build a cancer-curing healing ray, and it works, I'd say that's its own win. Then we can spend however long it takes trying to understand how it works. It's depressing and disempowering in a way, but I think overall I'd be happy with that future.

It may not be the most prescient or innovative sci fi series, but I read The Three Body Problem a few years ago and it's really stuck with me. Specifically the description of how humanity reached an inflection point in math & physics research that almost immediately unlocked novel innovations in applied science ... which then made space exploration & settlement practical. Moreover, that the antagonist society in the series decided their absolute best bet at avoiding complete annihilation was to hamstring humankind's scientific research -- and that's it.

It feels like frontier models are starting to approach an asymptote where what you suggest could become reality, and we'll begin seeing not just AI research but AI-designed & led applications of that research into fundamental parts of our society & culture. For better and for worse.

100% agree. In fact, this issue of verifiability is not at all unique to AI. It was a profound and growing issue before the advent of useful AI. Perhaps the issue was best elucidated by Dr. Anthony Fauci when he suggested that we "Believe the science" as a rational for why people should follow his covid prescriptions. I side with those who feel that Dr Fauci was really just trying to do his best. Regardless, with that statement he cut the foundation out from under the whole scientific project! Science (and math) are not to be believed. They are to be tested!

We have moved quite a long way down the "believe the science" road already, and for good reason. Belief is much (!) faster and cheaper than proof, so those who are fed good science(math) and believe it tend to outcompete people who get stuck trying to prove things all the time.

But fraud is fraud regardless of the platform (meat or silicon) committing it. People who believe in frauds often end up worse off for it, though it hard to know which piece of BS has led you astray or who's to blame for it or how to deal with the fall out.

Obviously, we shouldn't believe AI any more than we believe humans. That said, the world was already suffering greatly under the weight of human generated BS long before useful AI came on the scene. Now that AI has reduced the cost of producing plausible BS by orders of magnitude, we may need some new methods for BS detection.

> the problem is that AI will soon be better at explaining itself than humans

(I assume you mean explain itself to humans here.)

I keep seeing people saying this as fact. It might, but it might not, and there are various reasons one might be skeptical that it will, using current techniques. Not least among these is that explaining something well to a human requires a degree of empathy and sophisticated theory-of-mind that LLMs have not yet exhibited yet*, and that is an area where humans are uniquely advantaged by being humans.

Someone will almost certainly reply by just stating as fact that they will achieve this goal, or pointing out that past predictions that LLMs wouldn't be able to do particular things have failed, and that's all very well. I certainly wouldn't be rash enough to claim it's impossible, but there are still models of all this available that are consistent with all the successes so far but don't predict "LLMs can do anything and will do everything". We'll find out in due course.

(I should clarify that the benchmark here is good human explanations. Of course many humans are capable of producing "explanations" worse than Markov chain text, let alone LLM output.)

* My idle speculation is that a lack of decent theory-of-mind is why LLMs still suck at using the "it's not X it's Y" construct. I doubt they actually use it any more frequently than humans when writing on the same topics, but they use it wrong and it's jarring. This particular rhetorical flourish works when there's some reason to think that X is an idea that might actually be present or forming in the mind of someone reading the passage (or in some other mind that they in turn might be imagining, eg. a fictional character), and that explicitly calling it out and negating it will have a particular dramatic effect. LLMs probably use it with about the expected frequency, but they use it for that reason (frequency) and then come up with something to put in the X and Y slots. The result often jars because the X it uses isn't something pertinent to the reader's thought process and/or the Y isn't a convincing, persuasive or relevant counterpoint to it. I suspect the result is that they stick out and seem more frequent than they are.

> an unfeeling corporate robot[1] will burn a rainforest to compile a list of 700 highly obscure barely-readable facts that might be true that nobody can understand

He'd have more of a point if a huge number of humans weren't occupied doing exactly this, and much worse on top.

Understanding math isn't just about "having a good explanation ready".

People fundamentally misunderstand the nature of mathematics: it's not "flat" like most of common people's daily pursuits. It consists of building upwards, on top of previous concepts.

In other words, AI is like an oracle: it can tell you all kinds of stuff, but since you probably don't understand, you won't act properly.

Your last sentence: "That is something that AI can never do on its own."

Never say never...

Well, we can try tying it to ground truth. AI does the math for magnetic field containment? Test it. AI predicts a particle? Test it. AI says P=NP? Ok, factor this in polynomial time.

And if it fails, and AI goes, "I don't know what happened. I relied on these papers" then I guess one of those must be wrong.

I'm not saying it'd be easy, but I think AI can also find the pieces of the puzzle that broke a pyramid of "discoveries" culminating in a disproval,

And the only other option is to simply never understand as much. AI has the potential to understand things humans cannot. Not necessarily a strict superset.

Humans can deal in 5+-2 things at once. AI doesn't have to, and can cut through leaky abstractions.

If AI says a new invention will do X, and it doesn't, it'll say "you're absolutely right" and try again until it does the thing.

I mean... doomsday scenarios aside.

As a mere software engineer, I found that many human written papers in my field (DSP, ML) aren’t exactly well-written, easily understandable or pleasant to read either, and it’s been the case for at least 15 years. In the past, I would frequently spend an hour or two trying to read a SOTA paper full of convoluted prose and dense pages of equations, only to realise that the algorithm is incredibly simple if visualised properly or even just written down as pseudocode.

Now with LLMs the process is much shorter. They can walk me through the algorithm step by step, translate it to pseudocode, explain equations, and most importantly, I can ask them questions and get clarifications, without worrying about seeming ignorant or exhausting their patience. With a paper, you’re stuck with whatever was written (and often, researchers aren’t good teachers, or intentionally over complicate simple concepts).