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Im not saying it cant do those things. The mathematical equivalent of that are the hundred proofs that OpenAI dumped. And probably we still have a few decades of AI exploiting low hanging fruit in Maths and Art.

I was refering to going beyond and deciding what to explore. There are infinite paths in mathematics and a lot of ways you can describe and denote a particular theory. And the choice of notation and exposition is an art in some way.

You could probably say that "no, but this is done by minimizing memory usage in human brains so that its understandable by humans, maximizing compressability of previous ideas, and a link with some utility in the real world, etc"

But that just one example of loss function. There are many possible ones.

Do i think that there is a universal loss function that captures it all? Probably yes, in the limit, on the infinite energy regime. Are we in that case in practice? Probably not.

I tend to think that AI will fully replace us the same moment we are able to master prime factorization with our time and energy constraints.

"Choosing which terrain is worth exploring" is more clear if you have an objective function (if you are doing engineering). But mathematics is closer to art in that regard. What is a terrain worth exploring in art?

Because the other option is that AI does what you say. And if you think about it (and you are a mathematitian and not an engineer) it means that AI is able to read our minds and know our desires. And at that point who cares about existence anymore?

You just described why its not trash for a big percentage of people...

I went into the blog, and saw only two entries in 2026. I dont know how to feel.

I dont know if its because the new state of things is that all knowledge is now secret and cant be shared.

Or if its because Opus 5.5 has turned even Karpathy into a product owner/manager so now the only interesting things are products (hackertube in this case).

Either of them makes me sad. Although its probably both.

Wake me up when true science is back.

In any case, im a big fan of Karpathy.

Whatever doesnt count as maths is just not maths. Its just carrying out instructions to get some "gain".

Other people usually care only about "gain", its their only motivation. Non "gain" results are just happy accidents.

And "gain" (once you have your survival covered) is just an invented abstraction with 0 real meaning. But people try to convince themselfs that it has meaning.

This goes back to the classic story for "kids" about the emperor that has no clothes.

I would want to hire a plumber that does both, because his/her solution would be better and higher quality 100% of the times.

The question is if Godel matters in practice, or if its is just a limiting behaviour with infinite resources

This is not at all what mathematitians are saying. They say LLMs obfuscate proofs even more. Saying that mathematitians obscure proofs is nonsense. Maths requieres a big effort from the brain to be deobfuscated as you say, and deobfuscating maths requires understanding, which takes even longer. Thats why textbooks dont exist just after a new proof appears, it takes some time to digest it and identify the key parts.

Maths is a language, and learning a language takes time. Its like if I say that japanese made an effort to obfuscate their language just because i cannot read it or read it as fast as english.

LLMs are autimating some part of maths which is formal manipulation. It happens that computers are much better than humans at formal manipulation. In the same way that computers are much better at mathematical computations. That is the huge change in the field. But any working mathematitian can tell you that formal manipulation is just part of the research job.

The powerfull thing about maths is that formal manipulation has allowed humans to go further "for free": you just need to understand the foundations, and the formal system allows you to compute new results for free without needing to reunderstand them.

I was thinking more about dictatorships that block the entry of outside knowledge into the population for example, because its not useful to their goals (which is a particular shape of what economic value is for them). But you dont have to go that far away, you can just see the difference between democratic cultures that value at different levels those fields. In the end "economic value" is less objective than what it seams.

I dont get this. What is the difference if you replace "AI" by "Tao"? And people still were doing math.

I get HN is a Software site. But all math posts are invaded by people that think Math=Software. Probably based on the way they were taught maths when they were young.

Why would a theoretical physicist spend 30 years developing a theory that could be made false by a new experiment with a new technology? Was Newton gravitation worth if einstein was going to come later?

We are heading directly into a world where people forget about what values, philosophy, poetry, math, physics, or any other "non economically valuable" things are. And we all know what happened any other times in history when that happened.

The main issue here is that people that are able to "Strong disagree" is shrinking with every model release, because it requires skills. So it will get more difficult to get funding.

You may say "hey, before AI people payed for math salaries even though they didnt understand the math or the economic outcome". But the issue is there are now "mathematitians" trying to convince not to fund.

In this new reality, you will get "mathematitians" trying to convince that only AI maths matter. And on the other side someone speaking about "understanding", "taste", "community". And the people deciding to fund dont have the skills to differentiate. So they will fund the AI boosters with a higher probability.

Thats how the job of professional mathematitian dissapears. By being replaced by something that on the surface looks similar, but its just an ugly copy.

I guess this AI wave will divide the population more between people that think that only economic value exists, and people that dont.

Thats one of the timeless human debates.

We are now living in the perfect combo of low morality and general human automation. So i expect the next few decades dominated by people who think (and have a "proof") that doing something without an expected economic gain is useless.

I know that is the whole point. But i may dream of being as tall as a house, but it does not matter how hard i dream, it wont happen.

In my experience, every new model release allows me to go further, although every time i see every time the limitations, and i identify where i add value. And this value gets bigger every time.

But on the other hand, every model release reduces the amount of people that are able to value this "added value", because it requires more skills.

So we have the paradox that the added value i can bring on top gets bigger and bigger, but the perception of the economic value for the majority of the population gets smaller.

Can we please stop reducing human activity to "taste", conferences, talks, "understanding"? I think this is a very unproductive trap.

There is a world where we get to the edge of AI capabilities, and we build on top of that. As humans have always done with every new technology.

There is another more pessimistic view where LLMs just replace every human capability, and our economic overlords dont need us for anything and we just eat the small pieces of bread that are left.

This comes down to the fact of:

is human existence/intelligence just the simbolic representations we make in our brain? Or are they just a tool?

I tend to think of Godels incompleteness theorem as a proof that on the limit LLMs are useless. The real question for me is at what point approaching this limit becomes an issue, and if it has any practical consequences.

For me this path means that our role as humans is just the understanding of intelligence?

Everything else is secondary (or the last of our priorities) and would be better automated?

This is a hard pill to swallow

Come on, they were working on this for more than 2 months. Dont fall for the corporate half truths.

Dont get me wrong, i am 100% impressed by the technical capabilities, and appreciate the significance, and the amount of the results. This is a very special time to be alive, never in my dreams i would have thought to see this.

To follow your methaphore, who is directing the spaceship?

This feels more like fireworks than a space launch. Space launches would not have happened without having fireworks first of course, but I am looking forward for the space launch moment.

What is the average value of humanities when the default is to write things with LLMs ? The same with maths.

Sshhh dont say it out loud, someone might hear you.

ASuperMegaI lab announces they have shrinked the space of unproved mathematical staments from infinity to infinity, giving us proof of their deep mathematical knowledge and understanding, and how they grasp the concept of infinities.

For me this reads as someone boasting about how they go to buy bread on a ferrari to the supermarket, while i sit listening to it, having no idea what they are talking about. And then i stand up and go walking to my favourite boulangerie.

Warning: if you are from the USA you may be triggered by this metaphore.

A step in the good direction, Science will definitely look similar to this.

But this guy is too high on AI, verging on AI psycosis. A more sober version is what Science will look like.

In contrast to what these philosophical pieces tend to convey, the main crisis in mathematics is a labour one.

Mathematitians exchanged proofs for employment. That was the currency. Now they cannot use that currency anymore, so the question is how does someone know if they should hire an unknow person or not?

Philosophicaly who cares if you like more theory building or theorem proving? You dont need to convince anyone. The only solution is to be curious and follow your interests and naturally humanity will redefine what the new mathematics feels like.

You cannot convince anyone about it, its not something rational.

> 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.

Good point! I was speaking from my experience (at non tech companies, thats true). What i have seen is that there is an internal self selection of people that "refuse to play the game". My point is that that could have been a fair choice before, but the stakes in this new AI situation are at a point where they seem too high for that to be a good choice.

But nothing would make me more happy than knowing that there are concerned people acting internally.

Im at a point where i think the way to steer the situation we are in is to steer the machine from the inside, not quit and leave the people with the opposite mindset keep all the economic resources.

I doubt a movement of the people from the outside will work this time when all of the capital is in the other peoples hands. We need at least some of it held by someone with the opposite view to make the movement credible. And I dont think VC and IPO dynamics are compatible with this.

If you are already thinking of quiting, you can organize and internal movement and use the power of your labor to steer things. One person quitting is nothing for the company. The risk of big group quitting at the same time on the other hand... The labor is the only thing the company cares about. So we cannot wait until we are all replaceable by AI and we lose that leverage.

I agree, but I may be talking about another level of "noticing". More about observing the act and being conscious about what is happening. Thats easier it you are not rationalizing it. If you are an expert on a topic to the point where it becomes second nature, then you probably again have it easier to enter into that state, which can be a door to great creativity. But you can also get lost in all of the details that take you away from the moment.

Both cases are compatible with "noticing that you are eating a sandwich". The issue usually is that its much more difficult to "notice it" if you are thinking about how to improve it. Its like the classic parable of the camel, the needle eye and the rich. But its not impossible.

Im an ex mathematitian too. And if i was in academia I would probably have the same reaction. Thats what i say that its the worst time for proving economic value.

But if you are in for theory building and understanding, then you are not constrained anymore by your motivation to grind through countless hours of formal theorem proving. And you do not need to have superhuman formal manipulation skills and memory.

For me mathematics is not the formal system, so LLMs will never be able to do end to end maths.

Part of the controversy here is that now the skill advantage that some Field Medalist had is much narrower. The fact that fields medals have an age limit implies that it favors brain power over understanding. And that was the guiding light award of the community. So i find it "funny" (and natural) when they are offended by AI. That is the main "crisis" of mathematics.

In my opinion there has never been a better time to be a mathematitian, and there has never been a better time to be a software builder.

But there has never been a worst time to have the need to prove your economic value as a mathematitian or software developer alone. Because "understanding" is not something you can prove in one afternoon, its something that you prove with a life.