Created 2026-10-09 ← All posts
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Luddite mathematicians

tldr: Mathematicians act like luddites because their vanity and pride got hurt, while many ignore the real problem – that science gets privatized – and they refuse to change and accept the new era.

Surprise from the best

I always had high respect for mathematicians because they operate on something that I have so little understanding of and the complexity of what they do is so great, it is like alien science language to me, and yet I never imagined them becoming the new Luddites.
Well, who would have thought that actually our smartest people, who are solving the hardest problems at the peak of intellectual activity, if anyone could consider that, would actually turn out to be such luddites with crab mentality.
Who is supposed to be the best, the smartest, one of the hardest thinking people in our world? Many of them have a level of thinking and abstract reasoning unattainable for a regular human.
The last people you expect to be luddites.
But if you actually start looking, just a bunch of bitter humans who got their feelings hurt.

Context

Recently AI progress in mathematics, which is its strongest field, has become so advanced that thousands of problems are being solved in a month. From the millennium problems to many small significant ones. And mathematicians are furious that they did not get to do it instead.

Is mathematics a science

I have just one question. Is mathematics a science?
Many argue it is not a science and stand aside, but for the purpose of the argument I would put it in the same field as physics, chemistry, medicine or any other hard science, which is very important for human progress.
Yep, yes, it penetrates everything. Every scientific progress in any other field depends on mathematics. Any advancement, any technology we have today depends on that. So you cannot really separate it aside in terms of importance.

It is different in that many fields allow you to participate in the process for its own sake.
For example, if you take chess, you could be a long time chess theory researcher. And yet, outside of that field, all of this is kinda useless. And yet you still enjoy it and make a career, possibly, I don’t know, out of it.
In mathematics you also have two possibilities: either to solve the science for advancement of all science, or potentially also participate in a process of problem solving for its own sake just because you like it. Many of those problems might not even see much practical application or might never be applied at all (not sure).

Yet, it is one of the fields where the process for its own sake was a force that sometimes produced results that were applicable in a real practical world.

Vanity dressed as ethics

And then, what is the point of science? To get an understanding of our world. But to get a shared collective understanding of our world. Not one person getting better understanding, not a group of people getting understanding, but we as a whole, all at once, through shared knowledge, getting better understanding.

Yet currently the ones who participate in math for the sake of math are crying that their idea is destroyed.
But consider that this idea was based on vanity first. We wanted the slow problem to get recognition. We wanted it not for the sake of solving a problem, just to share it, just to advance everyone else. We wanted it partially to get a medal, to get something, or in short, for vanity.

And yet they got schooled by arrival of a more efficient process that actually brings results for the sake of results. For the sake of making our grand mathematical science richer, better, able to have more answers, which may or may not lead to any results now or in future.

Therefore, I would argue that anyone who tries to stop or move against the development of mathematics in any way or by any method possible, I would consider them an enemy of humanity.

Today they try to stop the new problems from being solved – tomorrow that delays a cancer cure or anti-aging or great advancement in computer science allowing everyone to run everything faster or allowing our rockets to finally reach the corners of the universe.

Yeah, what if other scientists did that? What if doctors, biologists, physicists decided to slow research just so some people would get more credit? If that was the case throughout human history, would we have achieved what we have now – if we had to account for the vanity of people chasing their own recognition?

I see. Well, fuck them. They are hinting. There are not many pointing directly, many are hinting that you should stop the progress some way or another or change it in such ways so that humans are still involved and so on and blah blah blah. I see them for what they are. The luddite-likes always have same answer for everything – keep the status quo.

A person who is genuinely interested in advancing us all and pushing the frontiers of mathematics towards new fields and reaching it all would welcome AI with open hands, because now their capability to actually contribute increased tenfold.
When one person could solve one problem, conjecture or similar in a lifetime, now we potentially can do a hundred.
Ones who really care would be very happy about the entire field now because they see it grow and civilization grow.

A person who really cares about our shared progress would welcome progress of any kind, even if it destroys his life work, even if it destroys what he did. We consider it our ultimate good, because now it advances all, despite personal circumstances. And additionally, it enables them to do more. So a real person who cares would be happy. The ones who are unhappy are loaded with vanity.

But also consider that what they are crying about is AI as an entity taking away their credit, their proofs, their prizes and all that. But is AI a subject? Of course, fucking not! AI cannot do anything itself. Behind it, there stands a group of humans, a company who built the tool.
It is not the AI that did that. It is the humans who created that AI that did that.
If five years ago somebody wrote a computer program that solves many theorems and it does solve them, who is going to be attributed? Would you really assume attributing a program over the humans behind it?
That again just shows that those people are grieving not because they dislike automated solutions. It is because they deep down understand that they got outrun by another group of humans with better tools.

I see left and right how those mathematicians are crying because the problem was solved and it was not solved by them. They are not happy with the problem being solved. They are unhappy that it is not them who solved it. Or another human. Or something else.
As if they are angry that a calculator now can solve integrals more efficiently than humans. They said the same about calculators in classrooms in the 70s through 90s – the machine will kill understanding, ban it from exams – and then everyone just calculated faster.

And it is all about feelings in the end. They got hurt, they are angry, and they point that anger at the companies making the software – yet they expect everyone to actually listen to them.

Did Microsoft apologize when Excel disrupted accountants and their workflows? Did anyone listen to draftsmen when AutoCAD automated so many of their parts? Have you seen anyone seriously claim translation apps are absolutely evil because they devalue the work of real human translators? That may be true – but see how much greater the absolute good of universal translation is.

Has anyone demanded an apology from those companies for changing the world? That would be ridiculed immediately. So why should we listen to the same song again?

They did not get to play it slow and enjoy the process – at the cost of a problem sitting unsolved longer than it needed to be.
That their little private club where they give awards to each other becomes obsolete and now they have to actually start doing something better?
When a new player comes and shakes down their hegemony of mathematics – that now it is not their privilege to keep it as a private religion, their semi-bureaucratic structures built over the years to keep themselves busy and existence justified. We have seen this protest in writing before: in 1999 some 200 prominent mathematicians and scientists signed an open letter to US Education Secretary Riley demanding withdrawal of reform math curricula (full text, Harvard Crimson coverage).
Instead of just focusing on real advancement.

Well, many of them claim this destroyed the process. But I say they don’t defend the field as a whole – they defend their routine, their rituals, the stuff they are used to, what they consider the normal way of doing research, with all that bureaucracy. They are not even protecting any advances. They are just protecting their current way of life, their way of doing things. Sounds exactly like grumpy old luddite vibes.

Let them play. Let the ones who want to do it for its own sake continue doing it, whether only by their efforts or with AI.
We should deny them the vanity, because for many of them now the vanity replaced the progress.
Selfish desire to be recognized instead of advancing us all.
Just listen to what they worry about. They worry about recognition, the credit, what they get to win, some prize and all that. What other people consider them, good in their field or something? Is this science or ego?

Let them play, while we welcome ones who remember what science and progress is.

While I absolutely hate ClosedAI I cannot be but happy and smug that they are actually doing a great deal of help to the whole humanity by doing math directly – go and solve it – without having to "cooperate" with academia bureaucracy.

I say, the science of mathematics should be advanced as much as possible by any means necessary using whatever resources we have.
There are not even any kind of ethical issues here compared to other fields like medicine. In mathematics you don’t even have anyone being physically hurt by doing such science. That some of the feelings got hurt or whatever you value – that is just life. Suck it up and deal with it. Your problems are nothing compared to benefits of millions.

But also, consider if those mathematicians are so against AI, which actually helps them to get into more different areas of mathematics. And that allows them to solve and tackle more problems, even if they would not use AI specifically just as a solver. And if they ignore that or drown in hate, then you have no choice but just call them luddites like as many practitioners before, who cried that calculators ruined everything. They now cry that AI ruined everything.

As I say, we should be absolutely grateful that AI is the great equalizer. Ones who lived in the clouds got thrown down to the dirt. And ones who were in the dirt – people who had no hope of ever getting into mathematics – are now able to be on a much higher level.

The real problem is ignored – who does the science

Well, I understand that they are discussing what the mathematical community could lose, their skill and talent, for some purpose, but I think while their feelings are valid for some, you can understand them, they are partially pointed at the wrong picture.

They are talking about the way how science is being made, but I want to point out who is doing science. That’s more important here.

Previously in my essay about the two most dangerous companies on Earth, I discussed specifically how these companies would privatize science. And this is what we actually see now: the entire field is getting privatized by private companies doing everything with their private models. And this means they not only get control of what is getting released and how it gets released, they also keep the additional knowledge being generated alongside by their internal scientists and all that, because they do not publish absolutely everything. Which would be impossible to do in open institutions.

What is the actual problem that we missed? Because science and mathematics are now de facto getting privatized and could be privatized further.
What is the threat they do not or fail to see, when in fact it is a very important one to address?

In fact, the complaint is that the math science is done this way and another way, and yet they don’t attack the point directly, which is who is doing science.

But now the problem in mathematics is not who is smarter, but who is richer. Before you needed just basic tools, not that much compute – but now the ultimate models are on top. It creeps into experimental physics and biology territory, where without expensive equipment and an institution to operate it, with assistants and all that, it is impossible to actually do science.

Albeit, much faster. You don’t pay for the more expensive one for nothing – you get a lot more bandwidth. And this would not even be a problem if privatization did not bite so hard. Because now all of this money and power is concentrated in just a couple of companies and nothing else happens.

Okay, consider this situation.
If things were radically different, we have case 1 where the private company, using private models nobody has access to, solves the science and they keep it all and they decide which science they publish, which solutions everyone gets and how they get them and to which extent, which can be censored, which can be taken over by government and so on, blah blah blah.

And we have case 2 where the closed AI would actually be open and we would publish the model for everyone and just say, hey guys, you doing cute mathematics? Here is your model, anyone can just download it and use it. Here we just sponsor you the compute so you can just run experiments and advance us all.

See how in the second one it is different, the company stops owning anything. Now everything belongs to the people, to actually a thousand of different professors and students who are using the same models to advance the science, who are solving the very same problems. But now everyone owns the result directly. It belongs to everyone and while it does not solve the problem of replacing the thinking process arrived at solving, it is still much better than what we have now.

Actually, this should be the main argument against closedness. They keep bringing up the attribution problem – how do you cite an AI on a paper – and yet this problem only exists because private companies do it all behind closed doors.

Consider if the model were open. Who exactly do you cite alongside it? The model itself? Where it was run, by whom it was run? Which specific API endpoint participated?

Closedness funnels all the credit to a single company operating its own private model – whatever it is, and it is not even a black box, it is just a promise, we have no fucking idea what it is.

While openness reduces the value of the tool itself, in a good way. It is no longer some fancy private model – it is the same tool everyone has access to. Therefore the value of the human operating it becomes much greater. Even if he vibe-solves everything.

Higher abstraction is still science

Okay, consider also this. We also have a genuine problem where because it is being automated the humans lose touch with actual proof methods when all of it is AI delegated.

Yes, I see you are concerned how you could suffer mental degradation because of it. And yet, I see it the same as the calculator analogy.
Because a calculator gives you the result, it does not mean you stop understanding how the process works.
You may start losing nuances. Yes, you may start, when you enter a very long formula into it and it gives you results, losing an understanding of how individual parts of this formula work. But you don’t need to. You just operate on a higher level of abstraction.

And yet they completely ignore that AI actually gives them such a massive boost of actually increasing the level of understanding which previously would be unattainable by limited human brain capacity and energy.
When you have a thousand PhDs at your disposal, being able to explain every aspect, every facet of the mathematics down to your personal level, which is like everything one could ever dream of. They have at their personal disposal the resource of a thousand professors available to anyone, as if you could consult personally the greatest mathematicians of all time and ask them what they think and how they think. And yet all of those little deeds suddenly ignoring the greatest tool we have to actually advance the science further.
We are now in the golden era where specialization becomes less important because you have direct access to the specialists now, thus allowing you to specialize on something even more, or go in the width direction instead. Now you really have a choice and both of your choices are augmented.

They also cry that fewer and fewer people are getting into mathematics, but that is bullshit. If anything, mathematics was never as accessible as it is now – AI lets anyone participate, even without deep understanding.

I ask it to speed up an optimization problem, to do some fancy math, and I accidentally end up with a new algorithm. Rare, but possible.

And that also angers some of them – that the new guys don’t do it the way we did forever.

Do you need to know how a car works? Really, down to the very nuance, to operate it. Of course not. You just need to know what an engine is and how it works. Maybe if you want to know more, you know what a fuel pump is, how a conditioner works, how at all. And yet you can perfectly operate the car without it, and produce meaningful real-world results by providing value of your car to yourself and others.

And yet, at any time you can still get into the nuances.

Well, I see the luddite part of vanity. But I also see one genuine concern underneath it – that knowledge disappears, becomes less accessible: all the proofs, all the paths taken, all the accompanying expertise, motivation, the development of how you arrive at something.

And yet I have a clear solution for it. The product made with AI must be held to the same standard as one made by a human. And it is not even a problem, because it can be made at the same speed as the proof itself is being made.

Solving anything must mean full: expanded, with failed trajectories included, and every part of the proof explained in parallel. Include everything – all the failed paths, all of it – and process it for further learning. You already have the whole chain that led to the conclusion, so you don’t stop at theorem proved. You keep going: you expand all the little paths along the way, explain them more and more. So the total proof is not just some fucking compact thing, but a big corpus of knowledge, saved and preserved for others to use later.

Well, I can’t help but bring again the software development analogy where if you are a CEO you have only limited understanding of how software works because you cannot know everything. Then you have the next person, your chief technical officer, who actually knows the architecture, how many parts you have, how they connect, and yet even he may not even read the code his subordinates are doing and only when it fails, when you have problems that require you to dig in, you actually need to get acquainted with it.

But oh, okay, okay, also consider that before, the speed of getting acquainted and having understanding was very limited because human minds are limited and have bandwidth and energy levels and you just cannot do it fast enough. With AI, actually your speedup on track of understanding of almost anything gets massively boosted. So it again becomes less of a problem.
Yet, I would also do you a bad favor if I didn’t say that as complexity grows, so it still. The speedup of understanding also hits limits. So, in essence, despite having progress in many areas, I would say we are still almost on the same level. Maybe we improved a little, but still almost on the same level. You get a boost of understanding and yet complexity grew again.

I might be mistaken to equate mathematics with software development entirely, but yet I see this analogy very clearly. And many would agree this is exactly how scientists are working already. They start dismantling something step by step and get an understanding, therefore getting a complete picture.

The future of all sciences

Yeah, this is about mathematics. But see how the same would soon occur in other areas of science.
It already happened in software development. And you see exactly the same kind of thing. Ones who did it for its own sake and drew pride and vanity out of it were devastated, while ones who cared about advancement of all, advancement of possibility of themselves and everyone else were absolutely happy about the possibilities that AI provides now.

Many would question now the future of mathematics and of traditional scientists, the question how do you continue working on something knowing that a problem you worked years to solve now gets solved in a day, and I had the same thing when I developed software, when I did something for an entire week and a month and now you can generate it in five minutes.

Am I sad for the lost time? Kinda yes, in a sense. I am sad that I had to waste so much time for bullshit. And yet, it is just the reality. I have to accept the reality that the tools did not exist at that time. And I had literally no other choice but to waste time instead. But now I don’t. Now we should be grateful that we finally have a choice not to waste time on bullshit, and get straight to what we wanted.

And yet everyone should reconsider that the definition of how science is made now always involves AI. You just have to accept it as you have accepted the already commonly accepted truth that computers are required to do science. Like literally everything involves them. If you would say that you want to be a physicist or a chemist and say that you refuse to use computers everyone would just laugh at you and consider you crazy. Now, the same with AI: if you don’t want to use it or refuse, then we should consider you a very strange person who just kinda wants to sit calculating stuff on paper, when you just could do it faster.

Now we all can rise up to the next level of abstraction and solve more complex and ambitious problems.
However, there is still… I think the best way of doing science forward is to develop in both directions – increasing the level of abstraction, or in simple terms to be able to automate more and hide away more complexity that you don’t need to concern yourself with all the time. And at the same time, increase the AI capability to help you drop down levels of abstraction fast and efficiently. The first one would happen naturally with general AI advances as the model becomes more powerful and better. We would have more long-term tasks. But the second one does require special fine-tuning or rather special attention from labs to teach AI to help humans quickly switch between high level and low level of abstraction, of detail, of how much you want to know about this particular mechanism or these connections. In simple terms, it is explain-like-I-am-5, but for everything, and being able to jump between levels, to start with simple and move to more complex in exploration as your understanding grows at the same time.
I think this way we will secure both our advance in science and still keep under control our understanding of ever increasing complexity.

We already have a precedent for this. When Perelman solved the Poincare conjecture – one of the Millennium problems – he dropped something almost like an AI-level solution: just the proof, very compact, so that only a handful of people on Earth could understand it. And over the next ten years mathematicians slowly expanded and expanded that corpus of work so everyone could get to that level and understand it the same. It took them a lot of time.

But with AI you could do it at the exact same time the proof is being made. You don’t drop just the proof – you drop everything at once, for maybe 2 or 3 times the compute.

They claim understanding dies with AI, but I say fuck it, it does not. Because understanding could be produced on demand at any time – not only for newly solved problems, but retrospectively for many older existing ones too.

Just hold AI work to the highest standard. If good human work was extensive, explained on many levels, letting others flow through it and build on it – demand the same level from AI. It is much easier for AI to bring work to that level, because it already operates on the whole picture, much better than any human tasked with expanding some existing work.

Sure, it would explode paper size 10x. But the knowledge is retained, so anyone can get to whatever level of abstraction they want. And one might argue this is wasteful – I say fucking not. This is exactly the great dataset for future recursive improvement. If you only shit out the proof, you have nothing to serve as a good signal for much better reasoning in the next generation.

So, what do we do with mathematicians? I say keep it simple, you will very quickly see whether it is a true desire to advance the entire field or a desire to advance yourself.
Ones who truly want to develop it will now use the new tools to make the field better anyway. You don’t need to argue with them about anything. They are already working towards the future, they are already laying the foundation for the new era.

After all, if AI solves all the problems in mathematics, who is going to invent the new ones?
Question for them: Would it be a real mathematical problem or is it a human ego problem?