I hope you are right - the point about energy efficiency is certainly spot on, and I do think it is possible that people are getting carried away by analogies when discussing the topic (I wrote something about that too, but will avoid linking to it here to avoid excessive self-promotion).

That said, the article doesn't assume such a thing will happen soon, just that it may happen at some time in the future. That could be centuries away - I would still argue the end result is something to be concerned about.

> he energy efficiency perspective human brain is very, very effective computational machine

Can you explain why you think that? Very often, mechanical efficiency outperforms biological. Humans have existed for thougsands of years, neurons even longer. Computers and AI and relatively recent, we haven't really begun to explore optimisation possibilities.

Thanks for the positive feedback on my writing style! Based on feedback in this thread it seems to be a divisive topic, haha.

A recurring problem I see is that people have absolutely drunk the koolaid of the utilitarian worldview. They've been marinating in it for so long, with no exposure to anything else beyond this parochial and base existence, that they have no idea they've been marinating in it. Everything is reduced to economic exchange. Everything is reduced to economic output. Learning is reduced to something that has value only if it is "marketable", only if it results in more units of toilet paper. The human being disappears from the picture as a mere instrument of the economy, and economy that exits for its own sake, that hovers over us like a god.

Given that kind of picture of reality, it is little wonder that AI seems like such a profound threat to so many people (putting aside for the moment the distinction between the aspirations of AI companies and the actual affordances it possesses). If being human is to be an economic instrument, then any AI that could eliminate the economic value of human beings is something akin to extinction. The god of economics has no further need of you. You may die now.

But this utilitarian view of the world reeks of nihilism. It is the world of total work, of work for work's sake. We never inquire about the ends that are the very reason for work in the first place. We never come to an understanding that economies exists for us, that we create them for mutual benefit. And we never seem to grasp that the economic part of human life is only part of human life, that it exists for the sake of those parts of life, the more important and most important parts of life, that are not a matter of economics. We have come to view life as meaningless, so we run into the embrace of the god of economics, losing ourselves in its endless churn, its immediate goals, truncating our minds so that we do not conceive of anything else, longing to escape the horror of the abyss that awaits us outside of its dreary confines...

The point of studying something in a theoretical capacity is to understand it, not to produce something of economic value. Each person must come into understanding from a state of not understanding. Homo economicus does not comprehend this. Homo economicus lives to eat and shit and cum and to accumulate things.

> The camera didn't kill painting

But it did. Painter used to be a trade where you could sell your painting skills as, well, a skill applicable for other than purely aesthetic reasons, simply because there were no other ways to document the world around you. It just isn't anymore because of cameras. Professional oil portrait painter isn't a career in 2025.

> nor the motor-car killed running

Is running an art/vocation comparable to photography and/or painting? We no longer have mailmen who run the length of the country afaik.

But running did heavily contribute to sedentary lifestyles in western countries, along with a bunch of other things.

> mathematical research isn't even a significant employment area

I agree, I think it will move from mathematicians "doing" math, to managing computerised system that do it instead. I'm sure we already have such systems.

I think far more important to humanity is improving mathemetical-literacy. From my perspective, math is made for mathematicians - it could be more accesible. As "pure" amth matures, there is still plenty opportunity in "applied" math (however you might define it).

> we can keep on building theorems on top of theorems with increasing complexity

This is a somewhat bleak picture of math. We also have the other phenomena of increasing simplicity. Both statements and proofs becoming more straightforward and simple after one has access to deeper mathematical constructions.

For example : Bezout's theorem would like to state that two curves of degree m, degree n would intersect in mn points. Except that you have two parallel lines intersecting at 0 instead of 1.1 =1 point, two disjoint circles intersect at 0 instead of 2.2=4 points, a line tangent to a circle intersecting at 1 point instead of 1.2=2 points. These exceptions merge into a simple picture once one goes to projective space, complex numbers and schemes. Complex numbers lead to lots of other instances of simplicity.

Similarly, proofs can become simple where before one had complicated ad-hoc reasoning.

Feynman once made the same point of laws of physics where in contrast to someone figuring out rules of chess by looking at games where they first figure out basic rules(how pieces move) and then moves to complex exceptions(en passant, pawn promotion), what often happens in physics is that different sets of rules for apparently distinct phenomena become aspects of a unity (ex: heat, light, sound were seen as distinct things but now are all seen as movements of particles; unification of electricity and magnetism).

Of course, this unification pursuit is never complete. Mathematics books/papers constantly seem to pull a rabbit out of a hat. This leads to 'motivation' questions for why such a construction/expression/definition was made. For a few of those questions, the answer only becomes clear after more research.

> the possible number of such relationships are infinite

I think you need to be careful taking about "infinite" in the context of math. If the number of quantities, relationships etc is finite, so are all their combinations. Even things like the infinit-ude of available numbers might have fixed patterns that render their relevant properties effecively finite, and lead to further distinctions e.g finite vs countable, etc.

Personally, I feel like math has a bit of a legacy problem. It holds on to the conventions of an art that is very old, with very different initial assumptions at its conception, and this is now holding it back somehow. I lack the background to effectivly demonstrate this other than "Things I know/understand seem less intutive in standard mathenatical terms" e.g. generating functions and/or integrals feel easier to understand (to me) when you understand the, to be software-like 'loops'.

In fact, the idea of "constructivist math" seems (again, to me) to beg for a more algorithmic/computational approach.

> a language for defining relationships between quantities

Could you expand on this? I don't see maths as a language for quantities specifically (i.e. what does symmetry have to do with quantities).

> just too tedious (but not impossible) for a human being to work through the proof.

Already happened with the four colour theorem arguably.

just the zfc axioms alone are already infinite. It's an axiom schema ranging over an infinite number of actual statements. That's just statements, without even considering symbols as you're saying.

> I think it's fair to assume that the possible number of such relationships are infinite

That’s easily proven to be true. “Two plus two equals four” is a theorem, so is “three plus three equals six”, etc.

> We'll know that the time draws nearer when an AI confirms or refutes Mochizuki's proof of the abc conjecture. As of right now, I don't think they're capable of doing that. And, as they can't even check a very (very!) complex proof, they won't be able to conjure any inhumanly complex proofs de novo.

I agree, but... Spend time formalising a large part of existing mathematics and proofs, train a bunch of sufficiently powerful and generative models with that, and with cooperative problem solving and proof strategies, and give them access to proof assistants and adequate compute resources, and something interesting could happen.

I suspect the barrier is finding a business model that would pay for this. Turning mathematics into an industrial, extruded-on-demand product might work, but I dont know who (except maybe the NSA) would stump-up the money.

I am not suggesting models will be capable of generating 'all' proofs - that is clearly impossible. Merely that they will get better at doing so, and there is no clear reason at the moment to believe they will never reach a human level of competence. If you have one model functioning at such a level, it is presumably trivial to have a million of them, none of which will need to be paid, housed, or sleep etc.

Why would an AI confirmation or rejection be more convincing than the proof itself?

also why would capitalists expand resources on churning out proof after proof when mathematical proofs are not patentable?

How is that any different than people programming for fun?

At a young age?

In my case, when you aren't paid to do it, and don't have (much) time to study it formally anymore.

When you do it with love

In poker?

>>I live by myself in a remote mountain cave

= I live in California, and the nearest Starbucks is more than 20 miles away.

>>can only be contacted during a full moon

= As a night person, I am awake when the streetlight outside my house turns on.

>>certain arcane rites that are too horrible to speak of

= In order to contact me, you must install Microsoft Teams.

Overall, it's not that bad, except for the MS team thing. ;)

Perhaps the writer is a fan of Grothendieck who did almost exactly this - lived in a remote village in the Pyrenees

https://en.wikipedia.org/wiki/Alexander_Grothendieck#Retirem...

"Local villagers helped sustain him with a more varied diet after he tried to live on a staple of dandelion soup." - like most people would.

As always, HN has no sense of humour...

Agreed if I had saw that first I wouldn't have clicked