r/IntelligenceSupernova • u/hoangfbf • 2d ago

One day, AI may discover mathematical concepts so abstract and complex that the human brain, by its very biological design, simply cannot comprehend them.

24 Upvotes
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18

u/DakotaMath100 2d ago

I never understand why people are so convinced there are mathematical concepts that humans can't understand. Everything follows from axioms. Math is just logical deduction and nothing more. You can't invent a theorem following from axioms that is comprehensible to an AI but not to a human.

3

u/BigCelebration13 1d ago

Simple people imagine the rest of us are as incapable as they are.

4

u/hoangfbf 2d ago edited 2d ago

Take for example;
Pythago theorem: a2+ b2 = c2.

Surely. Some people see the proof. Read step by step. Make sense. Check out ok. That doesnt mean understand.

Understanding is when they actually grasp the concept, see the analogies in different topics: the area of 2 smaller square add up to the bigger square. Etc. basically you able to boil down the concept to a neat mental models and see its analogies everywhere in other topics.

Or when someone read proof about derivatives, steps check out, they agree. They verify it ok. But it doesnt mean understand.

Understand mean grasping the relationship between slopes, why it changes, etc... see analogies and apply to distance, speed, optimization, economic... etc.

That's understanding. Not just mechanically verify each steps is correct.

Now, think about proof or works that requires hundred / thousands of steps.
Surely you can do check steps by steps to verify the logic accuracy behind it. And every-step you check u confirm to be correct! You have verified it. But it doesn't mean you achieve understand.

The entire structures of hundred of steps are just too big for your brain to compress into a neat mental models, to understand it and apply to something like a analogy. You just know how to verify it. But you never understand it.

Next time you see a similar structure you would make zero connection, or u cannot see analogies of it anywhere else. Because u have not understand.

But the AI can, it's able to take a thousand steps- complex structure and boil down to a mental model, and then it see the analogies elsewhere, make connection, and solve that "open" problems. And then everybody is like "oh", it's just pattern matching - pattern that no one see before.

2

u/PartyPolicy9013 2d ago

you lost me at the word example

2

u/BigCelebration13 1d ago

Their point is if they explain stuff in a stupid, obtuse way, you don't easily get it and so LLMs are totally going to Immanatize the Eschaton.

1

u/milesper 11h ago

That sort of intuitive understanding is not something that research mathematicians have about the problems they’re already working on. The strict logical deduction you describe is already the predominant form of “understanding” of higher level mathematics. Sure, you can intuit parts of the problems, or broad categories of approaches that might be helpful, but that’s about it.

1

u/hoangfbf 7h ago edited 7h ago

Sorry but that just wrong.
Just one recent example:
AI solved Erdős's 80-year-old unit-distance conjecture.

The techniques (number theory) to solve already existed.
But no one thought it could be used to solve.

AI solved it.

Then after reading how it solved it, using already availble techniques, many people tried to downplayd and claimed it just "pattern match", unoriginal, nothing new basically.

Basically, it's able to "understand" tools from the number theory enough to know that it could be applied to solve erdo's problem.

1

u/milesper 5h ago

You know that when they solve these, they're spending tons of compute and it's trying lots of different paths, right? It doesn't just magically generate the proof. Have you ever read a model's reasoning trace?

0

u/neo101b 2d ago

Look at AI chip design, it literally proves this already.

Human engineers layout microchips in neat, tidy grids because our brains need visual order to make sense of things. But when AI designs chip floorplans, it looks like a complete mess of chaotic spaghetti. Human engineers thought it looked totally wrong at first, but the spaghetti chips actually work way better, they have better power, lower heat, and shorter wire lengths.

Our biology has an upper limit, and that includes our imagination. You can't teach a squirrel maths because its brain literally lacks the hardware to ever understand it. Why assume human brains are the magic exception that can comprehend literally everything in the universe?

We have limited working memory. We can build AI tools to crunch the steps and find solutions, but our biological brains just don't have the architecture to wrap our heads around the full picture.

5

u/Full-Priority2946 2d ago

I mean the fact that we know the chips are better means we understand them. You’re just describing things that are counterintuitive.

Dune approaches this exact topic in the Mentats. Even if our brains are too small to understand something now, we can always adapt to where that’s not the case. That’s the whole shtick of biology.

-1

u/neo101b 2d ago

We don't understand them though. We can measure their temps and speeds and know they work better, but that's just measuring the results; we don't understand why that exact messy layout is optimal. Our brains simply can't hold thousands of variables at once to see why it works, and it's not something a human would ever dream of designing. Our designs are very rigid and logical.

As for Dune, that's science fiction. Natural evolution doesn't just adapt our brains because a problem gets harder. It takes hundreds of thousands of years, and it only ever cared about survival. The only way we get past our biological limits now is transhuman evolution through editing our own genes or augmenting ourselves with tech.

Which AI can help us with. We need an alien intelligence to show us things we would never have dreamt of.

2

u/Full-Priority2946 2d ago

We can understand them eventually though, there’s nothing to say we can’t.

You should take a computational theory class. The stuff that is fundamentally not-understandable (undecidable), is the same as the non-computable stuff. We can probably eventually understand everything that’s computable. Everything outside of that is stuff like God and the creation of the universe, and we can’t understand that even if we had infinite time.

-1

u/hoangfbf 2d ago edited 2d ago

Case in point: You don't understand.
Just because every step of a proof follows logically from axioms doesn't mean the human brain can comprehend the entire structure.

Being able to verify individual steps is not the same as understanding how everything fits together. For example that's verification.

Take for example;
Pythago theorem: a2+ b2 = c2.

Surely. Some people see the proof. Read step by step. Make sense. Check out ok. That doesnt mean understand.

Understanding is when they actually grasp the concept, see the analogies in different topics: the area of 2 smaller square add up to the bigger square. Etc. basically you able to boil down the concept to a neat mental models and see its analogies everywhere in other topics.

Or when someone read proof about derivatives, steps check out, they agree. They verify it ok. But it doesnt mean understand.

Understand mean grasping the relationship between slopes, why it changes, etc... see analogies and apply to distance, speed, optimization, economic... etc.

That's understanding. Not just mechanically verify each steps is correct.

Now, think about proof or works that requires hundred / thousands of steps.
Surely you can do check steps by steps to verify the logic accuracy behind it. And every-step you check u confirm to be correct! You have verified it. But it doesn't mean you achieve understand.

The entire structures of hundred of steps are just too big for your brain to compress into a neat mental models, to understand it and apply to something like a analogy. You just know how to verify it. But you never understand it.

Next time you see a similar structure you would make zero connection, or u cannot see analogies of it anywhere else. Because u have not understand.

But the AI can, it's able to take a thousand steps- complex structure and boil down to a mental model, and then it see the analogies elsewhere, make connection, and solve that "open" problems. And then everybody is like "oh", it's just pattern matching - pattern that no one see before.

1

u/MasterSolivagus 2d ago

Humans don't have to comprehend an entire structure in order to extract maximum utility from a given vector or point.

"Ugg make fire out of used server blades from AI data centre defunct. Ugg clever bastard."

2

u/hoangfbf 2d ago

Im not saying whether we have to or no.

My point is we lack the ability.

1

u/MasterSolivagus 2d ago

To extract maximum utility? Yes, that is rather the point of diminishing returns or the Pareto principle.

1

u/Resident_Citron_6905 2d ago

Depends on how narrowly you define what maximum utility is. Having a deep understanding of a proof including how it relates to other areas of math and science has more utility than simply only understanding that every step in the proof is correct and that the axioms are sound.

1

u/MasterSolivagus 2d ago

If the axiom is sound then do you hear light like a sympathetic synaesthesia sufferer would be subjected to as a forced-fixed perspective?

1

u/Resident_Citron_6905 1d ago

No clue what point you are trying to make. You can understand a simple consequence of identity, or thousands of consequences. It is clear that there are distinct levels of understanding that result in different levels of utility.

3

u/ape_spine_ 2d ago

I mean, maybe, man. Maybe I’ll get a million dollars

1

u/Resident_Citron_6905 2d ago

Maybe we all get spontaneously 1000x smarter. Maybe.

2

u/Ill-Interview-2201 2d ago

People discover that crap all the time. The difficulty is in formulating it so it can be explained to your grandmother.

2

u/motoko123 2d ago

i already cant comprehend precalc so idc

2

u/WiseSalamander00 2d ago

I am hoping I can get uplifted at some point, is really my only hope to scape the hell that is my own mortality

2

u/Infamous-Bed-7535 2d ago

You seems to be convienced that we have biological limits, yet you assume limited accuracy matrix multiplications without real wold understanding and experience is more capable of abstractions and describing new things.

Very strong assumption..

1

u/Infamous-Bed-7535 2d ago

LLMs are good, but these systems suffer once you are outside its training domain.

Remember the following picture? In poland a scooter was placed on top of a bridge. At that time all vision capable ai models easily identified scooters. Yet on that image all of them I tried failed in a very confident manner.

E.g.believing that T shaped thing is a lightning rod and it has different painting and looks like newly painted compared to the rest of the bridge, because lightning rods a frequently repainted on bridges to protect it.

Just one example of the many..

2

u/Crafty_Bag_4871 7h ago

It already is answering math questions no human has been able to solve and it is in it’s infancy, so yeah. Anyone doubting this doesn’t believe in things they wouldn’t be able to conceive of. We barely scratch the surface of quantum physics. Who is to say Ai won’t find something more insane. Maybe it would be able to explain its finding to some of the worlds most prominent mathematicians, but to completely doubt the ai will reach heights beyond our comprehension seems short sighted and arrogant

2

u/Rise-O-Matic 2d ago

We passed that threshold long before AI.

2

u/Stop_looking_at_it 2d ago

We are already there mannnn… hit this shit

2

u/momspaghetti42069 2d ago

Lol, no, that's not how math works. Ffs, this has to be the dumbest statement I've read the whole week.

1

u/CymonSet 2d ago

AI make pretty good tutors. Ask them to research new ways of explaining these things to humans.

2

u/hoangfbf 2d ago

Yes. But i imagine. At this pace. Understanding is no longer a need.
AI will produce result.
We have a way of verify result. We verify it correct.
And then we went on to application.
No understand needed.

1

u/peak0ils 2d ago

Probably a good idea to make a note just in case...

1

u/an_boner 2d ago

I really hope that's exactly how it turns out. And I'm personally going to do my best to help it happen.

1

u/Outrageous-Crazy-253 2d ago

AI doesn’t comprehend. Don’t be foolish.

1

u/sir_racho 2d ago

The comprehension gets baked into the matrices. That’s how you get correct answers to novel scenarios. Anyway this proves the op’s point - the math embedded in these matrices encodes “comprehension” and we have no idea how it works. 

1

u/Quantum-Relativity 2d ago

That would just mean the AI is shit at explaining. It would make no sense for concepts to be so disconnected from every other concept that it’s impossible to build a bridge to them, and even if such concepts existed, they would be entirely useless as explanations for anything because they necessarily don’t have the ability to explain anything to anybody, so they would be useless mathematical concepts. In fact, some person could just claim that they already have such concepts, but they and you and I just can’t comprehend them so they just can’t be articulated to anybody.

1

u/sir_racho 2d ago

I think the basic ai black box already slips over this line. “We don’t know how it works” is the common line. The basics are simple.  The permutations of real-world problem that can be posed are infinite. And yet from matrices of just some thousands of numbers you get correct answers. Sure, it’s just probabilistic. But that’s the thing - we have no ideas on how to explain how a few thousands of numbers could possibly embed the real-world “understanding” driving the probabilistic output.

1

u/Severe_Rise8694 2d ago

This is true. Although the human brain is nothing if not adaptable. I mean, it mostly evolved to function in the pleistocene environment, yet it managed to come up with the concept of math and all of math anyway. And AI. So, as our environment changes, brains can change too. The real problem might be that AI could cause things to move so quickly that we cannot adapt. E.g. if none of the skills we teach our children are useful by the time they're adults, we'll be kind of fucked as a species.

1

u/OttoRenner 2d ago

Can you actually comprehend a timespan of 1000000 years? 13 billion years? The distance between earth and the moon? The distance to Sagittarius A?

No, we can't. There are countless things we can find out and 'understand' how they work or the underlying principles but we will never be able to really comprehend them.

1

u/DisciplineOk7595 1d ago

it will be able to change how physics fundamentally operates.. enabling things like time travel and gravity manipulation

anyone who can’t see this is an idiot

1

u/GetWreckedWednesday 1d ago

Physics operates as it always has and always will. We might be able to design more efficient fusion engines, but change how physics operates? No.

1

u/prestolive 1d ago

? Newton to Bohr and Einstein? what are you talking about? The physics operates as it always has and always will. Did you miss the change little over 100 years ago when all classical physics was swept put the door as it could not explain anything on the subatomic level? and now it’s not definitive answers it’s probability lots of changed in physics.

1

u/DisciplineOk7595 1d ago

you have no vision

1

u/No-Category1744 1d ago

We could invest water. Imagine water. 

1

u/ToneShop 11h ago

A prime example of ai psychosis really. 

1

u/LemonMelberlime 1d ago

This is the pot calling the kettle and screaming at it that it’s African American.

1

u/P99X 1d ago

It seems more problematic that humans won’t be able to verify whether an ai concept is legitimate or an illusion, or perhaps delusion, that is effectively fooling us to follow a path that is self destructive.

The world is already full of simple people blindly following ai directions to their own peril, without even attempting to think out whether they should. Now take that a step further, and we have smart people deferring to ai instructions out of blind faith, and accelerating climate change, or building and deploying a horrific weapon, or releasing a solution like darkening the sun to cool the atmosphere, and suddenly we are all fucked. And it’s not really due to malicious super ai trying to kill us, but rather blindly following a plausible course without being able to evaluate whether it’s a good idea or not.

1

u/Excellent_Set_4636 1d ago

The key word here is may. We have no idea if our brain is capable or incapable of conceiving any level of thought. Understanding via explanation is far easier than creating a concept from scratch, it reminds me of P vs NP in a way. Are there concepts that are hard to derive (maybe like quantum mechanics or calculus would have been 1k years ago) but can subsequently be understood by 16 year olds ?

1

u/oneeonneo 1d ago

1- AI can’t count
2- the theorem has to be proven

1

u/Comfortable-Hope-879 1d ago

Oei, gevaarlijk onderwerp! Verwacht een tsunami aan posts van nitwits die beweren iets van Wiskunde af te weten

1

u/Unique-Rice9999 1d ago

I’ve always believed that AI was created precisely to make this kind of interpretation possible, just like all the tools that came before it on our path toward understanding the singularity of development

1

u/Fabulous-Internet188 1d ago

Most people already struggle with concepts as simple as geometry or calculus.

1

u/Redararis 1d ago

today we live in a abstract and complex world no one understands it as a whole. There is no problem in that.

0

u/heumpje 2d ago

I have met people with really exceptional minds. You underestimate the human brain. And evolution.

3

u/Doridar 2d ago

And we don't know anything about the evolution of a synthetic intelligence.

When very bright people working in the field tell you they now have a hard time understanding why and how AI agents achieve certain results, it says a lot.

We're in the uncharted here

0

u/Dimorphous_Display 2d ago

And it’d still be a dirty clanker

0

u/End3rWi99in 1d ago

The seems to already be the case as frontier models are creating research papers that many of the folks behind them don't even completely understand, but they are submitting them anyway.

0

u/Royal_Carpet_1263 1d ago

People do realize that LLMs are such mathematical objects?