Comment by metalspot
18 hours ago
There is a failure to understand that the process is the result. You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind. The output of an LLM is useless without a human mind to comprehend it. We can have Super Intelligence, but if humans are incapable of comprehending it, it is just another useless dead artifact. Practice, applied over a lifetime, is what creates the capability for comprehension. Asking an LLM to give you an answer creates an artifact. Humans being humans, most of their requests boil down to "make me rich without having to work for it," so the request itself is paradoxical and impossible to satisfy. Philosophers have only been saying this for all of human history, so don't hold your breath for any breakthroughs.
> You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind.
As a taxpayer I do not fund CS and math research because it "transforms minds." I fund it because it produces commodities. If you want to transform your mind, whether through math or meditation retreats, you are free to do so, but don't expect research funding to do it.
If you only fund “commercially viable” mathematics, then you are going to miss out on the majority of the most commercially important mathematics.
At least historically, we haven’t really been able to tell what will be transformative in terms of real world applications ahead of time.
That's only relevant insofar as it can be a long time before the commercial viability is realized or apparent.
If an AI can make 100 commercially unviable discoveries (for now) on its way to each immediately commercially viable discovery, that's great - bank them in the discovery library for later.
Still doesn't mean we need mathematicians doing everything with pencils instead.
>At least historically, we haven’t really been able to tell what will be transformative in terms of real world applications ahead of time.
This is mostly false. There are certainly some famous cases where math pursued for theoretical reasons later resulted in major practical applications but historically a great deal of math was developed either in response or alongside practical problems with anticipated real world applications, with war, industry and commerce being the major drivers.
As another taxpayer I find I don't have much say as to which sort of math the money goes to and I'm sure a lot ends up in stuff that doesn't produce commodities.
Transformed minds are what produce 'commodities', or more so an envionment conducive to a comfortable world; the mentality that does not even stretch to the ramifications of a civilization shaped by enhanced humans is a dangerous thing, producing policy guided by misaligned and incomplete rationale. Perhaps most problematic, potentially causing a reduction in those who can even consider and interact with such systems at all.
>We can have Super Intelligence, but if humans are incapable of comprehending it, it is just another useless dead artifact.
Animals are incapable of comprehending much of what humans do. Nonetheless, we humans have vastly transformed their world and caused the extinction of many species.
Yeah, for someone stating how important mathematics is, their reasoning is leaky as hell.
And we have also saved some.
I had to catch a stray cat recently and take it to the vet for an infection. It's healthy and spry now but ever since then it's been deathly afraid of me.
"Treat stray cats the way you would like a superintelligence to treat you."
Precisely. I don’t really care whether LLM’s can produce code more and better than me. I learn languages, program and study computation to understand better the world we live in. Being a human being means increasingly being technologically augmented. To have any deep understanding of that world requires deep understanding of maths, physics, programming etc. that you can only gather by doing those things and solving problems with your meat brain.
There’s a Twitch-streamer Tsoding who programs on C for fun calling it “recreational coding”. Maybe human programming will be a form of art in the future, virtually useless for big corporations to make money. I don’t care, I love it anyway.
Great but you will no longer be paid to do what you love.
History teaches us that understanding deep problems in mathematics finds natural applications elsewhere. So, either AI completely solves mathematics (unlikely for the moment), or we use marginal amount of funding to keep the mathematical communities alive.
I have never been paid to do what I love. Well, I got couple of art grants some years ago.
> To have any deep understanding of that world requires deep understanding of maths, physics, programming etc. that you can only gather by doing those things and solving problems with your meat brain.
There is tons of evidence against that. Someone armed with just LLM, can have much better uderstanding of problem then "meat brain expert" who studied the subject for decades.
We seen in last decades how "experts" are clueless, and how they predictions work.
> don’t really care whether LLM’s can produce code more and better than me
So on one side there is monopoly on "deep understanding", but on other no one really cares about quality?
You are both reading too hastily to quite grasp what I am claiming as well as making claims and assumptions you do not back with evidence. If there is tons of evidence how a person with LLM can understand - I was speaking of the world and times we live in, not just single problem - a problem an expert does, it is quite trivial for you to present that evidence.
Mind you,solving a problem is not same as understanding it. Anyone can just take a science calculator and bunch in some function without understanding anything about how to solve it.
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> the process is the result.
For who though?
Is it important that each person understand it on their own?
Why does it impact me if another human understands something or not?
It impacts me right now because that human can use that knowledge to explain things to me or to build new things using that knowledge.
But if an AI can explain and build better, then what good does it do having the other human know the thing?
Understanding might have intrinsic value to me, but intrinsic value to me doesn't pay the bills.
What am I missing here? I kinda expected better from Terrance given such an audacious title.
> For who though?
For the collective (humanity, mathematical/scientific community etc). Math is not done in isolation, and if somebody does so then feedback to the community does not work as well.
Mathematics, and basic science to a degree, face the issue that they create their own problems and paths through this kind of tranformation, where external feedback is secondary. It is not as if "I want to build an app/car/robot, I let AI do it". It is as if you decide to let AI decide what to build for you and how to build it, and you do nothing at all. Instead, the pursuit of understanding is the goal itself, and through the course of humanity we have learnt that this understanding can also be useful, but this is not necessarily guiding how this understanding is gained.
Most of the contexts people here have in mind are when problems are well and externally defined. Cure a disease, optimise an engine, make an app that does X, etc. This is not exactly the case in theoretical math and never was really.
Expertise changes perception, not just knowledge.
I have dyscalculia so the math world is dead to me, I can't even add 2 numbers together in my head, but I've read here on HN many times over the years people describe some version of new maths frameworks tangibly changing how they view the world. For me, I went to film school - I have a natural ability to think in movies and pictures, memory is very visual for me, before film school I had a good sense of shape, colour, light. After film school and to this day some 20 plus years later, I mostly look at the world starting with the shadows. Russian speakers, whose language has separate basic words for light blue and dark blue, are slightly faster at telling those shades apart. Speakers of languages that use compass directions instead of "left/right" appear to develop a strong, constant sense of orientation.
These things can only happen through the process, so for who? For people who want to live richer lives, want to think differently, and for you, to be around people who have such.
> For who though?
For math, the value of proving a theorem is often not proving the theorem (which most people already believe correctly to be true or false), but the path taken there, the new math invented, and how it can be applied to other problems. The end result is therefore almost inconsequential in moving math forwards.
> the path taken there, the new math invented, and how it can be applied to other problems.
What happens when AI is better at that part too? Are you confident it's not already better?
That’s a very narrow world view. Some people are driven by the pursuit of knowledge, while others want to use the knowledge to have an impact. I don’t care about the knowledge in my head if I can’t use it to make the world a better place. LLMs are fantastic tools to make that a reality. I have a computer science degree and am now 10-100x more productive with AI assistance. I give zero shits about all the people going “but you’re not crafting the code by manipulating bytes using magnets, so it isn’t real.” The non profit using my vibe coded app finds it very real.
You mean artificial intelligence? Where did super intelligence come from?
*cite a research paper or something
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> The output of an LLM is useless without a human mind to comprehend it.
I don’t understand mRNA vaccines, but they are useful to me. The output of an LLM could at least in theory be the design to a major technological advancement, and its implementation with automatic tooling. We don’t have to understand that for it to be useful.
I find this line of argument unconvincing because it ignores the alignment problem. We only administered mRNA vaccines after a large and diverse group of experts with different backgrounds and experiences came together and said that we should go ahead. We only administered them after several rounds of careful testing to ensure that they wouldn’t have damaging effects. The decision to administer mRNA vaccines for to large numbers of people for the first time was arguable risky and certainly controversial, and yet that’s what happened.
I have no issue with LLMs aiding human scientists, but imo we absolutely would need to understand your hypothetical advancements completely and thoroughly before surrendering any agency to them - the LLM’s risk analysis will not reliably reach the same conclusions as a democratic human society
An LLM could also in theory fake alignment and create technology that seems really useful but secretly harms humanity in the long run. If humans don't understand what it does, that possibility becomes more likely.
mRNA vaccines were created by humans who understood them. You exist within a society (a networked distributed information system) where you accept the judgement of the humans who understand and create this things, which is how you end up benefiting without personally understanding.
If we imagine Super Intelligence, where NO human is capable of understanding, then how would it ever be possible for any human to identify what is actually beneficial or not?
This resolves in a paradox, common to all magical thinking. You can certainly wish that some all powerful benevolent entity will solve all of your problems for you, but it is not likely to work out well.
None of this is new. It is the same delusions as alchemy and the same thing that tales about genies warn of.
> mRNA vaccines were created by humans who understood them
If authors understood them, why most of their predictions were wrong? Time to decompose spike proteins, side effects, distribution through brrast milk....
Event the most basic promise 100% protection against infection was wrong! They lied and we allowed infected people into hospitals!
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> You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind.
Normatively, this ought to be true. Descriptively, this is of course false. Our entire society is organized around producing commodities, typically by consuming people as inputs.
Depends if you need to work or not. Plenty of people don't need to work, they can live off their capital returns indefinitely.
For the upper crust of our society, work is entirely optional. Presumably people therefore continue to work for the process or the reward of the doing.
It’s not ‘of course false’, and, to be honest, I can only assume you have little idea what mathematicians actually do.
Most pure mathematicians are no more interested in ‘producing commodities’ than any other academic is. That’s not what the subject is about — at all. The confusion arises because mathematics turns out to be extremely useful (no surprise; it’s quite useful to have a detailed understanding of the basic principles of reality).
Again, this seems to be an alarmingly common fallacy here on HN. As a commenter above observed, pure mathematics (and that is what we’re talking about here) is in important ways closer to the humanities than it is to other sciences.
I was talking primarily about the majority of people who study mathematics, or anything else, who don't end up full-timers at it. I think we'd live in a better society if there was a serious possibility that everyone who studied math in undergrad could actually go on to be a mathematician if they wanted.
Not exactly. The input to produce commodities is labour-power (the potential to perform labour). Education or study is the process of producing the commodity of labour-power, the potential labour of a mathematician who can do some sort of specific work.
People don't always understand all the different theorems involved in a proof and can still gain from it. Can even do who layers with things like oracle machines where you just posit it finds a proof and opens up a whole rich hierarchy of stuff. Math understanding will probably get more like physics.
> You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind.
That's nonsense. Of course you study them to meet demand.
> you study them to meet demand
nobody who has ever achieved notoriety in any intellectual field ever did it to "meet demand." if your goal is to be an interchangeable widget that produces value as part of a corporate machine that exists for the enrichment of your shareholders, you are certainly free to choose that path, but don't imagine that is the limit of human existence. also, don't be surprise when you are replaced by AI, because it is a superior widget.
The desire for novelty and to be first is demand. The publishing and grant writing. The whole funding and tenure apparatus. It's nothing but demand gradients.
People who study STEM for the enrichment of their intellect are privileged. Most of us had to study STEM (or whatever else) because we had bills to pay.
I feel like so many people here are part of that crowd. going on about how it's like humanities and how it's super valuable and those who are seeking to get paid are just missing the point
how is it even possible to think like that? or maybe it's some kind of coping mechanism
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That's not why I studied. Maybe abstractly to prepare myself for the workforce, but the primary goal was to learn.
Unfortunately many countries like the US are very under-developed, and have trained it's citizenry to approach education as job training. This is obviously an abject failure, and probably a contribution to our anemically slow and pathetic growth rate.
sad
>The output of an LLM is useless without a human mind to comprehend it
This is like saying software is useless if the user doesn't read the source code of it. This what happens >99.99999% a person uses software. People want to be entertained or have their problems solved.
Your analogy doesn't work. A "product" in research pure math is not the same as writing code.
You can import a theorem that another paper proves without having to understand the mechanics of the proof itself.
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> There is a failure to understand that the process is the result
I'm glad to hear people say this now, because for the longest time they've also been bullshitting the public to think that pure math studies would someday lead to some kind of useful outcome.
"transforming the mind" is an exercise in ego-driven self-gratification, no different than getting ten degrees and never getting a job, nor any different than straight up porn or gambling. You have been put on earth to contribute to the progress of humanity, so get dirty and start making commodities. no more useless math-monks.
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