He should have just installed the multicraft panel then called the software good. This is less than an afternoon's worth of work. Scam.
Also for the price of one of these you could rent over a year of hosting on an actual server instead of an embedded device that is sharing 1 GB of RAM with the OS.
It's even better. Then tons of people can work together with it on more problems. Work with it on understanding more things. Ask it about random stuff. The time of a single human cannot be parallelized as easily.
Claude has been used to build awesome things, but it’s not “speaking from experience” when I ask it to help me prototype a weather model, for example.
It has no memory or experience of working on similar problems. Even if it made one of the foundational libraries that I use in a weather forecasting program, it still has no comprehension of the thought process it takes to understand the problem and build it from zero, and if I’m building on that library it just makes fresh assumptions about how things should work.
It’s not a human with experience or expertise, it’s a computer program that’s really good at turning English descriptions into functioning code
>it still has no comprehension of the thought process it takes to understand the problem and build it from zero
If it did it once, it can do it again from zero, and this time you can watch as it works and even it ask it questions. Many of the agents that worked on the problem did not have comprehension of the whole problem. I don't think you need that many tokens to be able to query it for the insights it had during the process.
> Many of the agents that worked on the problem did not have comprehension of the whole problem
Isn’t this the issue with using it the way you’re suggesting? At best the model can come up with an after-the-fact rationalization of how to get to the solution, but it doesn’t know what actual path it took to get there - what were interesting traps it fell into, where was a place it was close to the solution but didn’t realize at the time.
Those are things that are valuable to share between humans, those which teach us how to think better, and give us deeper understanding ourselves, and which a model doesn’t have any comprehension of.
Then have it discover it again and have it answer based off that run. Or if you are more curious have it solve it 10 times. See what it did differently each time.
Of course, if we get ridiculous polynomials it doesn't mean much in practice. People who hope for P=NP generally hope for nice polynomials O(n^3) or something like that at worst.
It's disappointing to see the author having such a low view of AI native mathematicians. The excitement from solving these problems should be considered a good thing. More people engaging and having fun with math is positive.
>Some view the future of mathematics as a dystopian...
>I believe Erdős would have found this future grim indeed
If you describe something as dystopian that is going to majorly bias someone's opinion towards being grim. That doesn't mean that dystopian description is reality.
Maybe, maybe not. But your "AI native mathematicians" aren't actually doing math, they are letting a machine do math for them. That is a lamentable future.
Not to argue off of authority or anecdote, but the vision of mathematics described is disparaging to anyone who already is or is on the path of being a mathematician. In particular, I think your view is only amenable to armchair/recreational mathematicians, and I really do not see the world being described as being one that is mathematically elegant or “better”.
I found that this article was supportive of recreational mathematicians. See the closing passage.
>Find a question that is meaningful to you, find other humans who are interested in it, and talk about it. Be confused, be stuck, be inspired. Find a messy proof, then find a better one. Get tired, get hungry, get into a flow state. Argue, laugh, give up, drink some coffee, and attack it again.
You clipped a lot of incredibly relevant context to make his point sound far more inflammatory than it is.
> Some view the future of mathematics as a dystopian arcade of button-pressing, staring at a screen waiting for AI to do the thinking for us, with the main human involvement limited to asking the initial question and offering sporadic words of encouragement. Each new proof is then thrown into a repository, to only ever be read by other AIs, and the human presses the next button.
Is that your view of all AI native mathematicians? It's not mine, but it seems apparent to me that many people think that this is our future, or even should be our future. Same with building software (which is my field, unlike math).
I would find that personally, to use his word, grim.
It doesn't matter what he wrote there. If he had wrote
>Some view the future of mathematics as a dystopian where the terminator hunts down any person who tries to publish a new math proof so he can maintain a monopoly on proofs
People would find that as grim. Even if the chance of that future being realized was 0%.
Works fine for me. I didn't explicitly say decompile but it had no issue digging into executables to give me information on how it and various file formats were designed.
>There are not many computer file formats I would trust to still be readable fifty years from now, but plain text is one of them.
Just the other day I had opus read a 10 year old proprietary file format. The idea that we will lose the ability to use file formats is not consistent with reality.
>Can every interesting mathematical question be answered that way? Probably not, and even questions that can may have more interesting and satisfying solutions that invoke novel ideas and insights. Perhaps, in the near future, AI systems will be able to come up with such insights, but, at the very least, let’s recognize that we are not there yet.
This keeps being repeated by AI skeptics, yet AI keeps solving more and more complex tasks. We've reached the point that it's even started solving Millennium problems.
>Telling us that some AI agent is spinning out theorems that are highly interesting to it and other AI agents does nothing for us.
This is the future of pushing the frontier though. AIs need to be pushed to get better and better. AI understanding of math is millions times more important than human's.
>AI understanding of math is millions times more important than human's.
This is a persistent misconception that I see on HN (although not usually framed as abrasively as you have chosen to frame it).
Math is not an engineering discipline. Pure mathematics research is not done with an eye towards practical applications in other fields. You should think of it more like the humanities--it is done because it enriches the human experience (and it's not very expensive).
You could give us a black box oracle that could tell us, with 100% certainty, whether the 50 most famous and important open conjectures in math were true or false, and it would be more or less worthless. What does it actually get you? This isn't a rhetorical question.
AI in math is valuable only insofar as it ultimately helps drive human understanding.
There is another side of math that is more driven by practical applications: statistics and "applied math" and whatnot. This is what most people think of when they try to imagine math research, because it is much closer to the math that they have learned in their school education. A lot (but not all) of this math would get more value out of black box results, yes. But don't conflate this with the entire field of mathematics as a whole.
But why? Responding to vulgar economism/instrumentalism with, "Well actually mathematics is this and that, human understanding/journey etc. etc." does not explain why mathematics ought to be those ways. Without elaboration such assertions amount to professional dogmatic narrative in the other direction. Professionals can be very good at that kind of rationalization too.
If you're asking why should we value something simply because humans do, the answer is simple: because we are human. It should be obvious, but it tends to get forgotten, that the ultimate goal cannot be anything other than actual human (and generally life) flourishing. Even the search for truth has to bend to this goal.
I'm not asking why. I am pointing out that most answers here are not applying the very critical habits required of mathematics itself. The explanations and justifications are not good enough.
When mathematicians speak of pure mathematics having “intrinsic value” or being for the sake of improving human understanding, what they really mean is that no applied value (in engineering or science usually) is necessarily known at present, but it improves our understanding of mathematics as a system in itself. Why mathematics is this way is not an easy answer, you would have to first have an agreed upon definition of what mathematics actually is, and we don’t have this. Most people have an intuitive notion and “know it when they see it,” but mathematicians and philosophers of mathematics don’t have a clear answer, and different schools like the (neo-)platonists, formalists, constructivists, etc. have different contradictory approaches in even trying to get to a clear definition.
Which gets closer to my real point, mathematics is inherently philosophical and I’d argue it is a kind of analytic philosophy. A close reading of late 19th/early 20th-century history of mathematics, I believe, shows us how closely mathematics developed alongside analytic philosophy, such that at the foundational level at least, they seem to be the same branch of knowledge. It wasn’t too long ago that in some parts of the world mathematics was (rightfully in my opinion) considered a branch of philosophy and there was no clear separation between a philosopher and a mathematician. So, in my mind, mathematics is the way it is, or is beneficial to humans because, or is worth pursuing ourselves instead of handing most of it to machines because of the same reason as philosophy is all of these things: human beings are naturally curious and we satisfy our curiosity by trying to learn and understand things, it’s a natural drive and it’s among the things which help us grow as individuals and as a collective.
Personally, I consider the above a very practical value, so I’d argue that pure mathematics does have “applied” value at a more basic level than what engineering or science disciplines are usually concerned with.
Some things are valuable, because they keep people alive and healthy in the short term. Some are valueble, because some people find them inherently valuable. Pure mathematics is in that category. And then there is bureaucracy.
Bureaucracy has no direct value, but it may have indirect value, if it helps us achieve things that are more directly useful. Pure mathematics has had a lot of indirect value until now. It turns out that training people to do mathematics for the sake of doing mathematics, at any level from schoolkid to mathematics professor, teaches skills that transfer to other domains. If human thinking becomes obsolete, that indirect value may be gone, but the direct value will remain.
The results in pure mathematics are largely irrelevant, except as means of acquiring transferable skills. Sometimes they have practical implications, but such situations are exceptional. And there is not much correlation between the practical value of a result and its value as seen by mathematicians.
See we're taking about inherent value but part of that is my valuing a not nonsensical explanation. And saying math has intrinsic value because some of us treat it as that is nonsensical and anti-science or anti philosophy. It is not based on an intelligible definition of value. Which goes to my original point that when people trot out these arguments they are really thinking carefully about what they are saying. And the more you see these talking points repeated I have to ask who is putting forth these notions. And so every time it is someone making these sweeping declarations about "value" and other people are supposed to accept that. It is a kind of ideological being talked-down to, what gave them the position to declare the ontology of value and so forth. And that is pattern once pointed out you'll see people keep doing it.
What you're saying, if I read you correctly (see note at the bottom) it that you find it unacceptable that something can be valuable simply because we find it worthwhile, without having a reason for why it is so. I don't see it like that. The capacity to reason didn't come along with a guarantee that all ignorance will evaporate instantly under the action of the scientific method. We can't just go by reason, because in many areas of our lives, reason alone doesn't go far.
PS: @calf, I've re-read your message above a few times and I must agree with others elsewhere in this thread that incoherence is afoot. Please review your own comments before sending, from the point of view of a reader who doesn't yet know what you want to say.
Why does anything have value? Ultimately because we can use them to get something we need or want. For the former, there is some sense in trying to reach an objective definition of value. The latter is inherently subjective. Some things are valuable to some people, because those people find those things valuable. That circular definition is the root of subjective value that cannot be reduced any further.
I think I already answered this in my comment. I claimed that I don't see much value in a magical black box theorem-proving oracle whose proofs could not, and would not, be understood by humans.
If you disagree (as the GP does, apparently), I ask you--what value do you see in it?
You claimed it would be worthless but did not give any supporting rationale for that claim. That is the ideological move. Professionals are often blind to this.
I have no idea what you're trying to say. Once again, if you see value in it then feel free to explain why.
The only reason most pure mathematics research exists right now is because it is interesting to the mathematicians who conduct it. I think a black box is not interesting to mathematicians and therefore has little worth. That's the argument.
You're wasting your time - people here aren't smart/honest enough to engage with your reasoning. As someone who did math professionally for a long time, I agree with you. I think it has as much value as chess (a game we made up which we play for fun).
A lot of people here are smart enough, they just don’t agree with the premise but maybe don’t know how to express that. Being purely for the sake of improving human understanding is more akin to philosophy than chess I’d say, and that is beneficial on its own if truly sought for that purpose.
they're really not because clearly their sole method of engaging with this discourse is projection.
> Being purely for the sake of improving human understanding
no matter what anyone tells you, there is absolutely no working mathematician that wakes up every day and goes to work based off that desire. it's not a priesthood, it's a job.
I don't really see much "reasoning" that they are presenting. Their contributions to this thread have been closer to sealioning than any kind of positive argument or thesis. What do you see in their comments that the rest of us are too stupid and dishonest to engage with, exactly?
>As someone who did math professionally for a long time, I agree with you. I think it has as much value as chess (a game we made up which we play for fun).
I mean, I don't see how this is much different from what I argued, no? Nobody really cares about computer chess all that much at this point except as a benchmark of technological achievement, and except to the extent that it helps human players better understand the game and improve their own play. We still play chess, even though computers can do it better than we can, because we find it interesting.
> We still play chess, even though computers can do it better than we can, because we find it interesting
people are making this comparison so often it's borderline embarassing. yes we do and there's seemingly a possibility that math goes the way of chess. now answer this: do we award doctorates in chess? do people get paid to study and teach and publish on chess on the same scale that they do with math today?
You seem like a bit of an asshole so I'm not really interested in continuing further, but I will say that a large amount of that activity is financed by demand from students in one shape or another.
> does not explain why mathematics ought to be those ways.
He simply said what pure mathematics is. You brought the "ought" part in. By what standard do you determine what pure mathematics ought to be good for?
The specific proof may be in pure math but Navier-Stokes problems did originate in applied math. A lot of what we consider pure math has it’s origins in something applied. As one of my math professors implied, a lot of mathematicians liked to pretend they came up with theorems from scratch in their final published form, but in practice it was often from seeing examples, often practical ones in applied math, then making conjectures that eventually led to more generalized theorems.
My point was that OpenAI did not solve the problem for a practical purpose. There is no utility to having a proof for a liquid that can't exist in reality. It was solved purely to push the frontier of what is known in mathematics.
"The field of mathematics" is something that humans engage in, chiefly to advance human understanding in about the most abstract way possible. It's not some self-sufficient, sentient being that exists for its own sake. Also, contrary to what's often repeated by AI maximalists, it's not a major source of innovation in other disciplines; most of the math the world actually runs on is hundreds of years old.
There are plenty of very difficult math problems with practical application. Just because they don't interest some subset of academic mathematicians does not mean they don't exist. And you don't have to literally invent a field of mathematics to do valuable work applying it (and applying it may be difficult).
>It's not some self-sufficient, sentient being that exists for its own sake
If humans didn't exist do you think a^2 + b^2 = c^2 would cease to be a thing? Math is built on top of logic and it is something that exists independent from the physical realm.
> This keeps being repeated by AI skeptics, yet AI keeps solving more and more complex tasks. We've reached the point that it's even started solving Millennium problems.
Yes, so? Still not "novel ideas and insights", which is what you responded to ... and the statement wasn't made by an AI skeptic.
> This is the future of pushing the frontier though. AIs need to be pushed to get better and better.
It would be far more honest to say "I want AIs to get better and better". But there are costs. What are you willing to accept?
> AI understanding of math is millions times more important than human's.
Ah, it seems that "replace humans with AIs" is not too much for you.
To whom is that more important? Not mathematicians.
Math as a field is unbounded. There's always more to discover, new systems to invent, new problems to find. It's not just some predefined set of unsolved problems.
Math is also a matter of what is both interesting and useful to humans.
For some reason there is this virulent strain of anti-human AI rhetoric that machines will replace us. But what is the purpose of math as a field of study if we're not in the loop?
It’s like people think problems are given to us by God.
We make our problems up!
> For some reason there is this virulent strain of anti-human AI rhetoric
It’s just… nasty, isn’t it? Facts aside, one does have to wonder what motivates not the beliefs themselves, but the, well, frankly aggressive, way in which they’re expressed. Bitterness and envy felt towards those who have actually done the hard work and achieved things?
Brace for impact.. OpenAI are going to dump their load
Looks like they are betting the downer from AGMAI is not going to hurt their cred where it matters (investors, and whales-- a mix of b-tier profs, postdocs, uni admins, and wealthy crackpots)
My own is there won't be prompts, traces, whatever, like AGMAI asked for. Same old style. Navier-Stokes "worked". People outside unglamorous analysis swallowed it.
One hope is that everyone will know someone whose years of work went for nought. By hearsay, the pipeline of whales will be broken (only hitting openAI revenues in a couple of years postIPO, however)
...but math does have applications! maybe there is some math that people can't understand, but which has engineering applications, and which machines might apply to solve problems?
Tasks are not simply integer “difficulties” where, if your “intelligence” exceeds the “difficulty” then you will solve it.
The question is to what extent AI will affect creation of new branches and elegant ideas in mathematics. This question applies to every area. Has it created an interesting new way of thought in any area other than those where massive tree search can be mistaken for such?
I don’t think it’s impossible but the evidence doesn’t point clearly to it.
"They should pay for it because they can afford it"
I don't think they should have to pay for some private company profiting off their publicly-available resources. It's a bit like some restaurant sending swarms of their employees to the local food bank and then reselling the free food they've gotten in their restaurant.
Also for the price of one of these you could rent over a year of hosting on an actual server instead of an embedded device that is sharing 1 GB of RAM with the OS.
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