So what they are saying is that humans, in this case Charles Fefferman (a math prodigy, going by his history), failed to specify the problem correctly?
No, that‘s not the issue. If you look at https://www.claymath.org/wp-content/uploads/2022/06/navierst..., second page, you will see an option C is one of the four that is asked to be solved. And that option is the one that allows for an external force, which is what OpenAI solved. There is no question that OpenAI solved what the Clay institute is looking for. But that specific option C isn’t what the larger math community cares about, it’s a pretty niche case
It is interesting that there's a gap between the "prove N–S existence" conditions, which assume no forcing term, and the "counterexample" conditions, which allow a nonzero forcing term. In theory both (A) and (C) could be true.
I'm pretty sure Fefferman's formulation of the problem got a lot of vetting before the Clay Institute accepted it. As such, it probably does reflect the math community's understanding of the problem. The "problem" such as it is, is that it might be the least interesting case especially given the solution that was obtained.
But Clay chose Fefferman to represent "the larger math community"? I'm calling out Clay/Fefferman here, not the community. Though the community also had over 25 years to contest the problem statement, and had no problem with it until now.
> But Clay chose Fefferman to represent "the larger math community"?
Surprisingly enough, being chosen by another actor as proxy for some group doesn’t actually resolve the problem that an individual may not always be an accurate proxy for the concerns of the group (and especially for the same descriptive aggregate group a generation after the proxy acts on their behalf.)
A solution to any of the four options made by an LLM armed with a theorem solver and millions of dollars of compute would still not be that interesting to the math community since it is not likely that any new insights oe questions can be derived from the result
> There is no question that OpenAI solved what the Clay institute is looking for. But that specific option C isn’t what the larger math community cares about, it’s a pretty niche case
I think you are agreeing with me? My point is that "the larger math community" failed to set the bounds of the problem correctly.
Fefferman was right to include option C as someone could have come up with less contrived counterexample accompanied by some interesting theorems that actually shed light on the general case
Doesn't the way OAI's proof is formulated essentially rule that out, in that as long as an alternative solution concerns option C, it'd have to live in this same solution space they carved out?
Yes. And more humans—in this case OpenAI researchers—similarly failed in choosing how to direct the AI tools.
And yet another set of humans—Open AI marketers—made an error in how they sold the result of the preceding errors.
But its not news that computers are mere tools and that any error blamed on a computer involves at least two human errors, one of which is blaming the computer instead of the human(s) responsible.
Its perhaps a bit less obvious that every thing for which credit is given to a computer involves at least one human error—that of crediting the computer—and certainly can be more amusing when it involves a bunch of human errors.
> that ChatGPT usage (even 6 Astra Pro) is essentially unmetered on the 20x plan
LMAO, I wish this were true, I hit limits (and the "we are disabling access to protect your data" warnings) all the time, or have chats just...fuck off and get into weird/invalid states (interrupted chats, chats that are spinning and stuck, returning "/mnt/" paths instead of images/md files, file links being returned with no file backing them, image classifier firing...and then returning the image anyway (though now I know that GPT-Image-X really really wants to generate NSFW even when that isn't the request)).
Though I am probably an outlier, I have both 20x Claude/ChatGPT plans and max both out every week, so... (in my defense I am a hobbyist and this is out-of-pocket)
> DingusPPC does not take patches written with the help of AI, so maybe someone wants to re-do these fixes based on the explanations in the commit messages. (The patches for this wasm version are on this branch.)
As an example, it costs like three dollars to board a bus here. The maximum cost per day is two of those, but come on. If I needed even just to take a bus to work and back each weekday, that's already over a third of my car payment, and I lose carrying capacity, climate control, social distancing etc.
Also I have to walk to/from bus stops, which I can't easily manage due to my disability. That's why I keep an electric scooter in my vehicle nowadays, but I highly doubt a bus would allow me to bring one of those on board. So at that point just use the electric scooter without bothering with the bus, except when I did that, I got hit by a pickup and needed to go to the hospital and counseling, etc.
I prefer to just pay in bulk. I care about more than simply raw cost, but the little microtransactions always seem to be a worse experience.
I mean it seems like you have a valid reason, but the raw cost in terms of just the loan payment isn't a trivial difference. "already over a third of my car payment" means your car payment alone is 3x the total cost otherwise, which is... a lot. Once you factor in maintenance, insurance, depreciation (which has been lower in recent years), it seems like it would be quite a leap if you didn't have a disability that made public transit more difficult.
I think the difference between transit methods within a city that has built-in alternative options has been interesting to examine now that I have a motor vehicle myself (that I got for free, but costs a lot to actually drive). I went without one for 8 years before someone offered it to me, and I do value the flexibility to occasionally get out of town wherever I want, but the tires alone will cost $2000 when I need to replace them, and the gas is crazy, so it's perfect in the sense that it sits there taking up street parking until I really need to get someone that a bike, scooter, bus, train, or walking doesn't work as well for. I'm not encouraged to use it for anything that it's really not needed for, and if it died tomorrow I wouldn't replace it with anything.
Relying on only the bus, even if the transit system is well-funded, has never been a particularly ideal situation, but the advantage is that I get that time back instead of being singularly occupied by driving. If there's traffic, I'd wildly rather be on the bus, but the train is always better.
> forget to pay attention to the community energy and expectations
My problem is that I just...don't care about the community that much, and ended up just buying the tools I needed/outsourcing as needed. Though travel time/cost made it really uncompetitive (I don't drive, and neither of the large makerspaces in my city bothered to take transit accessibility into account...sigh). Even if I did drive, to me the commute time is just time better spent actually working on project du jour. All of that, plus the rise of sites like JLC(PCB|3DP) and sendcutsend where I can just get the part I want without any hassle really killed the value proposition for me.
I still like the idea of makerspaces, but it feels to me that the community has become the product. Which is all well and good, but if you don't particularly value that part, cheap tools + online fabrication services are already a tough comparison, and that's before burning a couple of hours on transit, before I've even touched a tool, well, the practical case completely falls apart for me.
> from what I saw at about 2016 the whole DIY machine thing switched.
GOOD! Those old DIY machines were awful. Even back then I wanted a printer that just worked, instead of spending hours just to get it printing somewhat accurately. I still have tubs of old ramps/smoothieboards/V6s and similar junk from that era, it was an awful experience. My X1C just works, I've printed more with it since I've bought it than all the other printers I owned combined. Sure there is still the occasional failure, but that is nothing compared to the failure rates I had before.
There's more than one form of intelligence, and being good at fixing people doesn't necessarily correlate with managing a business. As silly as it sounds, watching Shark Tank will really demonstrate that someone can have a legitimately great idea, but if they aren't business minded, it wont matter.
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