The problem with the article's line of thought is that mathematicians can't control what others do with models that are capable of generating proofs for hard problems. Sure, maybe there's a career in taking known proofs spat out by the oracle, and translating them for mortal digestion, but I'm not sure that's what most mathematicians signed up for.
Most mathematicians do compete for funding, based essentially on how many articles they can publish and where. Publication strongly favors problem solving. Universities are ranked on the same criteria.
What we see is a panic reaction to the fact that problem solving is "easy", which affects the future of the management of mathematics, not of mathematics itself.
Mathematicians are not luddites afraid of AI, is the academic publishing industry mixed with management interests speaking here.
- that it was stirred by the International Mathematical Union Committee on Publishing
- that is a mixture of the older San Francisco Declaration on Research Assessment DORA https://sfdora.org/read/ and recent fear of commercial AI competition
The academic system developed in the last ~50 years will crumble. On the broad scale of human intellectual history, this was a blip and not even the most productive phase. But it provided mass office employment and so this is all much more about the general knowledge work job replacement issue than anything specific to math. All desk/computer/office jobs will face the same fate. Math is just easier to verify. But engineering design, architecture, lower levels of lawyers and accountants where the selling point isn't charm and connections, they will all have this moment soon.
I've been working on something similar as well, but not yet ready to be shared. It's a geometry kernel and then an authoring layer on top. The idea is that the constraints are tests that get run after the geometry is defined, so it's more programmatic. Sol was able to generate STEP files for credible turbo machinery with it, and I have Astra building out the assembly for an inline three engine idea I had. The drawings are looking credible, but that's about all I can really say. I'm just blown away at how far the models have come in the last 12 months.
Hey, are you interested in collaboration? I did implement something similar to your approach of "constraints are static_asserts" inside the code CAD language and it works fairly well to assert volume/tolerance stack-up inline, but that is only half the answer, and the other half is "constraints are compile time types/requirements that are erased at runtime", as in TypeScript, which proved to be more significant. STEP roundtrip was proven months ago, so yesterday I had Codex Astra build a V8 engine assembly simulation in 3.JS last night to prove viability.
Sure, why not. I haven't uploaded anything to github/lab yet, and you'll have to give me a few days, since I'm busy juggling work and being a new dad.
Full disclosure, this is one of my pie-in-sky ideas that I've been letting AI loose on with only top down direction from me. I'm usually fairly hands-on even with the model in the loop, but this is an exception, because a geometry kernel is frankly beyond my ability to write solo (and I say that as someone with a reasonably strong math background). The gamble has always been that if a current model can produce "works, but crap under the hood", future models will be able to clean it up to "works, and is solid under the hood".
I'll push everything up by the weekend and drop you a line.
I switched from Claude to Codex because Claude just doesn't do what you actually tell it to half the time. It dances around the edges and does busy work without actually tackling a tough problem.
I'm not sure what others are doing that they're getting such different results, but I'll take Codex every day of the week.
My newest and most expensive car cost $5k in freedom dollars. It gets the job done. I have an older, more clapped out vehicle that cost $1500, and is in surprisingly decent knick for a 30 year old car, but it does need a paint job and some imminent TLC to keep it from deteriorating. That will cost more than it's worth, but I think it's worth doing in the long run.
Depends on the Mercedes. There was a time where Mercedes made cars that had a reputation for reliability similar to Toyota's today, and those cars are still fairly reasonable to keep running. The problem is that they're now becoming collectors items. Anything from the last 25 years though? Best to look elsewhere.
I think the only thing that stops this from becoming true is what Chinese and European labs decide to do. If they can keep up and keep opening their weights, then we might see some kind of democratization. But right now it looks like the gap has increased, and those groups can't replicate research that isn't published, or distill models that are internal only, or for select (very wealthy) customers.
Not necessarily. That's the best case scenario, but proofs can be intrinsically useful in and of themselves. It's just that for problems of that nature, speculative work is often done ahead of time, e.g. the body of work that already exists assuming the Riemann hypothesis is true.
This is the hope, but I suspect the reality is that we see an ever widening gap between the fortunate and the unfortunate. We're looking at the automation and commodification of all knowledge, and the best models will be kept locked behind closed doors so that they can't be stolen. And, of course, "for our own protection".
This is the real problem. We're looking at a future where those who control AI have an insurmountable advantage in everything. They can control the amount of intelligence the masses have access to -- for their own safety, of course -- and they will never, ever be able to close the gap.
They said "We're looking at a future". And if that future ends up developing the way these companies want it to then we're looking at extremely dystopian future where AI is essential to all work and people have to buy their "intelligence" from an oligopoly of large providers who have total control over the price and capabilities whilst simultaneously having unfiltered read/write access to people's stream-of-consciousness - their work life, their personal problems, their political opinions. This level of access and power is unprecedented in our society.
Yes. And for most applications it's more important that the open models get better in absolute terms and perhaps that they are competitive on a per-Watt basis.
- I think competitive open models are just an artifact of the AI race we're witnessing right now. What's the incentive for a company to spend billions researching, developing, and training a model, only to release it for free? Leading to the next point.
- Even if open models are good enough to be competitive, how are we going to run them? Doing so locally is next to impossible and I don't see that changing. The capabilities of models that you can run locally will always get better, of course, but the level of quality that is considered essential for work will always stay pinned at "near-frontier". Datacenters will always have better optimization and economies of scale, the industry will consolidate over time and eventually we'll end up with a handful of companies that operate the hardware serving 95% of all inference needs.
I'm not convinced that we can reach the fantasy world that they're trying to sell without killing the entire planet, but if we somehow do I don't see how we can avoid the world turning into a dystopian hellscape. We would need extremely radical interventions to avoid that scenario, such that these models and the hardware to run them would be owned and governed democratically, i.e. the end of capitalism.
So far we haven't seen much of that consolidation.
And a lot of people are using trailing edge models just fine already.
> [...] but the level of quality that is considered essential for work will always stay pinned at "near-frontier".
Why? When we'll finally all write our software in Lean and prove it correct and prove it fast, it won't matter that a slightly more clever model could have found a slightly nicer proof or whatever.
Just like today people happily use Python for many programs, even though rewriting in C might give you a performance boost. Good enough is often good enough.
At a certain point, you don't have a choice. Before China got into the game, the only way to avoid giving Luxotica money if you wanted a pair of glasses was to essentially not buy glasses. This is the same for many industries -- consolidation behind the scenes.
e.g. Zenni has sold $7 glasses for like 20+ years. They appeared shortly after Luxotica started buying retailers. If there's a problem, it's that advertising reduces consumer information (basically economic jamming) and distorts markets.
What is reasonably priced? Lenses are lenses so one vould debate the real cost, but the frames are incredibly overpriced for a piece of metal or plastic with two joints and those components that land on your nose.
Frames could literally cost 1 dollar (only happened after china entered this market), but good luck finding ones like this with good lenses.
You need to buy from one supplier who intentionally offers cheapest frames for 50+ dollars and those frames look like crap. The ones that look better (even if same plastic) cost 500+ dollars - and all due to price gouging.
For lenses I am not sure, but suspect something similar.
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