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Comment Re:Why do you hate yourself? (Score 1) 102

I don't actually use Apple Store all that often. A fair portion of the software I have installed, like LibreOffice and Firefox is just installed via DMG images. It kicks up a window about unrecognized source, but then just works. iOS devices are definitely more locked down, but the Macs are really no different as far as installing software than Windows or Linux.

Comment Re:For Insiders on the Experimental channel (Score 1) 102

I imagine the Mac Neo is the real source of their panic. Right now RAM prices are probably saving them from even more losses, but the hegemony is coming to an end. If a credible useful, at least for average users, non-Windows platform using smart device level hardware can sell as well as the Neo has, I'd say Microsoft's reckoning is finally upon them.

Comment I wonder (Score 2) 102

At what point in this long and seemingly endless list of fixes to even the most basic usability features in Windows do its users finally admit it is really a shitty and badly maintained operating system. I use Gnome or MacOS, which are streamlined and uncluttered, and then I head over to Windows and it's like looking into the mind of someone with severe ADHD. It's a colossal mess where nothing particular makes sense, there's no coherent approach, everything is slow and inundated with advertising, context menus that worked for decades don't function right or at all, even the simplest tasks just seems to land you in the wrong place.

I suppose under the hood it's still a fairly decent operating system, although tools like Powershell, which can be achingly slow itself, demonstrate that there's a lot of layers of cruft.

I don't play video games, and frankly Office isn't that much better for my needs than LibreOffice, and Outlook is a bloated pile of crap, so I rarely even access the Windows desktop I have at work via RDP, save for two applications I rarely use. Windows is rapidly becoming irrelevant in my world.

Comment Re:LLM output is Grey Goo and Ecophagy. (Score 2) 146

Or let's put this another way. Show of hands - how many of you "spicy autocorrect" / "stochastic parrot" people had "AI will start mass-solving Erdos problems" on your forecast list a couple years back? Huh, none of you? Fascinating!

Take some time to reassess your priors. And while you do so, understand that, yes, they are doing logic / reasoning.

Comment Re:LLM output is Grey Goo and Ecophagy. (Score 4, Interesting) 146

They weren't discovered by an LLM. They were known conjectures that were proven by an automated solving language that was linked to an LLM.

I'll take "Things That Didn't Happen For $200", Alex.

Only a handful of meaningful proofs have ever been done by automated formal theorem solvers (the Four Colour Theorem being the most noteworthy example - but its proof is so long that humans can't verify it). By contrast, AI tools have been solving Erdos problems en masse. The majority of them just bog-standard commercial models. In case you need help, the only ones on that list that were hybrid (AI / non-AI) in the actual solving phase are:

1) AlphaProof / DeepMind Prover Agent / AlphaProof Nexus
2) Aristotle (Harmonic)
3) Seed Prover / Seed Prover 1.5 (ByteDance)
4) AxiomProver (Axiom Math)

In each of the above, LLMs come up with the lemmas / strategies but then use Monte Carlo search ("brute force") or likewise to investigate what they came up with. These are a minority. In the "AI Standalone" category, these "hybrid" tools made up only ~20% of attempts and successful proofs. Hybrid tools actually made more of a contribution in the "AI Alongside Literature" (related literature found afterward) and even more of the "AI Building On Literature" (related literature known beforehand) categories, which is the opposite of what people like you expect.

And even with the hybrid tools, it's still the AI doing the heavy lifting when it comes to strategy. Non-AI theorem solvers, again, don't have a spectacular record for churning out novel proofs to unsolved problems. Tools like Lean are more about mathematical rigour - a passive environment that requires a driver (a human or AI) to feed it actual strategies, lemmas, and proof steps. And no, you cannot brute force "strategy" in the vast majority of cases, which is, again, why automated theorem solvers don't have much of a track record with unsolved mathematical problems.

Let's take a random example: the disproof of the unit distance conjecture. It was solved purely by a general purpose commercial GPT model, not custom-trained to mathematics, with no external tools. Read what the various mathematicians reviewing / commenting on it have to say (sections #3 and onward). Seriously, don't skip reading them, actually read them. This was one of Erdos's favourite problems. He mentioned it commonly in his lectures. Essentially every mathematician working in complex geometry has thought about this problem. The approach that the model came up with was highly novel approach, based on CM-fields and class field towers.

I know you don't want to accept this reality, but it is the reality, so you better improve your ability to accept it,. The field of mathematics is already doing so.

Comment Re: Wait...? (Score 2) 100

I would say that any kind of substantial level of investment in a jurisdiction is a reasonable indicator of an expectation of a return on investment, and thus confidence in the economic growth of at least some industries in that jurisdiction. I'm not sure why people are trying to hand wave away that kind of an indicator, unless the fact of it creates some problem for some narrative they have bought into, creating a level of cognitive dissonance necessitating peculiar denials.

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