For those who didn't follow it, it's not that it's a contact binary that is so neat in and of itself, it's that when they modeled it, they determined that, the collision that formed it was less than 5 meters per second (less than 11 mph / 18 kph). Like a parking lot fender bender, but with the cars being ~750 billion tonnes.

So you think that repeating Hitler's and Napoleon's mistake was a better idea? Damn. Sure, the Soviets got a shit-ton of weapons from the Allies, but all that did was move the defeat of Germany ahead a few years. Invading the largest country on Earth is never a good idea, especially when it consists of a population who has refused to submit to invaders EVER.

That horse left the barn years ago, our last presidential election pitted two candidates against each other who both swore to continue using US tax dollars to arm and fund a genocide.

There was a guy who did hard prison time and was put on the child predator list for life because he wrote a fictional story about it. Never underestimate the viciousness of puritans.

Yep, and it wasn’t even Sony, it was at a rival company that got bought out after the rootkit was made but before it became a scandal.

Yeah, there's two main problems:

1) People entering the wrong fields. For example, medicine really needs workers, at all levels, but not enough people are going into it.

2) Certain manual labour fields, like field work and home construction, because... well, I think we all know why there's a shortage of workers in those fields.

Well, they do say the Universe is expanding... now we know why - Galactic Sugar is everywhere.

They're desperately trying to keep the Chinese models out, but I doubt they'll be successful. Chinese AI is mostly outcome-based, they train a bot to wash dishes, a drone to recognize an insect infestation, or mining machinery to find and follow a vein, and equipment purchased from China is going to come with their AI baked in. Sure, they'll play with chatbots and AGI, but most of their work is devoted to actually accomplishing something besides stock manipulation. Once Chinese AI is seeded throughout the economy in machinery and devices more advanced systems are going to follow.

A lot of Asimov's subsequent stories were about end runs around the Three Laws, enabling robots to do things they shouldn't.

That's the normal outcome of a legal system run by and for lawyers. I was once added (without my permission) to a class action suit against Seagate. We "won" a coupon for $15 off our next Seagate drive of 500 mb or less (a month after Seagate had stopped producing 500mb drives). The lawyers made $5,000,000.

Ticket scalpers are overcharging for tickets? Say it isn't so! Inconceivable! /s

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.

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.

Dang, link didn't post.

Ah, good 'ol "Model Collapse" theory that people have been pounding on for years now, predicting an imminent collapse in model capabilities. How has that been working out for you?