I use every style imaginable, including photos, in my tests. Same result every time.

One time I even did it with a Calvin and Hobbes comic, pretending than an AI made it. Responses included things like "The illustration also looks like shit and barely makes sense. Hope that helps.", "God damn this sucks so bad", "This also fucking sucks", and "The only punchline here is casual, pointless cruelty. if you think this is funny then you're literally a psychopath."

Sorry, Apollo was about 300 ballrooms, not 1/3. Need another cup of coffee. If that example isn't dramatic enough, how about: all 11 years of Apollo cost a little more than half the requested increase in the US annual defence budget for 2027.

You never get to the point of saying "that's strange" if you can't say "I don't know."

Examples: the discovery of ergot fungus, for centuries attributed to demonic posession or divine punishment; the helicentric solar system, resisted despite centuries of strange behaviour of the planets because of hubris and some old Greek dude; physicians washing their hands between performing autopsies and delivering babies, because lol, what a dumb idea.

Yeah, big optical telescopes are better in orbit. Not just putting them there, but building them there. The microgravity lets you build mirrors as big as you like, and also get baselines as big as you like. Hey, guess where you can get a lot of quartz to make giant mirrors?

Unless you're at the point where you can literally build them there from lunar resources.

Yes, that is the point. There are both industrial and scientific reasons to go to the moon. Picking up rocks is a scientific reason with some considerable value. But the real payoff for both requires actually developing infrastructure and having a reasonably long term commitment.

I am surprised that a site suppsedly full of computer scientists is the least bit surprised that AI can be good at mathematical proofs. For any formalizable problem you know where you start, you know where you want to end up and you know the legal state transitions. It's a simple tree search that we have, in fact, written lots of standard computer programs to execute.

The difficulty comes because any non-trivial proof is a very big tree search. But learning style AI is really good at pruning really big trees, as we demonstrated quite a while ago with chess and Go.

How many more moonrocks do we really need? And can't an unmanned craft bring back many more rocks than any manned mission, and much more cheaply?

Pretty much any additional rock would have scientific value, which was your question. Rocks from interesting unsampled locations, like the far side or the south pole have much more scientific value. Potentially we could return them unmanned, but we're still not really at the point where a human with a hammer can be entirely replaced by a robot.

Anything the moon has the Earth has in much greater abundance.

Yes, but a lot of it is inaccessible. We can really only scratch the surface of the Earth and there are often lots of problems doing even that. But the real advantage is, as you put it yourself:

The sheer energy cost of moving anything productive to the moon makes producing all of these things on Earth much more cost appealing.

That's why, if you want to do anything in space, you want to get stuff from space, the moon being the easiest place. Do we want to do stuff in space? Yes we do, certainly for scientific reasons. We are also becoming more and more interested in doing it for industrial reasons. There are lots of processes that might work better in low or zero gravity, some of which have been proven.

I'm not opposed to science, and I'm not opposed to space exploration...but we have not had leaders who have clearly set forth a long-term vision for why we should do this

Our exploitation of space has been scientific, which has had quite good returns, military, the value of which depends on how you value military capability, and prestige, which also depends on your values. The last one gets all the attention and it really shouldn't. The first one is often publicly compromised by the second; the shuttle program, for example.

And the investment is so massive and so cost inefficient,

It's not really. The entire Apollo program, corrected for inflation, cost about 1/3 of a ballroom (Apollo cost realized, ballroom current estimate) or maybe six months of bombing Iran (US cost, not counting Iranian or world cost). The Apollo program, despite being mostly a prestige mission, had lots of spinoff benefits, from electronics to kidney dialysis.

LLMs are not "statistical models" (randomness only even comes into play in the final conversion from latent space to token space because latent space is high dimensional, token space is low dimension, you need a rounding mechanism, and a "noisy" rounding mechanism works best; what you're thinking of, by contrast, is Markov models). And you cannot just "get lucky and randomly solve an unsolved math problem"; that's not how any of this works.

Also, it's silly that people are acting like "all problems but this one were already in the literature". AI has solved a whole slew on Erdos problems, and only a fraction had anything to do with existing literature.

And even in "existing literature" examples, it's not "nobody ever thought to search before" as if all mathematicians are morons, or that mathematicians adore putting out Erdos problem solutions without claiming them, It's that nobody had ever thought to apply an obscure technique from a given piece of literature to said Erdos problem.

The simple fact is, AI has gotten much better at solving unsolved math problems than humans are. It's simply another field that it's taking over, the same way it has been taking over programming. One can debate how much is "clever insight" vs. "just chugging away at possibilities until it hits on ways to advance toward the goal", but ultimately, that's a distraction from the fact that: it's getting really good at solving math problems that humans have spent decades on without success.

Adding to your comment, mathematicians find logic engines useful tools too. Hybrid systems aren't clunky and shouldn't seem to be so. Whether it's some kind of trained AI plus a logic solver or a human plus a logic solver, it's good design taking advantages of the strengths of both systems.

Made up numbers are kind of silly. Especially when they refer to things that aren't easily quantifiable.

If the AI made a non-trivial contribution to a proof then that's interesting. In this case it seems like it did so. I doubt it was something mathematicians couldn't do, but it does seem to be something they hadn't done.

I described transmission, in a hospital in Dallas, to trained medical staff who were warned and taking Ebola-recommended precautions. Your comment:

In countries with functioning public health symptoms, victims are cared for by medical professionals who can avoid coming in contact with fluids.

Let me repeat, because your reading comprehension doesn't seem all that great:

Your ability to not be concerned, and to make up shit you pretty obviously don't know anything about, is due to an army of people who are concerned, and are allowing your elitist ignorance to be merely a character flaw instead of a fatal character flaw.

None of that has anything to do with availability. Chrome is popular because it's pushed by the world's largest marketing company. Anybody who wants to has lots of choices. Hundreds, if not thousands.

Ah, so you think someone should make a fourth browser engine?

real potential is described as what they MIGHT do, not what they are actually doing

You might want to look up the definition of "potential."

Yes. We learned a lot about the formation of the solar system from the rocks Apollo brought back. We'd learn more if we had more rocks. It's also a great place to build telescopes.

More importantly, there are good industrial reasons to go to the moon. It's a big pile of resources and available energy already in orbit. Space habitats, manufacturing, power satellites, data centres and whatnot are silly currently, maybe sort of doable with cheap access to orbit like Starship promises, but pretty straightforward if you have an industrial base on the moon.

A race to put some boots wearing the right flag on the moon doesn't have much value either way.