Lots of people like row houses. In places like New York and Boston, those sort of houses are in high demand. it turns out that lots of people want to live near other people and actually like the density. As for high population, we all benefit from the high population. More people mean more ideas, more comparative advantage, and more economies of scale, which translate into better standards of living in general. There's some point beyond which very high populations would cause standards of living to get worse, but we're not near that point, and given technological improvement, we're likely moving farther from that point.
Meanwhile, even if you put everyone into individual suburban homes, even with a lower population, you do tremendous environmental damage because suburbs spread out more, and because they require more roads, pipes and other infrastructure, they end up costing a tremendous amount of resources. Functionally, cities are often subsidizing the suburbs https://www.strongtowns.org/journal/2023-7-6-stop-subsidizing-suburban-development-charge-it-what-it-costs .
Yes, you do misunderstand. There are two different theorems frequently referred to as Godel's theorems which are closely related, but in this case, the relevant one you are referring to is the statement that says roughly that any axiomatic system which is strong enough to model the natural numbers must have statements that cannot be proved or disproved within that system. This is a rough summary of a somewhat subtle result. Note that one needs to be really careful about what one means by axiomatic system otherwise one could just take as one's axiomatic system all true statements. Also, although the theorem is normally phrased as needing to model Peano Arithmetic https://en.wikipedia.org/wiki/Peano_axioms one really only needs to model the much weaker Robinson arithmetic https://en.wikipedia.org/wiki/Robinson_arithmetic.
So, why isn't this relevant here? Well, the simplest reason is that empirically speaking, undecidable statements are in practice extremely rare. So the vast majority of the time, the existence of such statements being undecidable doesn't matter. We have good reason for thinking that as statements get very large, a positive fraction of all statements of a given length are going to be undecidable but this likely doesn't kick in until one is frequently looking at long, convoluted statements that humans don't normally think about https://mathoverflow.net/questions/4454/how-many-of-the-true-sentences-are-provable/7902#7902. So for math that we care about this doesn't really matter. But note that even when thinking about an undecidable statement, all the aspects of the problem are still in the problem itself, it just is that there may be no solution to the problem in the axiomatic system you care about. Closely connected to this last observation is the fact in so far as computers are limited by Godel's theorem, so are humans.
Does that help?
And while it is true that the United States is no condition for sainthood, Russia and China have been highly aggressive for their own aims. Russia has a long history of cutting off parts of neighboring countries. They took part of Georgia, they took Transnistria from Moldova, and they took Crimea from Ukraine. The Ukraine invasion is simply their most blatant version of that, a war of aggression to capture territory, of the sort that was common before the end of the 2nd World War. Putin has decided for his own reasons which are essentially to increase the size of Russia and make Russia larger to engage in this war.
In fact, this war is so blatantly a war of aggression that Putin started it when after Zelenskyy was elected. Zelenskyy is a native Russian speaker, and when he was elected, he was seen as someone who would be willing to work with Russia. In fact, many in the West were concerned he would be too pro-Russia. And even given that Russia still invased.
He plays down the idea that LLMs are about to come up with a game-changing new discovery. “I don’t think models are there yet,” he says. “Maybe they’ll get there. I’m optimistic that they will.” But, he insists, that’s not the mission: “Our mission is to accelerate science. And I don’t think the bar for the acceleration of science is, like, Einstein-level reimagining of an entire field.”
Notice the important part before the sentence; he's talking about "game-changing new discovery" not regular nuts and bolts of scientific work. And in at least some fields, we are seeing these used to accelerate work. He talks about in the article a bit. The article correctly notes that there's been inaccurate hype from his group in the past, including claiming to have solved open math problems where it really just found solutions in obscure literature. But it is important to note that there has been successful work using LLMs to do math, especially when the systems are paired with more traditional theorem proving software and proof checkers like Lean. There's a long list compiled on Mathoverflow of successful examples https://mathoverflow.net/questions/502120/examples-for-the-use-of-ai-and-especially-llms-in-notable-mathematical-developme and this list is now getting long enough and this is getting common enough that the Meta Mathoverflow has had discussion about stop expanding the list https://meta.mathoverflow.net/questions/6348/use-of-llms-in-notable-mathematical-developments. Right now, the most successful system seems to be Aristotle, which is a software which combines LLM style informal reasoning with automated proof checking.
Now, math has some major advantages over other fields here: all the content is in the paper. In a lot of other fields, raw data and the like is not in the papers. Moreover, the universe is weird and complicated, and LLMs cannot just run experiments. In contrast, in pure math, all the problem aspects are in the problem statement itself. I am pretty skeptical that LLMs will ever get to the point of making "Einstein-level" discoveries since by nature they are still working off their training data. Without some major breakthroughs, it seems like they will still be fundamentally limited. But we shouldn't use their lack of that ability to dismiss that they are being used now to do genuine novel work, and one shouldn't summarize articles in a way that suggests someone was saying something they were not.
Evolution is a million line computer program falling into place by accident.