There are several results that morally point in the direction of "you should expect endless rich beauty", but my favorite is this: You might naively worry that at some point we prove everything that's easy to describe, and we have to make up extremely complicated questions. And at that point, is it really that interesting to say that some 50 page contrived problem required some complicated theory to prove? However, we know this won't happen! If you take all questions of n characters, take the shortest proof of each, then look at the growth rate of the length of the longest such shortest proof, you find that the length must grow uncomputably quickly in n. Otherwise theorem proving would be computable by proof search, which would let you decide provability, thus a fortiori decide the halting problem. So, we must have a vast supply of very simple questions whose answers are spectacularly complicated. In practice, this is what we see, and the complexity seems to correspond to real richness! For example, as near as we know, the answer to "when does x^n y^n=z^n have solutions over Z?" is just massively incompressibly deep, requiring the development of extremely sophisticated tools. Likewise, "what can be said of a group that's finite and simple?" seems to just be a massively deep question. That simple questions can require thousands of pages of deep theory should be unsurprising in light of this "proof lengths must grow uncomputably quickly" result! And "grows uncomputably quickly" is an absolutely staggering growth rate. There is likely some short couple-paragraph question where resolving it would require you to develop one million pages of rich theory, beyond the intellect of any human.

The first large organism on land, Prototaxites, lived 400 million years ago and grew up to 3ft wide and 26 ft tall. Until this year scientists thought it was was some type of fungus, but a 2026 science paper says it's likely "an entirely extinct eukaryotic lineage"!!

I wonder if this algebra is finitely-generated? As in: can you derive every identity involving eml(x, y), 1, and free variables from a finite set of such identities?

Write a Python quine with a few hands tied behind your back: adam.scherl.is/static/quine-…

I've decided to be the change and live by the best standards: * SI units prefixes * UTC time * ASCII; no more emoji. * Anno Mundi (avoids BC / minus signs) but Gregorian month day * Driving on the left Proof I'm serious about this: It's been 5786-04-02 for 16 kiloseconds :-)

you've joked about a spherical cow, but have you thought about higher multipoles of a cow, thus the tetrahexacontapole cow, and the octacosahectapole cow? (figure showing 1, 2, 4, 8, 16, 32, 64 and 128-pole cow, and the full cow)

Longtermists: We need to engineer a breed of cats which will change color upon exposure to radiation, release them to the wild, then compose a ditty about these cats that will be so catchy as to be handed down for 10,000 years at least Musicians: on it boss Geneticists: what

I have on at least one occasion pulled money out of my wallet and handed it to someone for being a two-boxer, just to make a point about decision theory. I have never done this for one-boxers. (I'm a one-boxer tho)

"I flipped a coin. If heads, I planned to give one Claude instance this prompt. If tails, two instances. What probability do you assign to the proposition that the coin came up heads?"

This seems fine for measuring the relative impact of Claude (or LLMs in general) on different tasks/jobs/industries, but useless for measuring the fraction of human labor alleviated/displaced.