NEXP is nondeterministic exponential time, right? In that case we know that P /= EXPTIME by the time hierarchy theorem and EXPTIME is contained in NEXP. We also have a direct result that NP /= NEXP (reference given in https://complexityzoo.uwaterloo.ca/Complexity_Zoo:N#nexp).
You think it's bad now? Wait until you see what happens in 2026.
As many of you remember, the bottom dropped out of the US economy in 2008. As a result, many people delayed having children for a few years (or just decided not to). That means that the freshman class of 2026 is going to be significantly smaller than that of 2025, and that's going to shut down a large number of small and financially strapped colleges.
It's difficult to imagine exactly what's going to happen afterwards, but we can be confident that things will be different.
Concentration of measure. If you have a quantity that depends on a large number of random variables but not too strongly on any small subset of them, it tends to behave like a constant. That's the intuition behind the law of large numbers, the central limit theorem, a bunch of concentration inequalities, and model averaging.
Take a look at https://ocobook.cs.princeton.edu/OCObook.pdf, and in particular section 1.2. The online shortest path problem is a good example of an online optimization problem that's not related to machine learning.
This is nice to have. The classic reference on online learning is "Prediction, Learning and Games" but it's not ML focused and it predates pretty much everything on online convex optimization. I'm looking forward to seeing a more modern introduction.
2) The central limit theorem applies to the distribution of the sample average. It applies whenever the samples are iid and the second moment is finite. The fact that the samples are coming from a mixture of normals doesn't change that.
Not everyone starts a PhD right after undergrad. It'd be interesting to look at PhD students who started later in life and see how they take the program. Anecdotally, they have a lot of problems too.
The author of this article is a researcher in cognitive psychology specializing in education. He wrote a pop-sci book detailing how cognitive science explains what's wrong with school, and it's very much worth a read if you're at all interested in the topic. Link is https://www.amazon.com/Why-Dont-Students-Like-School/dp/0470....