532 karma · joined September 21, 2011
They provide a bit of the satisfaction that finishing a good graduate math course homework set does.
A tiny bit from section 9:
> The 20th century can be divided roughly into two halves. I would think the first half has been dominated by what I call the "era of specialization," the era in which Hilbert's approach, of trying to formalize things and define them carefully and then follow through on what you can do in each field, was very influential. As I said, Bourbaki's name is associated with this trend, where people focused attention on what you could get within particular algebraic or other systems at a given time. The second half of the 20th century has been much more what I would call the "era of unification", where borders are crossed, techniques have been moved from one field into the other, and things have become hybridized to an enormous extent. I think this is an oversimplification, but I think it does briefly summarize some of the aspects that you can see in 20th-century mathematics.
Also state universities are where most of the public school teachers and administrators trained, so they probably deserve a little of the blame for the state of public schools.
Note that this varies by where you are. Locally, there is no health care crunch: it's easy to get a flu shot or other vaccine with no wait, and ICUs still have capacity despite a huge increase in cases. We're probably screwed in a few weeks since there's only about a 60% vaccination rate here and the most recent surge didn't start until maybe two weeks ago.
They constantly try to escape
From the darkness outside and within
By dreaming of systems so perfect that no one will need to be good.
https://giorgiocalderolla.com/wipr-faq.html#what-is-wipr-ext...
found here (articles by author Thomas Fallace): https://muckrack.com/thomas-fallace/articles
There's also the Julia Robinson Math Festival that's supposed to be good but I don't have first-hand experience.
Ideally, a Math Circle would could be good for some kids if your area supports one.
If N is the number of uniforms needed to have a sum bigger than 1, you can see that P(N>n)=P(S_n<1).
P(S_n<1) is not too bad to compute, or you can wikipedia it (Irwin-Hall distribution) to find the expression P(S_n<1)=1/n!
Combining the things, E[N]=sum(P(N>n),n=0..infinity)=sum(1/n!,n=0..infinity)=exp(1).