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What is a gauge?: An article by the mathematician Terence Tao on the what a "gauge" really is. This, to my mind, is the clearest elucidation of what one means by a gauge "symmetry" not being a symmetry but a redundancy in description.
Some of the cute and amusing mathematical objects.
The Borewin integral: If there were a mathematical embodiment of a troll, it's gotta be this one!
The Aaronson Oracle: A stark reminder of how bad humans are at generating truly random sequences!
A topological proof of the infinitude of primes: Nothing more to say here...
Here is a mixed bag of articles that I have found myself returning to again and again over the years - some informative, and some just purely amusing:
There’s more to mathematics than rigour and proofs: Another one from Terry Tao's blog, on his view of how one learns mathematics, which I think applies quite well to theoretical physics as well.
In the beginning was the command line: An article by Neal Stephenson describing some of the early history of operating systems in his rather quirky way.
The 9 kinds of physics seminar: Haven't we seen 'em all!