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🔥 Top post: I'm not particularly practically minded, but I have a curiosity · 8 likes + reposts
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At the very least, I'm having some fun with AI.
Some interesting stories about some of the major figures in functional analysis linked below (open access even!). Surprisingly, I don't know much of the history of functional analysis despite being a (former) C*-algebraist. Maybe I should …
Within this book review is an interesting overview of recent history in the philosophy of mathematics, including a bit about the philosophy of mathematical explanations that I posted about before. https://www.tandfonline.com/doi/full/10.10…
When looking into philosophy of math, the main topics of the subject seem uninteresting from my point of view. But I recently read this paper which suggests that at least some recent ideas there may be of interest to a mathematician. This …
I wrote a little essay about my personal thoughts about the concept of mathematical stories on substack that I thought might be of some interest: https://minimalrho.substack.com/p/a-story-about-mathematical-storytelling
Today's AMS calendar puzzle was \[ \dfrac{\cot^3\left(\dfrac{\pi}{12}\right) - \tan^3\left(\dfrac{\pi}{12}\right)}{2} \text{ (round) }\]
I used a tangent half angle formula and brute forced the algebra to get \( 15\sqrt{3}\) which rounds …
The fact that the golden ratio does not have many good rational approximations is often stated as the reason why it's the "most irrational number," but I hope that this illustrates the opposite: having few good rational approximations is a…
Now let's turn to the golden ratio with Hurwitz's theorem: If x is irrational, then there exist infinitely many rational numbers such that \[| x - \frac{p}{q}| < \frac{1}{\sqrt{5}q^2}\]. Furthermore, the \(\sqrt{5}\) is optimal here, in th…
Notice that this Dirchlet's theorem characterizes the rationals as having only finitely many of approximations within this error. The intuition here (and proof for that matter) is that once our denominator reaches the actual denominator of…
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