Welcome to my digital garden. Here I share informal mathematical notes, historical curiosities, solutions to interesting problems, and personal reflections on academic life.
While exploring the distribution of primes modulo 4, I stumbled upon a visual pattern that seems to appear when plotting the gaps. Is it a mere coincidence of small numbers or something deeper? Let's explore using Python and some heuristics.
Read ArticleBefore modern rigor established the rules of analysis, Euler manipulated infinite series with a fearlessness that would make a modern undergraduate blush. Here is a look at his original "proof" that $\sum 1/n^2 = \pi^2/6$.
Read ArticleThe path to research is rarely a straight line. After a gap year and working in industry, I realized that the chalkboard was calling me back. Here are my reasons for returning to the academy.
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