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In the books [1], pp. 41-42 and [2], p. 67, it is stated that his name (and patronymic) is Mikhail Mikhailovich, confirming Anatoly Kochubei's comment to Kostya_I's answer. References also state that he was born on the 26 of April 1910 in Moscow, laureated from (the then called) Leningrad University in 1936, become "aspirant" (aspirant in science) ...

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Charles Sanders Peirce is credited with the beth notation ℶ, first introduced in a December 1900 letter to Cantor. Apparently, this was then forgotten for half a century. I reproduce the relevant text from Gregory Moore's Early history of the generalized continuum hypothesis.

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He was a docent in charge of the Chair of Mathematical analysis in what is now North Ossetia State University in Vladikavkaz. At the time, the city was called Ordzhonikidze, and the university was a "pedagogical institute". Source. There's an e-mail address there (the one starting with kmatan); you probably can enquire if you are interested in ...

3

On the more applied side of things, I'm quite fond of the following (sub)title: Estimating the number of unseen species: A bird in the hand is worth $\log n$ in the bush

1

Gian-Carlo Rota was perhaps thinking about Matroid theory. His work is cited for example in the preprint "Matroid for algebraic geometers" by Eric Katz. If Grothendieck has known about lattices, he may have defined a cohomology theory for lattices. Gian-Carlo Rota actually defined homology groups for certain subsets, called cross-cuts, of a lattice ...

5

I came to this post many years later, since I too was concerned about the absence of Riemann's formula in most texts, lengthy treatment in others, or reliance on more advanced techniques like Jacobi fields. I include here a direct concise proof which I think would be well suited for beginning students. We want to show that  g_{ij}(x)=\delta_{ij}+\frac{1}{3}...

1

I recently found the YouTube channel of the university of Uppsala (Uppsala Algebra : https://www.youtube.com/channel/UCPWnhR29VHTAk7rZUEDQdDQ/playlists) It contains mostly courses by Walter Mazorchuk on representation theory of finite groups, Lie algebras and the category O (and on linear algebra which if of less interest for me) and a course on commutative ...

1

Here are video lectures from Taiwan Mathematics School; some of them were delivered in Mandarin: https://sites.google.com/view/tms-home/media-archive?authuser=0 The following courses (all in Mandarin) were taught by Professor Chen-Yu Chi at National Taiwan University: Calculus 1 & Calculus 2. The topics in these courses are more like "advance ...

3

Having read his name among the commenters, I thought I ought to mention his theorem: Monsky's theorem is proved using valuations from algebra.

1

Niels Abel surely deserves a mention here. Mario Livio gives a detailed account of his and Galois' lives, but unfortunately not of their mathematical results, in The equation that couldn't be solved. Abel came from a very poor background and was always short of money. The Norwegian government gave him money to travel Europe to meet Gauss and other prominent ...

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