I thought that I knew all the best English-language and German-language podcasts about Mathematics, but some days ago I've found two that are not only alternatives, but may also be better than the others! The first one is called "My Favorite Theorem", and it is accessible on the following link:
The other is called "Breaking Math", and it is found here (Maybe I knew the title of this one, but I could not access it on another location for dead links):
Maybe there will be more. Thus I'm going to listen to these podcasts (EDIT: except Breaking Math, as it is only accessible through service providers which prohibit use for commercial purposes), even if I did not plan to listen to new podcasts in 2025. Earlier I have also started to read free google books, and I first read about the history of Mathematics. As far as I remember, I read "A General History of Mathematics" by John Bossut in 2024, and I'm currently reading "A Short Account of the History of Mathematics" by W. W. Rouse Ball, and I like the latter more than the former, so I can recommend the latter (maybe it is best to read both). I've also read "A History of the Mathematical Theory of Probability" by I. Todhunter in 2025, but although it has broadened my horizons, it was not entirely intelligible to me, due to its complicated integrals and other things hard to understand. It did not make me feel like doing this kind of Mathematics, although I still had a takeaway: the St. Petersburg Paradox. Apart from these resources, I've also found a very good resource for Mathematics, which can be found here:
It has a similar licence as WikiPedia, so maybe these two are the best places to read about advanced Math. I especially liked the proof of Lagrange's Four Square Theorem here:
https://planetmath.org/proofoflagrangesfoursquaretheorem
Recently I was also interested in Symmetry Groups and Point groups in three dimensions, but it is still hard to understand for me, whether these theories prevent me from discovering such polyhedra that are highly symmetric, but yet unknown. After these articles, it seems to be harder to imagine that I will be able to discover anything new in this field. That's why I'm also turning part of my attention to Number Theory, first by solving easier exercises, e.g. from KÖMAL. By the way, I have also received an old Number Theory textbook for Christmas (translated to Hungarian from Russian).
By the way, after listening an episode of the "My Favorite Theorem" podcast about the Gauss-Bonnet Theorem, I have found (again) that my discovery that I mentioned earlier on this blog is already known as Descartes's Theorem on the "total defect" of a polyhedron. So this was a summary of my recent Math life.
About Writing, I have also some things to share. Nowadays there are less international essay contests for adults (with acceptable terms) than there were earlier, but maybe it's good to know that there may also be opportunities to publish works in journals, and the best articles in those journals may win prizes. I've found the "Royal Economic Society Prize" and the prizes of "The American Finance Association". Apart from these, I could also subscribe to the newsletter of the "Independent Social Research Foundation", maybe there will also be some good opportunity there.
"A Short Account of the History of Mathematics" by W. W. Rouse Ball mentioned, for example, a formula for Pythagorean triples that is easy to remember: (m²-n²)²+(2mn)²=(m²+n²)², or otherwise formulated, a²+b²=c² if a=m²-n², b=2mn, c=m²+n².
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