Session reports of the Royal Prussian Academy of Sciences at Berlin Updated 2025-07-01 +Created 1970-01-01
Publications by the Prussian Academy of Sciences.
Links to their publications: de.wikisource.org/wiki/Sitzungsberichte_der_K%C3%B6niglich_Preu%C3%9Fischen_Akademie_der_Wissenschaften_zu_Berlin
Notable papers:
www.youtube.com/watch?v=-jIZ3bH-rAE "Illuminating biology at the nanoscale and systems scale using single-molecule and super-resolution imaging" by Xiaowei Zhuang (2017)
One of the most beautiful things in mathematics are theorems of conjectures that are very simple to state and understand (e.g. for K-12, lower undergrad levels), but extremely hard to prove.
This is in contrast to conjectures in certain areas where you'd have to study for a few months just to precisely understand all the definitions and the interest of the problem statement.
Bibliography:
- mathoverflow.net/questions/75698/examples-of-seemingly-elementary-problems-that-are-hard-to-solve
- www.reddit.com/r/mathematics/comments/klev7b/whats_your_favorite_easy_to_state_and_understand/
- mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts this one is for proofs for which simpler proofs exist
- math.stackexchange.com/questions/415365/it-looks-straightforward-but-actually-it-isnt this one is for "there is some reason it looks easy", whatever that means
- superuser.com/questions/133082/what-is-the-difference-between-hyper-threading-and-multiple-cores/995858#995858
- stackoverflow.com/questions/680684/what-are-the-differences-between-multi-cpu-multi-core-and-hyper-thread/73405312#73405312
- unix.stackexchange.com/questions/88283/so-what-are-logical-cpu-cores-as-opposed-to-physical-cpu-cores/739296#739296
cat-v.org/ by Rob Pike, co-creator of Go, looong time Unixer, and some kind of leader of a 9p resurrection cult. That one's spicy. E.g.: harmful.cat-v.org/, Ciro's version: good and evil.
Technique to solve partial differential equations
Naturally leads to the Fourier series, see: solving partial differential equations with the Fourier series, and to other analogous expansions:
One notable application is the solution of the Schrödinger equation via the time-independent Schrödinger equation.
- buy some at a cryptocurrency exchange. This is the only viable way of obtaining crypto nowadays, since basically all cryptocurrencies require specialized hardware to mine.
- send it to a self hosted Bitcoin wallet without a full node, e.g. Electrum
- then send something out of the wallet back to the exchange wallet!
- convert the crypto back to cash
where:
- : matrix in the old basis
- : matrix in the new basis
- : change of basis matrix
When we have a symmetric matrix, a change of basis keeps symmetry iff it is done by an orthogonal matrix, in which case:
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