Ciro Santilli @cirosantilli 37

A wiki that gathers mathematical proofs.

URL: proofwiki.org/wiki/Main_Page

MediaWiki-based.

This appears to be the creator: github.com/externl "Joe George".

A generalized definition of derivative that works on manifolds.

TODO: how does it maintain a single value even across different coordinate charts?

Harvard University + MIT combo.

As of 2022:Fuck that.

Also, they have an ICP.

November 2023 course search:

It is a shame that they refocused to more applied courses. This also highlights their highly "managed" approach to content creation. Their 2022 pitch on front page says it all:they are focused on the highly paid character of many software engineering jobs.

But one cool point of this website is how they hire tutors to help on the courses. This is a very good thing. It is a fair way of monetizing: e-learning websites must keep content free, only charge for certification.

We define it as a linear map where the domain is the same as the image, i.e. an endofunction.

Examples:

Solving differential equations was apparently Lie's original motivation for developing Lie groups. It is therefore likely one of the most understandable ways to approach it.

It appears that Lie's goal was to understand when can a differential equation have an explicitly written solution, much like Galois theory had done for algebraic equations. Both approaches use symmetry as the key tool.

Ciro Santilli believes that molecular biology technologies will be a large part of the next big things as shown at: Section "Molecular biology technologies".

Bibliography:

Advantages over Riemann:

The laplace operator for Minkowski space.

Can be nicely written with Einstein notation as shown at: Section "d'Alembert operator in Einstein notation".

Ciro Santilli's favorite music genre.

Ciro's 2020 perfect Friday evening: jazz fusion + study quantum field theory on an Amazon Kindle. Ahhhhhh.

If any of you ever read this, do send me an email to Ciro Santilli saying hi and we can agree on a clear separation of usernames.

Although if you are just starting out, maybe you should just go from scratch with a unique Internet alias.

A younger unrelated Argentinian homonym who likes soccer that can be found through Google:Ciro used to like playing soccer too! :-)

www.ancestry.com.au/genealogy/records/ciro-santilli-24-bkmssg documents a "Ciro Santilli" born 31 Jan 1887 at Castelvécchio in Subéquo, L'Aquila, in the Abruzzo region, just like Ciro Santilli's ancestors. Parents Francesco Santilli and Anna Silveri. The page also mentions:

Unknown:

Whenever you make a change to your material, people should still be able to access the previous version.

Maybe there was something in the previous version that they needed, and you just removed.

Git + GitHub is the perfect way to do versioning.

This is the only way to truly understand and appreciate the subject.

Understanding the experiments gets intimately entangled with basically learning the history of physics, which is extremely beneficial as also highlighted by Ron Maimon, related: there is value in tutorials written by early pioneers of the field.

"How we know" is a basically more fundamental point than "what we know" in the natural sciences.

In the Surely You're Joking, Mr. Feynman chapter O Americano, Outra Vez! Richard Feynman describes his experience teaching in Brazil in the early 1950s, and how everything was memorized, without any explanation of the experiments or that the theory has some relationship to the real world!

Although things have improved considerably since in Brazil, Ciro still feels that some areas of physics are still taught without enough experiments described upfront. Notably, ironically, quantum field theory, which is where Feynman himself worked.

Feynman gave huge importance to understanding and explaining experiments, as can also be seen on Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).