In mathematics, a "classification" means making a list of all possible objects of a given type.
Classification results are some of Ciro Santilli's favorite: Section "The beauty of mathematics".
Examples:
- classification of finite simple groups
- classification of regular polytopes
- classification of closed surfaces, and more generalized generalized Poincaré conjectures
- classification of associative real division algebras
- classification of finite fields
- classification of simple Lie groups
- classification of the wallpaper groups and the space groups
This month included several exciting extremelly user visible web developments.
I can't help to feel how the speed of developments reflects my relative mastery of the stack, I'm very happy about how it went.
Why you should give money to Ciro Santilli by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
So that he can work full time on OurBigBook.com and revolutionize advanced university-level science, technology, engineering, and mathematics eduction for all ages.
Donating to Ciro is the most effective donation per dollar that you can make to:
- improve hardcore university-level STEM education for all ages
- help make every child into the next Nobel Prize/Fields Medal/deep tech unicorn co-founder
Ciro's goal in life is to help kids as young as possible to reach, and the push, the frontiers of natural sciences human knowledge, linking it to applications that might be the the next big thing as early as possible. Because nothing is more motivating to students than that feeling of:rather than repeating the same crap that everyone is already learning.
Hey, I can actually do something in this area that has never been done before!
To do this, Ciro wants to work in parallel both on:
- the multi-user website e-learning platform of OurBigBook.com
- creating amazing teaching content that motivates that platform, and that deeply interests Ciro, notably quantum mechanics and its related applications:
- quantum computing
- molecular biology
- condensed matter physics and chemistry
- slightly more theoretical stuff in somewhat related fields of:
- continue to dump his brain/research in areas Ciro has expertise in: software engineering and open source software
Ciro believes that this rare combination of both:produces a virtuous circle, because Ciro:
- proven passion and capability to learn and teach science, technology, engineering, and mathematics subjects
- proven programming skills, including web development
- wants to learn and teach, so he starts to create content
- then he notices the teaching tools are crap
- and since he has the ability to actually improve them, he does
As explained at OurBigBook.com and high flying bird scientist, Ciro is most excited to make contributions at the "missing middle level of specialization" that lies around later undergrad and lower grad education:But on that middle sweet spot, Ciro believes that something can be done, in such as way that delivers:in a way that is:
- at lower undergrad level, there is already a lot of free material out there to learn stuff
- at upper graduate level and beyond, too few people know about each specific subject, that it becomes hard to factor things out
- beauty
- power
- in your face, without requiring you to study for a year
- but also giving enough precision to allow you to truly appreciate the beauty of the subjectCiro's programming skills can also be used to create educational, or actually more production-like, simulations and illustrations.
Ciro believes that today's society just keep saying over and over: "STEM is good", "STEM is good", "STEM is good" as a religious mantra, but fails miserably at providing free learning material and interaction opportunities for people to actually learn it at a deep enough level to truly appreciate why "STEM is good". This is what he wants to fix.
The following quote is ripped from Gwern Branwen's Patreon page, and it perfectly synthesizes how Ciro feels as well:
Omar Khayyam also came to the Vizier... but not to ask for title or office. 'The greatest boon you can confer on me,' he said, 'is to let me live in a corner under the shadow of your fortune, to spread wide the advantages of Science, and pray for your long life and prosperity.'
In addition to all of this, financial support also helps Ciro continue his general community support activities:
- writing and updating his amazing Stack Overflow answers: Section "Ciro Santilli's Stack Overflow contributions"
- saving the world from the CCP: Section "Ciro Santilli's campaign for freedom of speech in China"
You can feel the marijuana flowing out of this one, it's just great.
Yet, all breakthroughs, comes from them, because the people who are crazy enough to believe they can change the world are the ones who actually do ;-)
How to deal articles:
- web.mst.edu/~lmhall/WhatToDoWhenTrisectorComes.pdf What To Do When The Trisector Comes by Underwood Dudley (1983)
- academia.stackexchange.com/questions/111413/what-is-the-best-way-to-deal-with-cranks/111414
- www.laphamsquarterly.org/roundtable/beware-cranks
Sometimes systems of Diophantine equations are considered.
Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.
The general problem is known to be undecidable: Hilbert's tenth problem.
The Pythagorean triples, and its generalization Fermat's last theorem, are the quintessential examples.
A polynomial with multiple input arguments, e.g. with two inputs and :as opposed to a polynomial with a single argument e.g. one with just :
All those dedicated applied mathematicians languages are a waste of society's time, Ciro Santilli sure applied mathematicians are capable of writing a few extra braces in exchange for a sane general purpose language, we should instead just invest in good libraries with fast C bindings for those languages like NumPy where needed, and powerful mainlined integrated development environments.
And when Ciro Santilli see the closed source ones like MATLAB being used, it makes him lose all hope on humanity. Why. As of 2020. Why? In the 1980s, maybe. But in the 2020s?
Ciro Santilli likes to learn astronomy a bit like he learns geography: go down some lists of "stuff that seems most relevant in some criteria to us!", possibly at different size scales e.g.:
There are unlisted articles, also show them or only show them.