Ciro Santilli @cirosantilli 34

The proper precise definition of mathematics can be found at: Section "Formalization of mathematics".

The most beautiful things in mathematics are described at: Section "The beauty of mathematics".

Survey by Ciro Santilli: math.stackexchange.com/questions/1985/software-for-drawing-geometry-diagrams/3938216#3938216

Many plotting software can be used to create mathematics illustrations. They just tend to have more data-oriented rather than explanatory-oriented output.

The musical study of software engineering.

Ciro Santilli is obsessed by those in order to learn any new concept, not just for bug reporting.

This includes to learn more theoretical subjects like physics and mathematics.

Good Portuguese overview: www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172017000300301&lng=pt&tlng=pt

A fantastic sounding full time 4-year course that any student could transfer to called that teaches various natural science topics, notably mathematics, physics, chemistry and molecular biology.

Many past students Ciro talked to however share a common frustration with the course: in the first 2 years at least, the "basic cycle", you have infinitely many courses, and no time to study, and no choice of what to study, it is only in the latter 2 years (the advanced cycle) that you get the choices.

Also, if you get low grades in a single subject, your out. And exams are useless of course.

Here's a Quora question in Portuguese about the course: pt.quora.com/Como-funciona-o-tal-do-curso-secreto-da-USP, the only decent answer so far being: pt.quora.com/Como-funciona-o-tal-do-curso-secreto-da-USP/answer/Victor-Soares-31. Very disappointing to hear.

On the advanced cycle, you have a lot of academic freedom. You are basically supposed to pick a research project with an advisor and go for it, with a small amount of mandatory course hours. Ciro was told in 2022 that you can even have advisors from other universities or industry, and that it is perfectly feasible to take courses in another university and validate the course hours later on. Fantastic!!!

Students from the entire University of São Paulo can apply to transfer to it only after joining the university, with the guarantee that they can go back to their original courses if they don't adapt to the new course, which is great!

Not doing it is one of Ciro Santilli's regrets in life, see also: don't be a pussy.

Around 2007, they were in a really shady building of the University, but when Ciro checked in 2021, they had apparently moved to a shiny new entrepreneurship-focused building. Fantastic news!!!

This place has one of the best changes of spawning the first Brazilian Nobel Prize or unicorn.

One of the Brazilians who came to École Polytechnique together with Ciro was from this course. The fact that he is one of the most intelligent people Ciro knows gave further credit to that course in his eyes.

Techniques to get numerical approximations to numeric mathematical problems.

The entire field comes down to estimating the true values with a known error bound, and creating algorithms that make those error bounds asymptotically smaller.

Not the most beautiful field of pure mathematics, but fundamentally useful since we can't solve almost any useful equation without computers!

The solution visualizations can also provide valuable intuition however.

Important numerical analysis problems include solving:

Some possible/not possible sources that could be used to manually bootstrap content:

Existing lecture notes by students:

Lecture note upload website:

Exams uploads:

Mission: to live in a world where you can learn university-level mathematics, physics, chemistry, biology and engineering from perfect free books that anyone can write to get famous.

Live website: ourbigbook.com

Further information and rationale: Section "OurBigBook.com"

The project's mission is one of, or perhaps the most important, life objective of Ciro Santilli. Reproductive goals aside. These two types of goal are incommensurable. This is one of the great challenges of life.

This is ongoing project.

Ciro's goals in advertising this half done project are is partly to obtain some feedback, and partly to give the idea to someone else who might help push it further, be it in this stack or not.

Better editing support is a must, likely WYSIWYG.

But besides that, it is already in broad strokes the best approach Ciro Santilli can come up with to try and reach the mission statement only with technical advances, i.e. without large amounts of money or political influence which Ciro Santilli does not have.

Maybe that website isn't enough of a technical advance to reach its mission. Maybe there is some further not yet imagined technical insight that would push it into viability. Maybe not. But one must try. Only God can know the answer to these questions.

As of 2022, Ciro has spent about 2.5 years full time working on this project. First he spent about 1 year in 2014 on the first iteration: github.com/booktree/booktree, a GitLab fork, but then decided it was not the way to go.

Then around 2021 he put in some more 1.5 year of full time work, now with a possibly overly complicated (or perhaps just insane/immature) Next.js/Sequelize from scratch website stack.

It makes Ciro a bit ashamed to see that "so little user visible stuff was achieved in so much time". It is partly because he and many people underestimate the difficulty of web development. Perhaps there were some bad stack/useless feature choices issues. And a good dose of indulging in studying the natural sciences to bootstrap content and have fun. But really trying is the only way to learn.

Physics (like all well done science) is the art of predicting the future by modelling the world with mathematics.

And predicting the future is the first step towards controlling it, i.e.: engineering.

Ciro Santilli doesn't know physics. He writes about it partly to start playing with some scientific content for: OurBigBook.com, partly because this stuff is just amazingly beautiful.

Ciro's main intellectual physics fetishes are to learn quantum electrodynamics (understanding the point of Lie groups being a subpart of that) and condensed matter physics.

Every science is Physics in disguise, but the number of objects in the real world is so large that we can't solve the real equations in practice.

Luckily, due to emergence, we can use uglier higher level approximations of the world to solve many problems, with the complex limits of applicability of those approximations.

Therefore, such higher level approximations are highly specialized, and given different names such as:

As of 2019, all known physics can be described by two theories:

Unifying those two into the theory of everything one of the major goals of modern physics.

Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).

Learning it is one of Ciro Santilli's main intellectual fetishes.

While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...

The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!

Experiments: quantum electrodynamics experiments.

Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.

Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?

As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):

That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.

QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.

Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:

Where Sylvain Poirier dumps his mathematics and physics brain.

Notably, given the domain name, it is clear that he likes formalization of mathematics-stuff, like Ciro Santilli.

At first glance, looks a bit dry though, not many examples.

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:

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.

To do this, Ciro wants to work in parallel both on:

Ciro believes that this rare combination of both:produces a virtuous circle, because Ciro:

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:

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:

In addition to all of this, financial support also helps Ciro continue his general community support activities:

Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md

The most beautiful things in mathematics are results that are:

Good lists of such problems Lists of mathematical problems.

Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.

Ciro once commented that the best game is an infinitely hard one, where you can progress infinitely. To which his great friend J. replied:Or more broadly, one may argue that the perfect video game is life itself, or difficult life goals like making money, becoming famous or changing the world.

Thinking about it, "infinitely hard" is perhaps not a very precise term, as it could be interpreted as impossible. And if you have mathematical proof that something is impossible, it would be "pointless" to try, trying would be equivalent to pure meditation.

Maybe a better way to put it would be in terms of a difficulty curve. Real life also involves a lot of waiting, either for some experiment to finish running, of for you mental energy to restore a bit.

But so be it, you get the idea.

But this is basically what Ciro feels on every video game. It happens too often on PVE games that things are is either:

Not to mention the incredible breach of suspension of disbelief of most PvE games where enemies are unbelievably stupid. E.g., why doesn't Bowser just build one fucking wall 15 tiles high to prevent Mario from coming through to his castle? And then put a gate and a hundred guards in front of it? TODO there was a YouTube video of this, I think it was Toad pointing it out to Mario that it is quite weird that Bowser is so stupid, it almost feels like he wants to be beaten.

Everyone is beginner when the field is new, and there is value in tutorials written by beginners.

For example, Ciro Santilli felt it shocking how direct and satisfying Richard Feynman's scientific vulgarization of quantum electrodynamics were, e.g. at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), and that if he had just assumed minimal knowledge of mathematics, he was about to give a full satisfactory picture in just a few hours.

Other supporters of this:

When Ciro Santilli first learnt the old Zermelo-Fraenkel set theory and the idea of formal proofs, his teenager mind was completely blown.

Finally, there it was: a proper and precise definition of mathematics, including a definition of integers, reals and limits!

Theorems are strings, proofs are string manipulations, and axioms are the initial strings that you can use.

Once proved, press a button on your computer, and the proof is automatically verified. No messy complicated "group of savants" reading it for 4 years and looking for flaws!

There are a few proof assistant systems with several theorems in their Git tracked standard library. The hottest ones circa 2020 are:

And here are some more interesting links:

However, as expressed by the QED manifesto, is unbelievable that there isn't one awesome and dominating website, that hosts all those proofs, possibly an on the browser editor, and which all mathematicians in the world use as the one golden reference of mathematics to rule them all!

Just imagine the impact.

Standard library maintainers don't have to deal with the impossible question of what is "beautiful" or "useful" enough mathematics to deserve merged: users just push content to the online database, and star what they like!

We then just use GitHub-like namespaces for each person's theorem, e.g. "cirosantilli/fundmaental-theorem-of-calculus" or "johndoe/fundmaental-theorem-of-calculus" so that each person owns their own preferred definition IDs, which others can reuse.

No more endless bikeshedding over what insane level of generality do your analysis theorems need to be (Ciro Santilli attended at talk about Lean where the speaker mentioned this was a problem)!

This would move things more out of the "pull request and Git tracked code" approach, into a more "database with entries" version of things.

Furthermore, it is just a matter of time until the "single standard library" approach starts to break down, as the git clone becomes impossibly large. At this point, people have to start publishing separate packages. And when this happens, you would need to retest every package that you add to your project. This is why a centralized database is just inevitable at some point, it just scales better.

Interested in a conjecture? No problem: just subscribe to its formal statement + all known equivalents, and get an email on your inbox when it gets proved!

Are you a garage mathematician and have managed to prove a hard theorem, but no "real" mathematician will read your proof because your unknown? Fuck that, just publish it on the system and let it get auto verified. Overnight fame awaits.

Notation incompatibility hell? A thing of the past, just automatically convert to your preferred representation.

Such a system would be the perfect companion to OurBigBook.com. Just like computer code offers the backbone of Linux Kernel Module Cheat Linux kernel tutorials, a formal proof system website would be the backbone of mathematics tutorials! You know what, if OurBigBook.com becomes insanely successful, Ciro is going to add this to it later on.

Furthermore, it would not be too hard to achieve this system!

All we would need would be something analogous to a package registry like PyPI or NodeJS' registry.

Then, each person can publish packages containing proofs.

Packages can rely on other packages that contain pre-requisites definition or theorem.

Packages are just regular git repos, with some metadata. One notable metadata would be a human readable description of the theorems the package provides.

The package registry would then in addition to most package registries have a CI server in it, that checks the correctness of all proofs, generates a web-page showing each theorem.

All proofs can be conditional: the package registry simply shows clearly what axiom set a theorem is based on.

This is a close as we can get to Erdős' book.

Maybe Ciro will just stuff this into OurBigBook.com once that takes over the world.

This project could be seen as a more automated/less moderated version of ProofWiki.

Bibliography:

This mini-project walks the category hierarchy Wikipedia dumps and dumps them in various simple formats, HTML being the most interesting!

Scripts used: