Ciro Santilli @cirosantilli 34

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:

As Ciro has rambled infinitely at Section "University", the school system is hugely inefficient and a waste of time for everyone involved.

Instead, just use Section "OurBigBook.com" instead.

You can always learn pure theory later on for free or very cheap from books.

And above all, you can always learn software engineering later on for free, because the programming community is so much more open than any other so far, notably e.g. with Stack Overflow and GitHub, see also: Section "Ciro Santilli's Open Source Enlightenment". Ciro Santilli is trying to change that with OurBigBook.com, but don't hold your breath. But it is increasingly hard to understand why there isn't an university that forces teachers to publish all their notes and lecture videos (which should be mandatorily recorded) with a Creative Commons License, and then let anyone take whichever exams they want for a small fee or for free.

Actually, there is a good chance you will learn to program, like it or not, because chances are that you won't be able to find as decent a job doing anything else.

But there is one thing you cannot learn for free: laboratory work. Laboratory work is just too expensive to carry out outside of an institution.

Basically, if you don't do laboratory work in undergrad, you will very likely never be able to do so in your entire life.

Because laboratories are so rare and expensive, it is laboratories that put you in the best most unfair position at creating world changing deep tech startups, which is why when in doubt, choose the course that has the most experimental work. Yes, you won't be able to achieve those insanely concentrated equities of the early-Internet, as you will need more venture capital to run your company, but those days are over now, deal with it.

Because when this gets converted to a OurBigBook.com page, it will be easier for people to copy paragraphs/fork and write a canonical page about Ciro.

What do you do when creating a pull request? Do you say "I", which is not true because Ciro did not say that, or do you say "John Doe thinks" bla bla?

And because his name is awesome! :-) Just kidding.

This became a micro-meme in 4chan:Correction: cirosantilli.com is not Ciro Santili's resume. It is your life.

OMG they have that. Slightly slightly overlap with OurBigBook.com.

The venerable first wiki.

The pre-Eternal September feeling is palpable.

People could freely comment their thoughts and sign below, making it much closer to what Ciro Santilli wants OurBigBook.com to be. But with upvotes ;-)

Nothing can better encapsulate the nostalgia of early day Internet. Genius at times, banal at others, you will be forever in our hearts!