Ciro Santilli @cirosantilli 35

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:

This was THE craze thing in Brazil before Pokemon, it was shown from 1994 to 1997. In particular the collectible action figures! It was possibly more popular in Brazil than e.g. in the US: www.quora.com/Why-was-Saint-Seiya-so-popular-in-Brazil

The thing as quite violent, rated for 14-year olds, but no one gave a fuck, 7 yo Ciro was happily watching it. We protect children too much.

That series also had quite a religious feel to it (as obviously suggested by the series English name itself). It must also have been a great motivator to getting young kids into astronomy!

Ciro's favorite character was definitely Andromeda Shun. He was smart and thoughtful, and had the coolest most complex weapon: his chain whips. He's also a bit effeminate, with his pink clothing and a gentle way. Perhaps that is the reason for adult Ciro's mild fascination with the Andromeda Galaxy.

The English name is horrendous... the Portuguese/French name is so much better: Knights of the Zodiac! Saying this in English just reminded Ciro Santilli of the Zodiac Killer. But nevermind.

A cool thought: bacteria like E. Coli replicate every 20 minutes. A human replicates every 15 years. So how can multicellular beings possibly cope with the speed of evolution of parasites?

The answer is that within us, the adaptive immune system is a population of cells that evolves very quickly. So in a sense, within our bodies there is fast cell-level non-inheritable evolution happening daily!

He does lots of little experiments which is cool.

No research papers but has citations: www.yohei.me/publications which is cool.

The by far dominating DNA sequencing company of the late 2000's and 2010's due to having the smallest cost per base pair.

Illumina actually bought their 2010's dominating technology from a Cambridge company called Solexa.

To understand how Illumina's technology works basically, watch this video: Video 1. "Illumina Sequencing by Synthesis by Illumina (2016)".

The key innovation of this method is the Bridge amplification step, which produces a large amount of identical DNA strands.

By default, we think of polynomials over the real numbers or complex numbers.

However, a polynomial can be defined over any other field just as well, the most notable example being that of a polynomial over a finite field.

For example, given the finite field of order 9, $GP(3)$ and with elements $\{0,1,2\}$, we can denote polynomials over that ring aswhere $x$ is the variable name.

For example, one such polynomial could be:and another one:Note how all the coefficients are members of the finite field we chose.

Given this, we could evaluate the polynomial for any element of the field, e.g.:and so on.

We can also add polynomials as usual over the field:and multiplication works analogously.

How software engineers view science:

Ciro Santilli had once assigned this as one of Ciro Santilli's best random thoughts, but he later found that Wikipedia actually says exactly that: en.wikipedia.org/wiki/Reverse_engineering ("similar to scientific research, the only difference being that scientific research is about a natural phenomenon") so maybe that is where Ciro picked it up unconsciously in the first place.

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:

It is the norm induced by the complex dot product over ${\mathbb{C}}^2$:

The United Kingdom is a great place to cycle in general as there's plenty of small country roads and interesting new small towns to discover, perhaps much like the rest of Europe, as opposed to the United States, which likely has some huge infinitely long straight roads with a lot of nothing in between.

Of particular interest is the large amount of airfields and small air raid shelters in the fields, an ominous reminder of world war 2. The airfields are in various states, from functional military fields, many converted to civilian usage, some have barely any tarmac left but still see usage. And some were just completely abandoned and decayed and became recreation grounds and farms. The UK is therefore also a great place to be if you want to learn to fly as a hobby!

Good starting point:

Next, you want to decide about nice destinations to reach/go through, and these are good ideas to look into:

Ciro Santilli feels a bit like this guy:

One big divergence: obsession with translating every page into every language.

His Mathematics Genealogy Project entry: www.genealogy.math.ndsu.nodak.edu/id.php?id=56185

Old French website: spoirier.lautre.net/

singlesunion.org/ so cute, he's looking for true love!!! This is something Ciro often thinks about: why it is so difficult to find love without looking people in the eye. The same applies to jobs to some extent. He has an Incel wiki page: incels.wiki/w/Sylvain_Poirier :-)

What you see along a line or plane in a wave interference.

Notably used for the pattern of the double-slit experiment.

This is a good initiative. Since the government is incapable of doing shit in this area, individuals have to do it themselves.

They even have a scholarship program...: www.bolsas.gobrasa.org/

Many good albums, Ciro Santilli's favorites: