Ciro Santilli @cirosantilli 40 

Polynomial over a ring Updated 2025-07-16

The usual definition of a polynomial is over a field as shown at polynomial over a field.

However, there is nothing in the immediate definition that prevents us from having a ring instead, i.e. a field but without the commutative property and inverse elements.

The only thing is that then we would need to differentiate between different orderings of the terms of multivariate polynomial, e.g. the following would all be potentially different terms:

2 xx y + 2 x y x + 2 y xx + x 2 x y + x 2 y x + y 2 xx + xx 2 y + x y 2 x + y x 2 x + xx y 2 + x y x 2 + y xx 2

(1)

while for a field they would all go into a single term:

12 x^{2} y

(2)

so when considering a polynomial over a ring we end up with a lot more more possible terms.

If the ring is a commutative ring however, polynomials do look like proper polynomials: Section "Polynomial over a commutative ring".

Los Alamos From Below by Richard Feynman (1975) Updated 2025-07-16

Amazing talk by Richard Feynman that describes his experiences at Los Alamos National Laboratory while developing the first nuclear weapons.

Transcript: calteches.library.caltech.edu/34/3/FeynmanLosAlamos.htm Also included full text into Surely You're Joking, Mr. Feynman.

www.youtube.com/watch?v=uY-u1qyRM5w&t=2881s describes the computing aspects. Particularly interesting is the quote about how they used the typist secretary pool to emulate the IBM machines and debug their programs before the machines had arrived. This is exactly analogous to what is done in 2020 in the semiconductor industry, where slower models are used to estimate how future algorithms will run in future hardware.

Los Alamos From Below by Richard Feynman (1975)

Source.

From first principles Updated 2025-07-16

Frobenius theorem (real division algebras) Updated 2025-07-16

There are 3: real numbers, complex numbers and quaternions.

Notably, the octonions are not associative.

List of nuclear weapons Updated 2025-07-16

Polymerase chain reaction Updated 2025-07-16

This is an extremely widely used technique as of 2020 and much earlier.

If allows you to amplify "any" sequence of choice (TODO length limitations) between a start and end sequences of interest which you synthesize.

If the sequence of interest is present, it gets amplified exponentially, and you end up with a bunch of DNA at the end.

You can then measure the DNA concentration based on simple light refraction methods to see if there is a lot of DNA or not in the post-processed sample.

Even Ciro Santilli had some contact with it at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it", see: PCR!

One common problem that happens with PCR if you don't design your primers right is: en.wikipedia.org/wiki/Primer_dimer

Sometime it fails: www.reddit.com/r/molecularbiology/comments/1kouomw/when_your_pcr_fails_again_and_you_start/

Nothing humbles you faster than a bandless gel. One minute you’re a scientist, the next you’re just a pipette-wielding wizard casting spells that don’t work. Meanwhile, physicists are out there acting like gravity always behaves. Smash that upvote if your reagents have ever gaslit you.

and a comment:

PCR = Pray, Cry, Repeat

Politics of Europe Updated 2025-07-16

Poincaré sphere Updated 2025-07-16

A more photon-specific version of the Bloch sphere.

In it, each of the six sides has a clear and simple to understand photon polarization state, either of:

left/right
diagonal up/diagonal down
rotation clockwise/counterclockwise

The sphere clearly suggests for example that a rotational or diagonal polarizations are the combination of left/right with the correct phase. This is clearly explained at: Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)".

Lord of the Rings character Updated 2025-07-16

Loop (topology) Updated 2025-07-16

London Updated 2025-07-16

Yung Professional Move to London by Sans Beanstalk

. Source.

The sad thing is that the same author also has another accurate video criticizing British suburbia, so there's no escape basically in the UK: www.youtube.com/watch?v=oIJuZbXLZeY.

Video "Being a Dickhead's Cool by Reuben Dangoor (2010)" also comes to mind.

Video 2.

Werk by Sans Beanstalk

. Source.

LLVM IR vs C Updated 2025-07-16

List of version control systems Updated 2025-07-16

List of Stack Overflow users Updated 2025-09-09

Sponsor Ciro Santilli's work on OurBigBook.com / Progress updates Updated 2025-11-21

 Home Updated 2025-12-02

Check out: OurBigBook.com, the best way to publish your scientific knowledge. It's an open source note taking system that can publish from lightweight markup files in your computer both to a multi-user mind melding dynamic website, or as a static website. It's like Wikipedia + GitHub + Stack Overflow + Obsidian mashed up. Source code: github.com/ourbigbook/ourbigbook.

Sponsor me to work on this project. For 400k USD I will quit my job or not get a new job and work on OurBigBook full time for a second year to try and kickstart The Higher Education Revolution. Status: ~44k / 400k USD. At 4M USD I retire/tenure and work on open STEM forever. How to donate: Section "Sponsor Ciro Santilli's work on OurBigBook.com".

I first quit my job 1st June 2024 to work on the project for 1 year after I reached my initial 100k goal mostly via a 1000 Monero donation. For a second follow up year, I increased my requirement to 400k USD to give me more peace of mind as I'm destroying my career in the process. A second year greatly improve chances of success: on year one I improved my tech, on year two I want to come guns blazing to solve courses and get users.

Mission: to live in a world where you can learn university-level mathematics, physics, chemistry, biology and engineering from perfect free open source books that anyone can write to get famous. More rationale: Section "OurBigBook.com"

Explaining things is my superpower, e.g. I was top user #39 on Stack Overflow in 2023 ^[ref]^[ref] and I have a few 1k+ star educational GitHub repositories^[ref]^[ref]^[ref]^[ref]. Now I want to bring that level of awesomeness to masters level Mathematics and Physics. But I can't do it alone! So I created OurBigBook.com to allow everyone to work together towards the perfect book of everything.

My life's goal is to bring hardcore university-level STEM open educational content to all ages. Sponsor me at github.com/sponsors/cirosantilli starting from 1 $/month so I can work full time on it. Further information: Section "Sponsor Ciro Santilli's work on OurBigBook.com". Achieving what I call "free gifted education" is my Nirvana.

This website is written in OurBigBook Markup, and it is published on both cirosantilli.com (static website) and outbigbook.om/cirosantilli (multi-user OurBigBook Web instance). Its source code is located at: github.com/cirosantilli/cirosantilli.github.io and also at cirosantilli.com/_dir and it is licensed under CC BY-SA 4.0 unless otherwise noted.

To contact Ciro, see: Section "How to contact Ciro Santilli". He likes to talk with random people of the Internet.

https://raw.githubusercontent.com/cirosantilli/media/master/ID_photo_of_Ciro_Santilli_taken_in_2013.jpg

Besides that, I'm also a freedom of speech slacktivist and recreational cyclist. I like Chinese traditional music and classic Brazilian pop. Opinions are my own, but they could be yours too. Tax the rich.

Let's create an educational system with:

no distinction between university and high school, students just go as fast as they can to what they really want without stupid university entry exams
fully open source learning material
on-demand examinations that anyone can easily take without prerequisites
granular entry selection only for space in specific laboratories or participation in specific novel research projects

I offer:

online private tutoring for:
- any STEM university course
- passionate younger STEM students (any age) who want to learn university level material and beyond. Can your kid be the next Fields Medalist or Nobel Prize winner? I'm here to help, especially if you are filthy rich! I focus moving students forward as fast as they want on and on producing useful novel tutorials and results
Let your child be my Emile, and me be their Adolfo Amidei, and let's see how far they can go! I will help take your child:
- into the best universities
- into the best PhD programs
and achieve their ambitious STEM goals!
educational consulting for institutions looking to improve their STEM courses
- do you know that course or teacher that consistently gets bad reviews every year? I'll work with the teacher to turn the problem around!
- are you looking to create a consistent open educational resources offering to increase your institutions internationally visibility? I can help with that too.

My approach is to:

propose interesting research projects. The starting point is always deciding the end goal: Section "Backward design"
learn what is needed to do the project together with the student(s)
publish any novel results or tutorials/tools produced freely licensed online, and encourage the student to do the same (Section "Let students learn by teaching", digital garden)

For minors, parents are welcome to join video calls, and all interactions with the student will be recorded and made available to parents.

I have a proven track of explaining complex concepts in an interesting and useful way. I work for the learner. Teaching statement at: Section "How to teach". Pricing to be discussed. Contact details at: Section "How to contact Ciro Santilli".

I am particularly excited about pointing people to the potential next big things, my top picks these days are:

quantum computing
AGI research, in particular AI code generation, automated theorem proving and robotics
assorted molecular biology technologies

I am also generally interested in:

20th century physics, notably AMO and condensed matter
the history of science, and in particular trying to look at seminal papers of a field

Figure 1.

Ciro Santilli's amazing Stack Overflow profile

. Ciro contributes almost exclusively by answering question he Googles into out of his own need, and never by refreshing the newest question of big tags for low hanging fruit! More information at: Section "Ciro Santilli's Stack Overflow contributions".

Figure 2.
Ciro Santilli's Stack Overflow stats
. Further methodology details at: Figure "Ciro Santilli's Stack Overflow stats".

Linux Kernel Module Cheat presentation

The problem with education by Ciro Santilli

. Source. In this video Ciro Santilli exposes his fundamental philosophy regarding why Education is broken. This philosophy was the key motivation behind the failed OurBigBook Project.

Video 2.

Introduction to the OurBigBook Project

. Source.

Video 3.

OurBigBook Web topics demo

. Source. The OurBigBook topic feature allows users to "merge their minds" in a "sort by upvote"-stack overflow-like manner for each subject. This is the killer feature of OurBigBook Web. More information at: docs.ourbigbook.com/ourbigbook-web-topics.

Video 4.

OurBigBook dynamic article tree demo

. Source. The OurBigBook dynamic tree feature allows any of your headers to be the toplevel h1 header of a page, while still displaying its descendants. SEO loves this, and it also allows users to always get their content on the correct granularity. More information at: docs.ourbigbook.com/ourbigbook-web-dynamic-article-tree.

Video 5.

OurBigBook local editing and publishing demo

. Source. With OurBigBook you can store your content as plaintext files in a Lightweight markup, and then publish that to either OurBigBook.com to get awesome multi-user features, or as a static website where you are in full control. More information at: docs.ourbigbook.com/publish-your-content.

Video 6.

Top Down 2D continuous game with Urho3D C++ SDL and Box2D for Reinforcement learning by Ciro Santilli (2018)

Source. More information: Section "Ciro's 2D reinforcement learning games". This is Ciro's underwhelming stab at the fundamental question: Can AGI be trained in simulations?. This project could be taken much further.

Video 7.

Water Margin tribute to Chinese dissidents by Ciro Santilli (2022)

Source. Part of Ciro Santilli's campaign for freedom of speech in China, see also: cirosantilli.com/china-dictatorship/water-margin.

Figure 3.
Lenovo ThinkPad T430 running a BIOS hello world
. This uses Ciro Santilli's project x86 bare metal examples with source code at: github.com/cirosantilli/x86-bare-metal-examples

Video 8.

. Source. This project, with source code at: github.com/cirosantilli/linux-kernel-module-cheat, aims to be the perfect emulation setup to study and develop the Linux kernel, kernel modules, QEMU, gem5 as well as x86_64, ARM userland and baremetal assembly and more.

Video 9.

My Bitcoin inscription museum by Ciro Santilli

. Source. Introductory video to Section "Cool data embedded in the Bitcoin blockchain".

 -------------------------------------
|  Force of Will               3 U U  |
|  ---------------------------------  |
| |                  ////////////   | |
| |                ////() ()\////\  | |
| |               ///_\ (--) \///\  | |
| |        )      ////  \_____///\\ | |
| |       ) \      /   /   /    /   | |
| |    ) /   \     |   |  /   _/    | |
| |   ) \  (  (   /   / /   / \     | |
| |  / ) ( )  / (    )/(    )  \    | |
| |  \(_)/(_)/  /UUUU \  \\\/   |   | |
| .---------------------------------. |
| Interrupt                           |
| ,---------------------------------, |
| | You may pay 1 life and remove a | |
| | blue card in your hand from the | |
| | game instead of paying Force of | |
| | Will's casting cost.  Effects   | |
| | that prevent or redirect damage | |
| | cannot be used to counter this  | |
| | loss of life.                   | |
| | Counter target spell.           | |
| `---------------------------------` |
|                                     l
| Illus.  Terese Nelsen               |
 -------------------------------------

Code 1.

ASCII art of a Force of Will Magic: The Gathering card inscribed in the Bitcoin blockchain

.

Artist unknown, uploaded December 2014. Part of Section "Cool data embedded in the Bitcoin blockchain" where Ciro Santilli maintains a curated list of such interesting inscriptions.

This was a small project done by Ciro for artistic purposes that received some attention due to the incredible hype surrounding cryptocurrencies at the time. Ciro Santilli's views on cryptocurrencies are summarized at: Section "Are cryptocurrencies useful?".

Figure 4.
`YellowRobot.jpg`
. Source.
JPG image fully embedded in the Bitcoin blockchain depicting some kind of cut material art depicting a yellow robot, inscribed on January 29, 2017.
Ciro Santilli found this image and others during his research for Section "Cool data embedded in the Bitcoin blockchain" by searching for image fingerprints on every transaction payload of the blockchain with a script.
The image was uploaded by EMBII, co-creator of the AtomSea & EMBII upload mechanism, which was responsible for a large part of the image inscriptions in the Bitcoin blockchain.
The associated message reads:
Chiharu [EMBII's Japanese wife] and I found this little yellow robot while exploring Chicago. It will be covered by tar or eventually removed but this tribute will remain. N 41.880778 E -87.629210
This is one of Ciro Santilli's favorite AtomSea & EMBII uploads, as it perfectly encapsules the "medium as an art form" approach to blockchain art, where even non-novel works can be recontextualized into something interesting, here depicting an opposition between the ephemeral and the immutable.
At twitter.com/EMBII4U/status/1615389973343268871 EMBII announced that he would be giving off shares of that image on Sup!?, a Bitcoin-backed NFT system he was; making. In December 2023, he gave some shares of the robot to Ciro Santilli.

Figure 5.
2010 Wayback Machine archive of starwarsweb.net
.
This website was used as one of the CIA 2010 covert communication websites, a covert system the CIA used to communicate with its assets. More details at: Section "CIA 2010 covert communication websites".
Ciro Santilli had some naughty OSINT fun finding some of the websites of this defunct network in 2023 after he heard about the 2022 Reuters report on the matter, which for the first time gave away 7 concrete websites out of a claimed 885 total found. As of November 2023, Ciro had found about 350 of them.

Figure 6.
2010 Wayback Machine archive of noticiasmusica.net
.
This is another website that was used as one of the CIA 2010 covert communication websites. This website is written in Brazilian Portuguese, and therefore suggests that the CIA had assets in Brazil at the time, and thus was spying on a "fellow democracy".
Although Snowden's revelations made it extremely obvious to the world that the USA spies upon everyone outside of the Five Eyes, including fellow democracies, it is rare to have such a direct a concrete proof of it visible live right on the Wayback Machine. Other targeted democracies include France, Germany, Italy and Spain. More details at: USA spying on its own allies.
This investigative report by Ciro Santilli was featured on the Daily Mail after 404 Media reported on it in 2025.

Video 10.

How I found a Star Wars website made by the CIA by Ciro Santilli

. Source. Slightly edited VOD of the talk Aratu Week 2024 Talk by Ciro Santilli: My Best Random Projects about the CIA 2010 covert communication websites.

Figure 7.
Diagram of the fundamental theorem on homomorphisms by Ciro Santilli (2020)

Shows the relationship between group homomorphisms and normal subgroups.
Used in the Stack Exchange answer to What is the intuition behind normal subgroups? One of Section "The best articles by Ciro Santilli".

Figure 8.
Spacetime diagram illustrating how faster-than-light travel implies time travel by Ciro Santilli (2021)
Used in the Stack Exchange answer to Does faster than light travel imply travelling back in time?. One of Section "The best articles by Ciro Santilli".

Figure 9.
Average insertion time into heaps, binary search tree and hash maps of the C++ standard library by Ciro Santilli (2015)
Source. Used in the Stack Overflow answer to Heap vs Binary Search Tree (BST). One of Section "The best articles by Ciro Santilli".

Video 11.

Birch and Swinnerton-Dyer conjecture in two minutes by Ciro Santilli

. Source. Quick and direct explanation of the statement of the BSD conjecture for people who know basic university mathematics. This is one of the Millennium Prize Problems, and you will get a million dollars if you can solve it! This therefore falls in the Simple to state but hard to prove of Ciro Santilli's the beauty of mathematics aesthetics.

A quick 2D continuous AI game prototype for reinforcement learning written in Matter.js, you can view it on a separate page at cirosantilli.com/_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport. This is a for-fun-only prototype for Ciro's 2D reinforcement learning games, C++ or maybe Python (for the deep learning ecosystem) seems inevitable for a serious version of such a project. But it is cute how much you can do with a few lines of Matter.js!

HTML snippet:

<iframe src="_raw/js/matterjs/examples.html#top-down-asdw-fixed-viewport" width="1000" height="850"></iframe>

Education is broken Updated 2026-01-30

Once Ciro was at a University course practical session, and a graduate was around helping out. Ciro asked if what the graduate did anything specifically related to the course, and they replied they didn't. And they added that:

One has to put the bread on the table.

Even though Ciro was already completely disillusioned by then, that still made an impression on him. Something is really wrong with this shit.

Other people that think that the educational system is currently bullshit as of 2020:

Einstein, quoted in The New York Times, March 13 1949, p. 34:^[ref]
It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry.
Ron Maimon
Xavier Niel: fortune.com/2018/11/30/billionaire-xavier-niel/ "Want This Billionaire's Attention? Drop Out of School" (2018). He also created 42.
Year On
by Zach Caceres
- zach.dev/blog/unschooling-myself
- zach.dev/blog/mpc
Anand Raja submission "Students and Universities": publications.parliament.uk/pa/cm200809/cmselect/cmdius/170/170ii.pdf, www.linkedin.com/in/anandraja/.
xsrus.com/life-school-and-the-80-20-rule. Also GPA 2.0 linked from xsrus.com/ to xsrus.com/gpa-2.0 but down now
School rewards effort linearly [...]. Unlike school, the real world is nonlinear. By that, I mean most of what you do at work is a waste of time.
A Mathematician's Lament by Paul Lockhart www.maa.org/external_archive/devlin/LockhartsLament.pdf
www.learningforreal.org/ by Mary Ruth McGinn, a K12 teacher in the USA.
www.learningforreal.org/quotes/ quotes Elbert Hubbard:
School should not be preparation for life. School should BE life.
She's somewhat focused on the performing arts, but what she says applies basically equally well to the natural sciences. A talk: www.youtube.com/watch?v=ggYL9gQeVEk She talks about authentic learning.
www.youtube.com/watch?v=iG9CE55wbtY Do schools kill creativity? by Sir Ken Robinson (2017)
Erik Finman thinks school is broken
sociable.co/technology/silicon-valley-education-students-entrepreneurs/ Bringing Silicon Valley into Schools: How to Make Students Entrepreneurs of Their Own Education (2016)
hackeducation.com/2015/04/25/factory-model The Invented History of 'The Factory Model of Education' by Audrey Watters (2015)
www.forbes.com/councils/forbescoachescouncil/2025/04/17/the-ai-fear-factor-why-leaders-resist-and-how-to-move-forward/ The Single Best Idea for Reforming K-12 Education by Steve Denning (2011)