Algebra by Ciro Santilli 35 Updated +Created
Not to be confused with algebra over a field, which is a particular algebraic structure studied within algebra.
Applied mathematics by Ciro Santilli 35 Updated +Created
Mathematical notation by Ciro Santilli 35 Updated +Created
It is hard to decide what makes Ciro Santilli more sad: the usage of Greek letters, the invention of new symbols, or the fifty million alternative font styles used.
Only Chinese characters could be worse than that!
Mathematics bibliography by Ciro Santilli 35 Updated +Created
The best articles by Ciro Santilli by Ciro Santilli 35 Updated +Created
These are the best articles ever authored by Ciro Santilli, most of them in the format of Stack Overflow answers.
Ciro posts update about new articles on his Twitter accounts.
A chronological list of all articles is also kept at: Section "Updates".
Some random generally less technical in-tree essays will be present at: Section "Essays by Ciro Santilli".
Ciro Santilli's psychology and physiology by Ciro Santilli 35 Updated +Created
Ciro Santilli's energy throughout the day varies as follows:
  • morning: highest
  • 11AM: peak exercise performance
  • after lunch: brain death. Possibly due to Ciro's partial Spanish descent?
  • late afternoon and evening: can do some stuff
Ciro has low tolerance to sleep deprivation which makes him very irritable, and low ability to sleep if there is any light. It must have to do with those damned ganglion cell photoreceptors. On the other hand, Ciro Santilli's wife can sleep without any problems with some morning light! It is definitely genetic. Ciro conjectures that people from very Northern parts of the world must have a gene that allows them to sleep even if there is some light, while more equatorial people don't. Maybe: pubmed.ncbi.nlm.nih.gov/33049062/
Ciro has mild olfactory synesthesia for star anise (八角, bajiao), which is widely used in Chinese cuisine and makes Ciro think uncontrollably of the color blue. Ciro does not have any other known synesthesias. He is also prone to nerd sniping form time to time.
Ciro is a reptilian-like being with cold hands and feet and low blood pressure. For this reason he believes that he will die of cancer or some respiratory problem. If the Chinese government doesn't get him first that is. This also partly explains why Ciro is not a big fan of swimming.
Besides Chinese food, Ciro really likes eating fruits and roasted nuts, maybe partly because he was born in Brazil, and partly because of monkey nature, see his Chinese name. At home he is known as "水果大王" (the big king of the fruits). Ciro is also a sucker for yoghurt (natural without added sugars and full fat, fat-tree yoghurt is terrible, often eaten with fruits). Ciro's "favorite drink" could be tonic water with freshly squeezed lemon. Tied with fresh fruit juices. Chocolate-wise, although not a huge fanatic, a Lindt dark chocolate with whole hazelnut pieces bar will do the job.
Ciro does not like receiving or giving gifts on expected social situations like birthdays or Christmas. Ciro believes that every day is equally precious, and can be a day to give, be it through awesome open source software contributions, or if you find something that your friend will like
Ciro has some respiratory allergies. When he was around 5, he had relatively serious asthma crisis which scared his parents to death. Throughout his life, he appears to be allergic at an intermediate level to: mold or dust mites (or whatever it is that old books/pillows have), cats (itching on touch), hay fever (in May in the UK, likely grass pollen). But even outside of hayfever season, Ciro's nose is constantly either running in the cold, or often partially blocked while sleeping throughout the year. Ciro believes however that this also gives him higher resistance to viral infections, since it has been many many years since he had a cold/flu, and when everyone in the office is going down with it, he's just fine. Ciro wonders if his active immune system will actually kill off cancers early, which he ranks as his most likely causes of death, along with respiratory and gastro-intestinal problems. Ciro has low blood pressure and cannot get fat, so cardio vascular problems seem much less likely.
Ciro is generally democrat due to his high compassion level. He believes that politics is highly genetically determined, and that just like you enter a room full of people and immediately like some and dislike others, the same goes for politics. People just vote for whoever they want to see more of because their way of speaking makes them feel good. There is not rationality involved in it at all.
Ciro self diagnoses a slight graphomania in the early 2020's. This is largely what led him to create OurBigBook.com, and contribute to Stack Overflow. Literature Nobel Prize laureate Naguib Mahfouz also suffers from the condition however, so maybe good can also come out of it:
If the urge to write should ever leave me, I want that day to be my last.
When Ciro was quite young, maybe around 7-10, when he got very angry or sad for some stupid reason (bullying perhaps? Ciro forgot), he would have a psychosomatic manifestation: his spine would become visibly curved sideways (scoliosis). While writing this paragraph, Ciro Googled it, and found e.g. medium.com/@michaelrosen_94192/the-root-cause-of-scoliosis-5c461002b634 that describes:
The Root Cause of Idiopathic Scoliosis
It is proposed that Adolescent Idiopathic Scoliosis (AIS) is a condition created by emotional stress. Evidence is presented that unresolved emotional stress can cause unbalanced tensions in the fascia and growing muscles that gradually deform the spinal column.
so it is a somewhat well known thing! Incredible. Can you imagine the level of the passions that lead to such physical deformations? But of course, it was all for nothing.
Essays by Ciro Santilli by Ciro Santilli 35 Updated +Created
Artist by Ciro Santilli 35 Updated +Created
Comics by Ciro Santilli 35 Updated +Created
Music by Ciro Santilli 35 Updated +Created
Ciro Santilli took courses once upon a time, maybe that has influenced his passion? Ciro Santilli's musical education.
Sport by Ciro Santilli 35 Updated +Created
Ciro Santilli by Ciro Santilli 35 Updated +Created
Ciro Santilli is a male human software engineer and activist born in Brazil, Earth in 1989 AD.
Quick facts:
Other people with the same name are listed at Section "Ciro Santilli's homonyms".
Figure 1.
19th century illustration of the Journey to the West protagonist Sun Wukong
. Source.
Sun Wukong (孙悟空) is a playful and obscenely powerful monkey Journey to the West. He protects Buddhist monk Tang Sanzang, and likes eating fruit, just like Ciro. Oh, and Goku from Dragon Ball is based on him. His japanese name is "Sun Wukong" (same Chinese characters with different Japanese pronunciation) for the love. His given name "Wukong" means literally "the one who mastered the void", which is clearly a Dharma name and fucking awesome in multiple ways. This is another sad instance of a Chinese thing better known in the West as Japanese.
It is worth noting however that although Wukong is extremely charming, Ciro's favorite novel of the Four Great Classic Novels is Water Margin. Journey to the West is just a Monster of the Week for kids, but Water Margin is a fight for justice saga. Sorry Wukong!
Figure 2.
Ciro Santilli playing with a pipette at the University of Cambridge circa 2017
.
The photo was taken in an open event organized by the awesome Cambridge Synthetic Biology outreach group, more or less the same people who organize: www.meetup.com/Cambridge-Synthetic-Biology-Meetup/ and who helped organize Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it".
Taking part in such activities is what Ciro tries to do to overcome his lifelong regret of not having done more experimental stuff at university. Would he have had the patience to handle all the bullshit of the physical word without going back to the informational sciences? Maybe, maybe not. But now he will probably never know?!
Notice the orange high visibility cycling jersey under the lab coat, from someone who had just ridden in from work as fast as possible as part of his "lunch break". It is more fun when it is hard.
Figure 3.
Scribe Jean Miélot, 15th century
.
Ciro Santilli fantasises that he would have make a good scribe in the middle ages, partly due to his self diagnosed graphomania, but also appreciation for foreign languages, and his mild obsession with the natural sciences.
OurBigBook.com is Ciro's view of a modern day scriptorium, except that now the illuminations are YouTube videos.
Chill and eat your bread in peace comes to mind. A scribe, in a library, reading and writing the entire day in peace and quiet. The life!
The job of a Internet-age scribe is basically that of making knowledge more open, legally extracting it from closed copyrighted sources, and explaining your understanding of it to the wider world under Creative Commons licenses on the web. And in the process of greater openess, given a well organized system, we are able combine the knowledge of many diffferent people, and thus make things more understandable than any single/few creator closed source source could ever achieve.
Ciro once saw some cartoon on Wikipedia help pages of a turtle with a book in one hand, and typing into Wikipedia on its computer, TODO find it. That cartoon summarizes well the modern scribe life.
Another analogous version of this fantasy more in touch with Ciro's sinophily is the ideal of the Chinese scholar, notably including their stereotypical attributes such as mastery of the Four arts.
Figure 4.
Ciro Santilli piling boxes as a child
. A natural born engineer.
Home by Ciro Santilli 35 Updated +Created
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: 100k USD = I quit me job and work on it one year full time. Status: ~144k / 200k USD reached: 1st year locked-in, 2nd year stretch goal open at 200k USD. 1M USD = I retire and do it forever. How to donate: Section "Sponsor Ciro Santilli's work on OurBigBook.com".
I reached 100k USD after a 1000 Monero donation, so I quit my job for 1 year starting 1st June 2024 to solve as many STEM courses as I can from a world leading university to try and kickstart The Higher Education Revolution. If I reach 200k USD, then I'll do it for two years instead. A second year greatly improve chances of success: year one I solve a bunch of courses, year two I come guns blazing with the content and expand further.
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 https://raw.githubusercontent.com/cirosantilli/media/master/Ciro_Santilli's_learn_teach_apply_logo.png
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.
I offer:
My approach is to:
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:I am also generally interested in:
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".
Video 1.
Introduction to the OurBigBook Project
. Source.
Video 2.
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 3.
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 4.
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 5. 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.
Figure 3. . Source code: github.com/cirosantilli/x86-bare-metal-examples. Ciro's Linux Kernel Module Cheat is a closely related and much more important project that covers the Linux kernel and assembly language.
 -------------------------------------
|  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. .
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. .
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. .
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.
Video 9. . 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.
Figure 10.
Top view of an open Oxford Nanopore MinION
. Source. This is Ciro Santilli's hand on the Wikipedia article: en.wikipedia.org/wiki/Oxford_Nanopore_Technologies. He put it there after working a bit on Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it" :-) And he would love to document more experiments like that one Section "Videos of all key physics experiments", but opportunities are extremely rare.
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>
Test data 19 by Ciro Santilli 35 Updated +Created
Useful by Ciro Santilli 35 Updated +Created
Something is useful if it either:
  • makes money
  • creates novel knowledge, or present knowledge in a novel way, that others may find beautiful
Art trend by Ciro Santilli 35 Updated +Created
Algebraic geometry by Ciro Santilli 35 Updated +Created
Sensor by Ciro Santilli 35 Updated +Created
Exoticism by Ciro Santilli 35 Updated +Created
Video 1.
Emmenez-moi by Charles Aznavour (1968)
Source. The ultimate ode to exoticism.
Fan art by Ciro Santilli 35 Updated +Created

Unlisted articles are being shown, click here to show only listed articles.