Incoming links: Ciro Santilli
The beauty of mathematics Updated 2025-07-16
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:
- simple to state but hard to prove:
- Fermat's Last Theorem
- number of unknown rationality, e.g. is rational?
- transcendental number conjectures, e.g. is transcendental?
- basically any conjecture involving prime numbers:
- many combinatorial game questions, e.g.:
- surprising results: we had intuitive reasons to believe something as possible or not, but a theorem shatters that conviction and brings us on our knees, sometimes via pathological counter-examples. General surprise themes include:Lists:
- classification of potentially infinite sets like: compact manifolds, etc.
- problems that are more complicated in low dimensions than high like:
- generalized Poincaré conjectures. It is also fun to see how in many cases complexity peaks out at 4 dimensions.
- classification of regular polytopes
- unpredictable magic constants:
- why is the lowest dimension for an exotic sphere 7?
- why is 4 the largest degree of an equation with explicit solution? Abel-Ruffini theorem
- undecidable problems, especially simple to state ones:
- mortal matrix problem
- sharp frontiers between solvable and unsolvable are also cool:
- attempts at determining specific values of the Busy beaver function for Turing machines with a given number of states and symbols
- related to Diophantine equations:
- applications: make life easier and/or modeling some phenomena well, e.g. in physics. See also: explain how to make money with the lesson
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.
Am I achieving insight, or am I just memorizing definitions?
The best Caetano Veloso songs Updated 2025-07-16
Video 1. Alegria, Alegria by Caetano Veloso (1968)Source. Critique of Military dictatorship in Brazil.
- 1972
- Transa (1972) album. Literally: "The Fuck", good old seventies. Caetano himself later mentions that this is one of his own favorite albums.[ref] The album was composed when he was living in London.
Video 2. Triste Bahia by Caetano Veloso (1972)Source. Inspired by (or more likely: actually is) capoeira music.
Video 4. Você Não Entende Nada by Caetano Veloso (1970)Source.Amazing performance at Coliseu dos Recreios, Lisbon. 1981. Discogs says original album is Legal (1970), but wiki page and photos of back disagree...This song talks about a man's mixed desires to remain with his partner and also escape to adventure. It contains one of the most amazing sexual innuendo ever recorded: the man describes foods that his partner will serve him, and the he endlessly eats and eats and eats:translation:eu como, eu como, eu como, você [... huge intentional pause ...] não está entendendo quase nada do que eu digo.
which makes it unclear "you" is part of "I eat you" (to eat (comer) is a slang for fucking), or if "you" is part of the next sentence.I eat, I eat, I eat, you [... huge intentional pause ...] don't understand anything that I'm saying.
Video 5. Partido Alto by Caetano Veloso (1972)Source. Atheism song (theodicy)! Lyrics by Chico Buarque, but Ciro Santilli prefers this interpretation. From the 1972 "Caetano E Chico Juntos E Ao Vivo" joint album with Chico Buarque.
- 1975 Qualquer coisa album
Video 7. Samba e Amor by Caetano Veloso (1975)Source. Cover from original song by Chico Buarque, original album Chico Buarque de Hollanda - Nº4. Desperately reminds Ciro of his University day weekend nights. Except that there was no Samba. And little Amor. Mostly a silent and wholesome loneliness and emulation.Video 8. Georde de Capadócia by Caetano Veloso (1975)Source.Composed by Jorge Ben, but this interpretation is remarkable. corpo fechado (closed body) style song. This idea is much linked to Capoeira/African religion idea. E.g. a more traditional capoeira corpo fechado song: www.youtube.com/watch?v=tfd9j6XFmSg
- 1976 Doces Bárbaros (1976) album
Video 10. Um Índio by Caetano Veloso (1976)Source. Recording from 1992. Also appeared in the Bicho (1977) album. - 1977 Bicho (1977)
- 1978 album Muito (Dentro da Estrela Azulada)
Video 12. Sampa by Caetano Veloso (1978)Source."Sampa" is an affectionate slang for São Paulo City. The song perfectly captures the city, and reminds Ciro so badly of his University days there.Video 13. Terra by Caetano Veloso (1978)Source.Ciro used to watch a television nature show called "Planeta Terra" in the legendary TV Cultura with his parents in the couch when he was young, and under a duvet when it was a bit cold. Those days were the best. The narrator's lady voice was particularly soothing, and would easily put you in a kind of sleepy trance, her name is Valéria GrilloTODO what was the original show exactly? Here is a sample: www.youtube.com/watch?v=vNwfYEMdrRU Very likely just a translation of some British nature show with a custom Brazilian intro and presenter. Credits at end mention English narrator: "Eugene Fraser", and "Thirteen WNET Nature" production, which produced Nature (1982) that ran since 1982, making that a likely candidate. - 1980
- 1984 Velô (1984)
The best Gilberto Gil songs Updated 2025-07-16
Good selection: Acústico MTV - Gilberto Gil (1994).
- 1967 Louvação (1967) album
Video 1. Lunik 9 Gilberto Gil (1967)Source. Ciro Santilli prefers Elis Regina's interpretation however. - 1972 Expresso 2222 album.
Video 2. Expresso 2222 by Gilberto Gil (1972)Source. youtu.be/aSFahdu5ga8?t=4584 In the 2002 documentary Tempo Rei he explains the origin of the song as being based on seeing trains come by in Bahia, when they still existed before the automobile decimation. - 1975 Refazenda (1975) album. This album is just too Legendary. The cover is also legendary.
- Date unclear
Video 8. A Paz by Gilberto Gil (1967)Source. Performed 2009. The earliest recording we can find is from 1994: www.discogs.com/master/190615-Gilberto-Gil-Unplugged
The best personal webpages of all time Updated 2025-07-16
These are basically technically minded people that Ciro Santilli feels have similar interests/psychology to him, and who write too much for their own good:
- cat-v.org
- gwern.net. Dude's a bit overly obsessed with the popup preview though! "new Wikipedia popups (this 7th implementation enables recursive WP popups)" XD
- settheory.net by Sylvain Poirier
- HyperPhysics
- Orange Papers
Maybe one day these will also be legendary, who knows:
Another category Ciro admires are the "computational physics visualization" people, these people will go to Heaven:
Related:
Institution led:
- www.biology.arizona.edu/ The Biology Project
Other mentions:
- arngren.net/ lots of images of toys and gear with descriptions in Norwegian
The best popular Brazilian music (MPB) of all time Updated 2025-07-16
It is such a huge shame that you have to understand Portuguese to appreciate those songs... this is yet another great evil outcome of having more than one natural language is bad for the world.
The good songs stopped before of just after Ciro Santilli was born, they were originally heard by his parent's generation. Those young new kids are boring.
The place to start is definitely the Holy Trinity of popular Brazilian music:
- Caetano Veloso is arguably Ciro Santilli's favorite MPB artist, he has just too many amazing songs, best ones at: Section "The best Caetano Veloso songs"
- Chico Buarque. Ciro's second favorite.
- Gilberto Gil. Perhaps Ciro likes him third because he is the most lighthearted one, although not always: Section "The best Gilberto Gil songs"
Video 1. Preciso Me Encontrar by Cartola. Source. Present in the 1976 eponymous album though it is likely from much earlier.Video 2. Asa Branca by Luiz Gonzaga. Source. Translation: "White wing". Written in 1947Video 3. O vento by Dorival Caymmi (1949)Source. Translation: "The wind".Video 4. Panis et Circenses from the Tropicália: ou Panis et Circencis ()Source. Translation: "Bread and circuses", a famous Latin phrase. Composed by Gilberto Gil and Caetano Veloso and performed by Os MutantesVideo 5. Mistério do Planeta from the Acabou Chorare album by Novos Baianos (1972)Source. Translation: "The mystery of the planet".Video 6. "Senhor Cidadão" from the Se O Caso É Chorar album by Tom Zé (1972)Source. Translation: "Mr. Citizen". This is likely reference to Military dictatorship in Brazil-lingo. This is an anti-Military dictatorship in Brazil song, appears to reuse terms used by the dictatorship propaganda in the song.Video 8. Romaria by Renato Teixeira. Source."Romaria" is the name of a type of Catholic peregrination.Video 9. Metamorfose ambulante by Raul Seixas (1973)Source. Translation: "Itinerant metamorphosis". From the album Krig-ha, Bandolo!Video 10. Ouro de tolo by Raul Seixas (1973)Source. Translation: "Fool's gold". This dude should be a scientist. But well, he went for mystic/artist. Close enough.Video 11. Gita by Raul Seixas (1974)Source. "Gita" must be a reference to the Bhagavad Gita. From the album: Gita.Video 12. Maluco beleza by Raul Seixas (1977)Source. From the album O Dia em que a Terra ParouVideo 13. A telicidade by Tom Jobim (1958)Source. Translation: "Happiness". Composed for the Black Orpheus (1958) film. "Tristeza não tem fim, felicidade sim" (Sadness never ends, but happiness does). The movie itself is OK. Appeals to Ciro's Buddhist sensibilities.Video 14. Chega de saudade by Tom Jobim. Source. Translation: "Enough longing".Video 15. Jorge da Capadócia by Jorge Ben Jor (1975)Source. From the Solta o Pavão (1975) album. The Caetano interpretation is better however, poor Jorge.- Jair Rodrigues
Video 16. Disparada by Jair Rodrigues (1968)Source. This song is simply amazing. Not exactly MPB, a bit more towards country, but close enough. This was as the track of some soap opera.Video 17. Deixa Isso Pra Lá by Jair Rodrigues (1964)Source. Fantastic early example of early rap music!!! This is regocnized example at: www.youtube.com/watch?v=jfnDEuuPq4Q which builds upon the 1964 song. Amazing. An amazing live performance at: www.youtube.com/watch?v=O3E1uHdrJws, only not using that as the default link as it is not from the official channel. - Vinicius de Moraes. Many of his lyrics are poetry. Notably, he has some "children" songs that you think about as an adult and go "oh fuck". For some reason, Ciro can't help but think that he looks like a pedophile, but he doesn't have any scandals apparently, poor dude. He was a drunkard for sure though.
Video 20. Aquarela by Toquinho (1983)Source. This is a mega childhood hit, and it never gets old. Amazing. One of the most brutal memento moris ever?Video 21. Xô Saudade by Alceu Valença. Source. From the 1980 album "Coração Bobo"Video 25. Na Rua, Na Chuva, Na Fazenda by Hyldon (1974)Source. Translation: "On the Street, In the Rain, On the Farm".Video 26. Tudo o que você podia ser from the Clube da Esquina album by Milton Nascimento (1972)Source.Translation: "All that you could be".
The bullying of young Ciro Santilli Updated 2025-07-16
Ciro was even more stupid than as of 2020, and continued to try and hang out with those evil kids to show them he was cool too or that he was strong, and so continued to get hurt.
Advice to his children: stay away from evil people.
The bullied sometimes feels an almost masochistic desire to overcome the bullies' contempt, and to try and either become friends with the bullies, or to overpower them.
You must never give into those thoughts.
If you come across evil people, smile a fake smile to them, and walk away, but never give your back to them, and always be ready to fight.
If they laugh at you, know that you are shit like everyone else, pretend to laugh with them, take their post and repost it on your public profile, and silently stay away from those idiots.
Never show any weakness.
If a fight is likely, always be ready, always have your friends nearby, be as well armed as the enemy, and never be outnumbered.
On the Internet, never care about e-bully posts, either block them immediately, and anyone that likes their posts, or follow Ciro's reply policy.
Call parents or other authorities as soon as there is risk of physical harm. Better a living free pussy than dead or in youth detention for murder. Similar advice applies if you are going to jail I guess.
If a physical fight is inevitable however, ignore Jesus this once and don't give the other face, but rather follow the Talmud and fight all out on the beaches:References:
If someone comes to kill you, rise and kill first.
The Sikh knife, the Kirpan, which Sikhs must carry at all times as a religious obligation, also comes to mind. The Sikh must have been bullied out of the their minds at some point in history, Ciro understands.
Non-violence only works when you have bodies to spare from your followers.
Perhaps it was good to learn those lessons early, before the stakes were too high. Adults fake it much better, and therefore it is harder to learn those lessons from them, but they are still just as evil on the inside.
These experiences might have contributed to Ciro Santilli's self perceived compassionate personality.
The correlation between software engineers and Buddhism Updated 2025-07-16
Ciro Santilli believes that there is a positive correlation between being a software engineer and liking Buddhist-like things.
Maybe it is linked to minimalism and DRY, which software engineers value so greatly.
Even Ciro had to try an unoriginal Buddhist joke intro in one of this Stack Overflow answers.
Ciro also feels that his "minimal reproducible example" scientific language/concept learning method obsession of breaking things into tiny sub-problems has a strong link with Koans.
Some notable Buddhism/programmer examples:
- www.catb.org/~esr/writings/unix-koans/ "The Unix Koans of Master Foo - Rootless Root (无根的根)" by the legendary Eric Steven Raymond is notable
- thecodelesscode.com/ "The Codeless Code" by anonymous Qi.
- canonical.org/~kragen/tao-of-programming.html
- wiki.c2.com/?MysticalProgrammingKoans
- rubykoans.com/ even evil programming languages adopt them!
- The Zen of Python
Another thing that points the correlation out is the existence of wattsalan.github.io/ on a
github.io about Alan Watts. The Criterion Collection Updated 2025-07-16
The Entire Criterion Collection Supercut by Reckoned Opinions
. Source. Featured at: www.reddit.com/r/criterion/comments/13x14he/the_entire_criterion_collection_all_1190_spine/ Holy crap, how! The deplatforming of Donald Trump Updated 2025-07-16
Ciro Santilli believes that the Donald Trump bans were extremely unfair, and highlight the need for government to ensure greater freedom of speech in social media, more information at: cirosantilli.com/china-dictatorship/unjust-social-media-censorship-in-the-west, related: globalization reduces the power of governments.
The development cycle time is your God Updated 2025-07-16
New developers won't want to learn your project, because they would rather shoot themselves.
Of course, at some point software gets large enough that things won't fit anymore in 5 seconds. But then you must have either some kind of build caching, or options to do partial builds/tests that will bring things down to that 5 second mark.
A slow build from scratch will mean that your continuous integration costs a lot, money that could be invested in a new developer!
One anecdote comes to mind. Ciro Santilli was trying to debug something, and more experience colleague came over.
To reproduce a problem, ciro was running one command, wait 5 seconds, run a second command, wait 5 seconds, run a third command:
cmd1
# wait 5 seconds
cmd2
# wait 5 seconds
cmd3The first thing the colleague said: join those three commands into one:And so, Ciro was enlightened.
cmd1;cmd2;cmd3
The Employment Test Updated 2025-07-16
That's Ciro Santilli's favorite. Of course, there is a huge difference between physical and non physical jobs. But one could start with replacing desk jobs!
The Google Story Updated 2025-07-16
Has some good mentions, but often leaves you wanting more details of how certain things happened, especially the early days stuff.
Does however paint a good picture of several notable employees, and non-search projects from the early 2000's including:
- the cook dude
- porn cookie guy
- the unusual IPO process
Paints a very positive picture of the founders. It is likely true. They gave shares generously to early employees. Tried to allow the more general public to buy from IPO, by using a bidding scheme, rather than focusing on the big bankers as was usual.
The introduction mentions that Google is very interested in molecular biology and mining genetics data, much like Ciro Santilli! Can't find external references however...
Two of the most compelling areas that Google and its founders are quietly working on are the promising fields of molecular biology and genetics. Millions of genes in combination with massive amounts of biological and scientific data are an excellent match for the Google search engine, the tremendous database the company has in place, and its immense computing power. Already, Google has downloaded a map of the human genome and is working closely with biologist Dr. Craig Venter and other leaders in genetics on scientific projects that may lead to important breakthroughs in science, medicine, and health. In other words, we may be heading toward a time when people can google their own genes.
The book gives good highlight as to why Google became big: search was just an incredibly computationally intensive task. From very early days, Largey were already making up their own somewhat custom compute systems from very early days, which naturally led into Google custom hardware later on. Google just managed to pull ahead on the reinvest revenue into hardware loop, and no one ever caught them back. This feels more the case than e.g. with Amazon, which notoriously had to buy off dozens of competitors to clear the way.
Cover of The Google Story
. The Holy Trinity of popular Brazilian music Updated 2025-07-16
In Ciro Santilli's view, the following three artists form a Holy Trinity of popular Brazilian music:
Elis Regina is not far though.
Ciro remembers quite clearly when he was riding the car with his parents when he pre teen, and he could not understand why they seemed so obsessed with The Trinity et al. Ciro in particular remembers listening to Video "Refazenda by Gilberto Gil (1975)". They had picked it up of course from the 70's and 80's when they were younger.
Young Ciro would also always confuse who was whom from the three of them.
Then Ciro got older, and he understood, they are mind blowing. You do have to look back in time a bit though, lots of lukewarm stuff on later periods. The military dictatorship in Brazil was good for music.
The ideal university Updated 2025-07-16
This is Ciro Santilli's ideal university system. It is a system that actually lives up to the name "Open University":
- no enrolment, no prerequisites. Exam as a service examination style, likely free to anyone who wants to take them, only to determine:
- who gets to use physical facilities, notably laboratories
- which students do you want to pick as apprentices/workers/PhDs
- no tuition fees: free gifted education
- school must offer free accommodation for students
- force teachers to publish their teaching material with an open license
- how to teach
Related:
- reallyopenuniversity.wordpress.com/what-is-the-rou/
Apparently Leeds based. Focused only on student fees seemingly, not how to solve it with tech/efficiency:
So far as of the early 2020's, the university that comes closest to some but not all of these principles is the University of the People. It's sad that it's such a crappy unknown thing, but it is what it is.
The Legend of Zelda: Ocarina of Time Updated 2025-07-16
This game was mind blowing to Ciro Santilli and all kids. It felt so real. The perfect contrast between peaceful town work and saving the world. OMG.
The Math Genome Project Updated 2025-07-16
The website was dead as of February 2025. Last archive: web.archive.org/web/20240418004442/http://www.themathgenome.com/ Pings:They were seeking help on May 2024:
so its likely the followup death. LinkedIn post gives basic stack: MERN stack, Heroku, Supabase/MongoDB Atlas.
A discussion on the Lean Zulip: leanprover.zulipchat.com/#narrow/stream/113488-general/topic/The.20Math.20Genome.20Project/near/352639129. Lean people are not convinced about the model in general it seems however.
TODO not viewable without login?
Has conjectures feature.
Built by this dude John Mercer:He must be independently wealthy or something to do such a project? What a hero. But he seems to have jobs. On the side? Hardcore.
Ciro Santilli asked: discord.com/channels/1096393420408360989/1096393420408360996/1137047842159079474Owner:So apparently there will be proof checking, but no dependencies between proofs, you still have to pull request everything back and face the pain.
Does the website actually automatically check the formal proofs, or is this intended to be implemented at some point? And if yes, is it intended to allow proofs to depend on other proofs of the website (possibly by other people)
Hi Ciro, yes we will be releasing in-browser proof assistant environments/checkers (e.g. Lean). Our goal is not to replace the underlying open-source repos (e.g. Mathlib) so the main dependency will be on the current repos; then when statement formalizations and proofs come in and are certified they can be PR'd to the respective repos. So we will be the source of truth for the informal latex code but only a stepping stone and orchestration layer on the way to the respective formal libraries.
Bibliography:
The Matrix (1999) Updated 2025-07-16
All action scenes are useless crap, but the premise with Ciro's precious simulation hypothesis subject, related physics and the illusion of life.
It is a shame that the key premise of using human bodies to produce energy is completely and impossibly stupid. You would obviously get more energy by directing burning the food you feed into humans.
If the film had been made later, maybe the much more plausible concept of AI alignment would would have been used instead. What a shame.
- www.youtube.com/watch?v=aau8qa3xgFs Neo takes the blue pill mashup with Office Space with deepfake faces
The missing link between basic and advanced Updated 2025-07-16
One of Ciro Santilli's strongest feeling in education is that material often falls in either of the two categories:
- hundreds of too basic popular science, e.g.:
- a 5 minute popular science video trying to explain quantum electrodynamics (an advanced subject) for someone who doesn't know what a Riemann integral is (a basic subject)
- a few full university courses that takes 20 hours to deliver the first punchline of the course
Ciro believes that there is often an important missing link between them, e.g.:
If we as a society are unable to provide this sweet Middle Way sweet-spot, it is unreasonable to expect that learners will ever have the motivation to advance, because it is just too boring! They are just more likely to go play video games instead.
It is Ciro's hope that OurBigBook.com will help to fill exactly that gap.
In Ciro's view, as of the 2020's this critical gap generally lies somewhere between the end of undergraduate studies, and at the start of postgraduate studies.
Let's take the gloves off more often, and give the full thing to interested students! Let students learn what they want to learn, and do that as soon as possible! Life is too short!
This problem is basically the knowledge version of the last mile problem. When we reach the end of graduate, there are enough directions of knowledge to go off into, that the probability that a great free tutorial exists is relatively low. Of course, as one approaches the realm of novel research, the branching is so wide that having perfect tutorials becomes impossible. Ciro's goal in life go push the last mile marker a bit further out.
Related:
- universityphysicstutorials.com/ by Adam Beatty mentions:
There are myriad resources for physics and maths. The Kahn Academy and Patrick JMT were the best for me. They really helped me out. The question is, what resources are there for the advanced undergraduate courses?
In this video, the noted chemist mentions how he managed to get into a chemistry research development before he even joined university, due to a somewhat exceptional situation. Section "The only reason for universities to exist should be the laboratories" also comes to mind. This is exactly the type of thing that Ciro Santilli wants to make much more widespread.
Stories of Ainan Celeste Cawley fighting to advance his kids education beyond school, and being forbidden to do so by a stupid educational system, also come to mind.
Bibliography: