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
- 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?
Techniques to get numerical approximations to numeric mathematical problems.
The entire field comes down to estimating the true values with a known error bound, and creating algorithms that make those error bounds asymptotically smaller.
Not the most beautiful field of pure mathematics, but fundamentally useful since we can't solve almost any useful equation without computers!
The solution visualizations can also provide valuable intuition however.
Important numerical analysis problems include solving:
The most important projects done by Ciro Santilli by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli has sometimes wasted time with low impact projects such as those listed at Ciro Santilli's minor projects instead of doing higher impact projects such as those mentioned at: Section "The most important projects Ciro Santilli wants to do".
But maybe "Everything you did brought you where you are now." applies, maybe it is during the "low impact activities" that one gets the inspiration and experience required for the "high impact ones".
Accounts controlled by Ciro Santilli by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli controls the following accounts.
With non-trivial activity:
- github.com/cirosantilli on GitHub
- stackoverflow.com/users/895245 on Stack Overflow
- www.linkedin.com/in/cirosantilli on LinkedIn
- www.youtube.com/c/CiroSantilli on YouTube
- Twitter: see Section "Ciro Santilli's Twitter accounts"
- archive.org/details/@cirosantilli2 on the Internet Archive. Was archive.org/details/@cirosantilli but got deleted due to an "admin error" and the old username cannot be restored![ref]
- en.wikipedia.org/wiki/User:Cirosantilli2 and commons.wikimedia.org/wiki/User:Cirosantilli2: Ciro tries to upload all educational CC content he creates to Wikimedia Commons as an extra backup and sometimes to use in Wikipedia pages
- www.facebook.com/cirosantilli/ Ciro accepts all friend requests there, but expect a few non-technical posts. Unless you look like a massive honeypot account, please send context in advance in that case.
- www.quora.com/profile/Ciro-Santilli
- www.reddit.com/user/cirosantilli/ is Ciro's Reddit account, mostly computer and China topics
- maps.app.goo.gl/npV35XTppSBTmNqC8: Google Maps. Ciro Santilli likes to make additions to certain niche topics that are missing, having reached Local Guide Level 6 as of 2024. He can't do as much as he'd like so as to not reveal his current city however.
Trivial activity only:
- seqanswers.com/forums/member.php?u=90053
- answers.gazebosim.org/users/2289/cirosantilli/
- 4programmers.net/Profile/86786
- 500px.com/p/cirosantilli
- 9gag.com/u/cirosantilli
- addons.mozilla.org/en-US/firefox/user/cirosantilli/
- agoradesk.com/user/cirosantilli
- androidforums.com/members/ciro-santilli.1918307
- app.element.io/#/user/@cirosantilli:matrix.org. Proof: matrix.to/#/!OisxJPszSYdWdwXrrL:matrix.org/$YbrChbGFvlgYiDM5E2OgWXSp0vy7ayLfGkCXftAUyTI?via=matrix.org
- archive.org/details/@ciro_santilli_ourbigbook created during the account deletion mess.
- ask.libreoffice.org/en/users/2352/cirosantilli/
- bbs.archlinux.org/profile.php?id=116270
- bitcointalk.org/index.php?action=profile
- brilliant.org/profile/ciro-il1uxz/
- bugzilla.gnome.org/page.cgi?id=describeuser.html&login=ciro.santilli@gmail.com
- cirosantilli.blogspot.com/
- cirosantilli.itch.io
- cirosantilli.livejournal.com/profile
- cirosantilli.medium.com/ on Medium
- cirosantilli.substack.com/
- cirosantilli.wordpress.com/ on WordPress
- codeforces.com/profile/cirosantilli reverse proof codeforces.com/blog/entry/98393
- coderwall.com/Ciro%20Santilli Note that space on the username. Beauty.
- community.arm.com/people/cirosantilli
- community.atlassian.com/t5/user/viewprofilepage/user-id/680821
- community.fandom.com/wiki/User:Cirosantilli
- community.plos.org/people/cirosantilli
- community.skype.com/t5/user/viewprofilepage/user-id/2646858
- community.zimbra.com/members/cirosantilli
- connect.mozilla.org/t5/user/viewprofilepage/user-id/46889
- del.icio.us/cirosantilli
- dev.to/cirosantilli
- developer.mbed.org/users/cirosantilli/
- devtalk.nvidia.com/member/2118846/
- droit-finances.commentcamarche.net/profile/user/cirosantilli
- en.gravatar.com/cirosantilli
- en.wikipedia.org/wiki/User:Ciro.santilli also belongs to Ciro, but he lost the password
- eternagame.org/web/player/260828/
- figshare.com/authors/Ciro_Santilli/656781
- forums.developer.nvidia.com/u/cirosantilli
- forum.osdev.org/memberlist.php?mode=viewprofile&u=16372
- forum.pine64.org/member.php?action=profile&uid=17386
- forum.videolan.org/memberlist.php?mode=viewprofile&u=173503
- forum.xda-developers.com/member.php?u=7116837
- forums.androidcentral.com/members/cirosantilli-2734491
- forums.lenovo.com/user/viewprofilepage/user-id/1561639
- framasphere.org/people/78a975c0b6c40133a3032a0000053625 framasphere.org/posts/1519871
- freesound.org/people/cirosantilli
- gitlab.com/u/cirosantilli
- hackaday.io/cirosantilli
- hinative.com/en-US/profiles/5276462
- home.gamer.com.tw/homeindex.php?owner=cirosantilli but can't post anything publicly because cannot verify phone in many countries
- huggingface.co/cirosantilli
- identity.kde.org/index.php?r=people/view&uid=cirosantilli
- imgur.com/user/cirosantilli/about: Proof: imgur.com/gallery/mexv1Bk/comment/1734086983
- jsfiddle.net/user/cirosantilli/
- kiwifarms.net/members/cirosantilli.82011/
- launchpad.net/~cirosantilli
- leanpub.com/u/cirosantilli
- leetcode.com/cirosantilli/
- makandracards.com/ciro-santilli
- mastodon.social/@cirosantilli
- nanohub.org/members/146301/
- next-episode.net/user/cirosantilli/
- openclipart.org/artist/cirosantilli. TODO but not yet able to login after the "first upload". But it did get uploaded: openclipart.org/artist/cirosantilli.
- opencollective.com/ciro-santilli
- open.spotify.com/user/cirosantilli
- orcid.org/0000-0003-2895-7763
- parler.com/profile/cirosantilli/posts
- paypal.me/cirosantilli. United Kingdom account.
- peerj.com/cirosantilli/
- profile.edx.org/u/ciro_santilli
- profiles.3dgames.com.ar/profiles/1002278
- protonmail.uservoice.com/users/6491333990-ciro-santilli
- pypi.org/user/cirosantilli/
- raidforums.com/User-cirosantilli
- rubygems.org/profiles/cirosantilli
- software.intel.com/en-us/user/1090688
- soundcloud.com/cirosantilli
- sourceforge.net/u/cirosantilli/profile/
- stackshare.io/cirosantilli
- steamcommunity.com/id/cirosantilli/
- subreply.com/cirosantilli
- support.discord.com/hc/en-us/profiles/427813342894 on the Discord forum
- support.mozilla.org/en-US/user/cirosantilli
- tabmixplus.org/forum/memberlist.php?mode=viewprofile&u=59846
- talk.commonmark.org/users/cirosantilli
- talk.jekyllrb.com/users/cirosantilli
- talks.cam.ac.uk/user/show/81142
- tatoeba.org/eng/user/profile/cirosantilli
- telegram.me/cirosantilli on Telegram
- trac.ffmpeg.org/wiki/Waveform?action=history username
cirosantilli
- tuleap.net/users/cirosantilli
- tuleap.ring.cx/users/cirosantilli
- twittercommunity.com/users/cirosantilli/activity
- wefunder.com/cirosantilli
- wise.com/pay/me/cirod3. The name shows as "Ciro Duran Santilli" and that's correct.
- wiki.qemu.org/User:Cirosantilli
- www.airbnb.com/users/show/45794827
- www.behance.net/cirosantilli
- www.bibsonomy.org/user/cirosantilli
- www.biostars.org/u/50170/
- www.bountysource.com/people/25676-ciro-santilli
- www.bulletphysics.org/Bullet/phpBB3/memberlist.php?mode=viewprofile&u=11704
- www.codewars.com/users/cirosantilli
- www.codingame.com/profile/cddd0a711c22d97e8264361f7c8205567563841
- www.coursera.org/user/f65b08c191d792eb809fe2808d771ee7
- www.dailymotion.com/cirosantilli
- www.deviantart.com/cirosantilli
- www.digitalocean.com/community/users/cirosantilli
- www.ebay.com/usr/cirosantilli
- www.edaboard.com/member587087.html
- www.flickr.com/people/cirosantilli/
- www.freecodecamp.org/fcc8f660b91-167c-4b04-a8da-5d50cdb46def
- www.f6s.com/cirosantilli
- www.f6s.com/cirosantilli1
- www.gitbook.com/@cirosantilli
- www.hackerrank.com/cirosantilli
- www.hackster.io/cirosantilli
- www.html5gamedevs.com/profile/30103-cirosantilli/
- www.imdb.com/user/ur59802249 on IMDb
- www.instagram.com/cirosantilli/ Impossible to disable their notifications without removing your email. So all their notifications go to trash.
- www.kaggle.com/cirosantilli
- www.lesswrong.com/users/ciro-santilli on LessWrong
- www.linux.org/members/ciro-santilli.62540/
- www.linuxquestions.org/questions/user/cirosantilli-688439/
- www.meetup.com/members/252568305/
- www.mentebinaria.com.br/profile/1987-ciro-santilli/
- www.metacritic.com/user/cirosantilli
- www.metaculus.com/accounts/profile/163587/
- www.mohu.rocks/people/cirosantilli
- www.mudhut.com/user/1995000
- www.myopportunity.com/en/profile/ciro-santilli
- www.npmjs.com/~cirosantilli
- www.opengl.org/discussion_boards/member.php/40269-cirosantilli
- www.openstreetmap.org/user/Ciro%20Santilli
- www.patreon.com/cirosantilli
- www.physicsforums.com/members/cirosantilli.422056/
- www.pixiv.net/en/users/64347194
- www.plurk.com/cirosantilli
- www.raspberrypi.org/forums/memberlist.php?mode=viewprofile&u=273389
- www.shadertoy.com/user/cirosantilli
- www.strava.com/athletes/47913768
- www.tastekid.com/ciro.santilli
- www.ted.com/profiles/5822760
- www.thestudentroom.co.uk/member.php?u=5930160
- www.tiktok.com/@cirosantilli2
- www.transifex.com/user/profile/cirosantilli
- www.tripadvisor.com/members/cirosantilli
- www.twitch.tv/cirosantilli
- www.whatdotheyknow.com/user/ciro_santilli/profile
Profiles without URLs (OMG...):
- Discord: username
cirosantilli
, previouslycirosantilli#8921
Accounts in Chinese websites. These accounts might be banned or altered or offer other limitations, so Ciro only communicates briefly through them. All communication through those channels should obviously be assumed to be compromised:
- bbs.nibaedu.com/index.php?m=space&uid=70
- www.renren.com/338003848/profile
- www.tianya.cn/109285544 (can't post, no cell phone)
- hacpai.com/member/cirosantilli unable to login as of 2019-10-12, reason unclear, either ban or website too crappy.
- pincong.rocks/people/cirosantilli Lost account tested as of 2022-11 and likely much earlier. Last existing password not working, and there doesn't seem to be a reset password button. Creating cirosantilli2
- pincong.rocks/people/cirosantilli2
- tieba.baidu.com/home/main?id=5cd56369726f73616e74696c6c69c944
- v2ex.com/member/cirosantilli: Ciro was blocked and or account deleted on 2020-07-23: cirosantilli.com/china-dictatorship/v2ex
- v2ex.com/member/cirosantilli2: was created by someone else most likely and cannot be re-registered. Also blocked.
- v2ex.com/member/cirosantilli3: Ciro created this new account November 2023, let's see how long it lasts.
- www.zhihu.com/people/cirosantilli. Ciro was prevented from posting in 2018-06-25, and the account and all content mentioning him were taken down in 2019-11-03.
- www.weibo.com/p/1005055601627311: started requiring a cell phone to login in 2020, and Ciro didn't want to give his cell phone number to the CCP and didn't have the patience to manage a secondary phone number, so he is not logging in for now. The account was blocked in 2021: cirosantilli.com/china-dictatorship/ciro-santillis-weibo-block
Accounts in Russian websites:
Dead websites:
- www.citeulike.org/user/cirosantilli (2019-05)
Ciro Santilli never did any illegal drugs, because he:so don't expect any amazing stories here.
- doesn't want to help fund organized crime. Notably, Ciro is for complete legalization of drugs of all drugs
- already has better more sustainable drugs like love, cycling, learning the natural sciences and fame. He (or more realistically, the world) chose life for him.
Like LDS believers, Ciro never drinks coffee nor smokes, and only drinks alcohol and tea sparingly, because they are all addictive drugs and bring no net increase of energy and concentration.
Ciro prefers to only enjoy a glass of tea when going out cycling on a cold day (Earl gray, with milk, no sugar), or get a half pint of beer when going out with friends to a pub.
Ciro only got reasonably drunk twice on his life:
- once when he was quite young, likely pre-10 years old, while visiting an uncle's home, and adults were having a very nice sweet and thick type of alcoholic cocktail, and Ciro drank a bit too much and that made him really really stupid
- once while studying at University of São Paulo, somehow someone was giving free beers at one of the parties (at which Ciro practiced Cirodance). And since Ciro had always been a cheap-ass, he thought, hey, this is a good chance to try it out. Ciro remembers that this made him a bit euphoric, active, very stupid, and a bit horny (though of course, he got no pussy as usual).
Later in life, around the time of his wedding, there were guests around all the time, and he was drinking beer with them all the time. Then one day, during lunch, Ciro felt a weirdly strong desire to drink one more pint. It was at this point that Ciro realised first-hand what mild, but real, alcohol addiction felt like, and he didn't get that drink, and swore from then on to never drink more than one glass a week, and only with friends at a bar after work. Richard Feynman tells a very similar story on his book Surely You're Joking, Mr. Feynman chapter O Americano, Outra Vez!, see: Section "Richard Feynman's drug use".
One day, someone will invent a way to take the hash of a piece of hardware and see its history log, like software engineers do with version control. Until then, this is as close as you can get.
Ciro one day guessed that hardware would certainly be a slang for something naughty, and yup, here we are: www.urbandictionary.com/define.php?term=Hardware, drug paraphernelia. Read on!
Stuff that is beautiful but useless because it does not make food or houses cheaper.
Or from Ciro Santilli's best random thoughts:
Without technology, one cannot survive. Without art, one cannot live.
But that sure enough has a Jesus semi-precursor, and likely many others: man shall not live by bread alone.
There is some art however that lives in the fine intersection between beauty and usefulness:
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