Incoming links: Millennium Prize Problems
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.
GitHub | Stack Overflow | LinkedIn | YouTube | Twitter | Wikipedia | Zhihu 知乎 | Weibo 微博 | Other accounts
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:and achieve their ambitious STEM goals!- into the best universities
- into the best PhD programs
- 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:For minors, parents are welcome to join video calls, and all interactions with the student will be recorded and made available to parents.
- 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)
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:
- 20th century physics, notably AMO and condensed matter
- the history of science, and in particular trying to look at seminal papers of a field
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".
Ciro Santilli's Stack Overflow stats
. Further methodology details at: Figure "Ciro Santilli's Stack Overflow stats".Introduction to the OurBigBook Project
. Source. 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.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.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.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.
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. .
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?".
YellowRobot.jpgJPG 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: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.
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
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.
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.
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.
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".
Spacetime diagram illustrating how faster-than-light travel implies time travel by Ciro Santilli (2021)
Used in the Stack Exchange ansewr to Does faster than light travel imply travelling back in time?. One of Section "The best articles by Ciro Santilli".
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".
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>The BSD conjecture states that if your name is long enough, it will always count as two letters on a famous conjecture.
Maybe also insert a joke about BSD Operating Systems if you're into that kind of stuff.
The conjecture states that Equation 1. "BSD conjecture" holds for every elliptic curve over the rational numbers (which is defined by its constants and )
Equation 1. . Where the following numbers are defined for the elliptic curve we are currently considering, defined by its constants and :
- : number of elements of the elliptic curve over the finite field, where the finite field comes from the reduction of an elliptic curve from to . can be calculated algorithmically with Schoof's algorithm in polynomial time
- : rank of the elliptic curve over the rational numbers. We don't really have a good general way to calculate this besides this conjecture (?).
- : a constant
The conjecture, if true, provides a (possibly inefficient) way to calculate the rank of an elliptic curve over the rational numbers, since we can calculate the number of elements of an elliptic curve over a finite field by Schoof's algorithm in polynomial time. So it is just a matter of calculating like that up to some point at which we are quite certain about .
The Wikipedia page of the this conecture is the perfect example of why it is not possible to teach natural sciences on Wikipedia. A million dollar problem, and the page is thoroughly incomprehensible unless you already know everything!
Birch and Swinnerton-Dyer conjecture by Kinertia (2020)
Source. The $1,000,000 Birch and Swinnerton-Dyer conjecture by Absolutely Uniformly Confused (2022)
Source. A respectable 1 minute attempt. But will be too fast for most people. The sweet spot is likely 2 minutes. Existence and uniqueness of solutions of partial differential equations Updated 2025-02-22 +Created 1970-01-01
If you have a PDE that models physical phenomena, it is fundamental that:
- there must exist a solution for every physically valid initial condition, otherwise it means that the equation does not describe certain cases of reality
- the solution must be unique, otherwise how are we to choose between the multiple solutions?
Unlike for ordinary differential equations which have the Picard–Lindelöf theorem, the existence and uniqueness of solution is not well solved for PDEs.
For example, Navier-Stokes existence and smoothness was one of the Millennium Prize Problems.
There are two cases:
- (topological) manifolds
- differential manifolds
Questions: are all compact manifolds / differential manifolds homotopic / diffeomorphic to the sphere in that dimension?
- for topological manifolds: this is a generalization of the Poincaré conjecture.Original problem posed, for topological manifolds.Last to be proven, only the 4-differential manifold case missing as of 2013.Even the truth for all was proven in the 60's!Why is low dimension harder than high dimension?? Surprise!AKA: classification of compact 3-manifolds. The result turned out to be even simpler than compact 2-manifolds: there is only one, and it is equal to the 3-sphere.For dimension two, we know there are infinitely many: classification of closed surfaces
- for differential manifolds:Not true in general. First counter example is . Surprise: what is special about the number 7!?Counter examples are called exotic spheres.Totally unpredictable count table:
Dimension Smooth types 1 1 2 1 3 1 4 ? 5 1 6 1 7 28 8 2 9 8 10 6 11 992 12 1 13 3 14 2 15 16256 16 2 17 16 18 16 19 523264 20 24 is an open problem, there could even be infinitely many. Again, why are things more complicated in lower dimensions??
visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) is a good quick visual non-mathematical introduction is to it.
One of the Millennium Prize Problems and Hilbert's problems.
What is the Riemann hypothesis REALLY about? by HexagonVideos (2022)
Source. - www.youtube.com/watch?v=-_qNKbwM_eE Unsolved: Yang-Mills existence and mass gap by J Knudsen (2019). Gives 10 key points, but the truly hard ones are too quick. He knows the thing though.
Yang-Mills 1 by David Metzler (2011)
Source. A bit disappointing, too high level, with very few nuggests that are not Googleable withing 5 minutes.
Breakdown:
- 1 www.youtube.com/watch?v=j3fsPHnrgLg: too basic
- 2 www.youtube.com/watch?v=br6OxCLyqAI?t=569: mentions groups of Lie type in the context of classification of finite simple groups. Each group has a little diagram.
- 3 youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=728 the original example of a local symmetry was general relativity, and that in that context it can be clearly seen that the local symmetry is what causes "forces" to appear
- youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=933 local symmetry gives a conserved current. In the case of electromagnetism, this is electrical current. This was the only worthwhile thing he sad to 2021 Ciro. Summarized at: local symmetries of the Lagrangian imply conserved currents.
- 4 youtu.be/5ljKcWm7hoU?list=PL613A31A706529585&t=427 electromagnetism has both a global symmetry (special relativity) but also local symmetry, which leads to the conservation of charge current and forces.lecture 3 properly defines a local symmetry in terms of the context of the lagrangian density, and explains that the conservation of currents there is basically the statement of Noether's theorem in that context.
Millennium Prize Problem: Yang Mills Theory by David Gross (2018)
Source. 2 hour talk at the Kavli Institute for Theoretical Physics. Too mathematical, 2021 Ciro can't make much out of it.Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem
. Source. Unknown year. He almost gets there, he's good. Just needed to be a little bit deeper.