Totient summatory function by Ciro Santilli 35 Updated +Created
Quadratic Diophantine equation by Ciro Santilli 35 Updated +Created
Pre-university knowledge olympiad by Ciro Santilli 35 Updated +Created
Euler's totient function by Ciro Santilli 35 Updated +Created
TODO wtf is a "totient"? Where else is that word used besides in this concept?
Knowledge olympiad by Ciro Santilli 35 Updated +Created
Events that trick young kids into thinking that they are making progress, but only serve to distract them from what really matters, which is to dominate a state of the art as fast as possible, contact researches in the area, and publish truly novel results.
Financially backed by high schools trying to make ads showing how they will turn your kids into geniuses (but also passionate teachers who fell into this hellish system), or companies who hire machines rather than entrepreneurs.
The most triggering thing possible is when programming competitions don't release their benchmarks as open source software afterwards: at least like that they might help someone to solve their real world problems. Maybe.
On a related note, hackathons are also mostly useless. Instead of announcing a hackathon, just announce a web forum where people with similar interests can talk to one another instead, and let them code it out on GitHub if they want to. Restricting intensive development to a few days tends to produce crappy code and not reach real goals.
Some irrelevant people highlight that knowledge Olympiads can have good effects, because they are "an opportunity to meet university teachers and their research organizations". Ciro's argument is just that there are much more efficient ways to achieve those goals.
As an alternative way to get into university, this is not 100% horrible however, e.g. the University of São Paulo accepted students from olympiads in 2019 and then again 2023: jornal.usp.br/institucional/usp-oferece-200-vagas-em-mais-de-100-cursos-de-graduacao-para-alunos-participantes-de-olimpiadas-do-conhecimento/?a
Millennium Technology Prize by Ciro Santilli 35 Updated +Created
Greatest common divisor algorithm by Ciro Santilli 35 Updated +Created
Crunchbase by Ciro Santilli 35 Updated +Created
Data as a service by Ciro Santilli 35 Updated +Created
Polynomial over a commutative ring by Ciro Santilli 35 Updated +Created
Unlike over non-commutative rings, polynomials do look like proper polynomials over commutative ring.
In particular, Hilbert's tenth problem is about polynomials over the integers, which is a commutative ring, and therefore brings mindshare to this definition.
Algebraic equation modulo n by Ciro Santilli 35 Updated +Created
Algebraic equation over a field by Ciro Santilli 35 Updated +Created
In this section we collect results about algebraic equations over more "exotic" fields
Domain of a polynomial by Ciro Santilli 35 Updated +Created
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Video 1.
Intro to OurBigBook
. Source.
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
    Video 2.
    OurBigBook Web topics demo
    . Source.
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    • to OurBigBook.com to get awesome multi-user features like topics and likes
    • as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact