The geometry of divisors is a topic in algebraic geometry that deals with the study of divisors on algebraic varieties, particularly within the context of the theory of algebraic surfaces and higher-dimensional varieties. A divisor on an algebraic variety is an algebraic concept that intuitively represents "subvarieties" or "subsets", often associated with codimension 1 subvarieties, such as curves on surfaces or hypersurfaces in higher dimensions.
Crush the current grossly inefficient educational system, replace today's students + teachers + researchers with unified "online content creators/consumers".
Gamify them, and pay the best creators so they can work it full time, until some company hires for more them since they are so provenly good.
Destroy useless exams, the only metrics of society are either:
  • how much money you make
  • how high is your educational content creator reputation score
Reduce the entry barrier to education, like Uber has done for taxis.
Help create much greater equal opportunity to talented poor students as described at free gifted education.
Give the students a flexible choice of what to learn, which basically implies that a much large proportion of students get a de-facto gifted education.
In some ways, Ciro wants the website to feel like a video game, where you fluidly interact with headers, comments and their metadata. If game developers can achieve impressively complicated game engines, why can't we achieve a decent amazing elearning website? :-)
Wikipedia CatTree by Ciro Santilli 40 Updated 2025-07-16
This mini-project walks the category hierarchy Wikipedia dumps and dumps them in various simple formats, HTML being the most interesting!
Figure 1.
Mathematics dump of Wikipedia CatTree
. Source.
Some of the contributions are subjectively self evaluated based on:
  • How many significant lines changed (no indentation changes, moves, mass refactoring, trivial tests, etc.):
    0only trivial changes
    1< 20
    2< 150
    3
    150
  • How hard it was to make it. 4 algorithmic lines are harder than 100 web development/documentation lines.
  • I opened and was confirmed or generated considerable interest
  • I wrote comments pointing out a non obvious cause/fix/duplicate.
  • I reviewed the patch
This shall not list bugs solved by my accepted pull requests.
Gravity by Ciro Santilli 40 Updated 2025-07-16
In 2020 physics, best explained by general relativity.
TODO: does old Newtonian gravity give different force results than general relativity?
How to teach by Ciro Santilli 40 Updated 2025-07-16
Off-the-shelf techniques to become a teaching superhero.
Customized website idea at: OurBigBook.com.
Once you have crated something awesome, you have to advertise it, otherwise no one will ever find it.
This means:
  • whenever you walk into a classroom, give students a link to the material
    Then ask them if they want to talk about anything.
    Then leave the classroom and go produce more good material instead of wasting your time there :-)
  • whenever someone asks as question on an online forum, answer it, and link to the section of your material that also answers that question.
    The material will answer many of their future questions.
  • after you've done something awesome, Google possible relevant keywords that should hit it.
    This will lead you to other websites that talk about the same content.
    Then, leave comments on those pages linking to your stuff, or email the authors of those pages.
    It is borderline spam, but if the subject is closely related, it is a win for everyone.
Eventually, people will find you on the front page of Google searches, and then you will know that you've truly made something useful.
William Austin Starmer, commonly known as Keir Starmer, is a British politician and lawyer who has been the leader of the Labour Party and the Member of Parliament (MP) for Holborn and St Pancras since 2015. Before entering politics, he had a distinguished career in law, serving as the Director of Public Prosecutions and leading the Crown Prosecution Service in England and Wales.
The De Rham-Weil theorem is a result in the field of algebraic geometry and homological algebra, primarily concerning the relationships between algebraic varieties and their cohomology.
"Topos" can refer to several things depending on the context: 1. **Mathematics (Category Theory)**: In mathematics, particularly in category theory, a topos (plural: topoi or toposes) is a category that behaves like the category of sets and has certain additional properties. Topoi provide a framework for doing geometry and topology in a categorical way, and they can be used to study logical systems.
Cherry Lane Music is a music publishing company that has played a significant role in the music industry by acquiring, managing, and licensing a diverse catalog of songs across various genres. Founded in 1960, the company is known for representing a wide array of songwriters and composers, particularly in the fields of popular and contemporary music. Cherry Lane also provides services related to music licensing, sheet music publishing, and other rights management functions.
Adolf Martin Schlesinger (born on December 3, 1883, and died on December 16, 1960) was a German-born American composer and conductor known for his contributions to music in the early to mid-20th century. His work spanned various musical forms and genres, although he is less widely recognized than some of his contemporaries.

Pinned article: 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!
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
  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:
    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 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . 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