Notable mentions:
Other notable people that are likely also awesome but Ciro has less familiarity with their contributions:
We can then immediately see that the matrix is symmetric, then so is the form. We have:
But because is a scalar, we have:
and:
Neuro-symbolic AI by Ciro Santilli 40 Updated 2025-07-16
An IBM made/pushed term, but that matches Ciro Santilli's general view of how we should move forward AGI.
Ciro's motivation/push for this can be seen e.g. at: Ciro's 2D reinforcement learning games.
Congruent matrix by Ciro Santilli 40 Updated 2025-07-16
Two symmetric matrices and are defined to be congruent if there exists an in such that:
In this chapter Richard Feynman talks about his experiences in Brazil.
"O Americano, Outra Vez!" means "The American, once again!" in Portuguese, which is what one of the samba school boss exclaimed when Feynman was not playing well his instrument, the frigideira, during a rehearsal.
Feynman really enjoyed Brazil's (and notably Rio's) stereotypical "take it easy and enjoy life" attitude.
Key quote that names the chapter:
My friend Matt Sands was once going to write a book to be called Alfred Nobel's Other Mistake.
One of the most simply classification algorithm one can think of: just see whatever kind of point your new point seems to be closer to, and say it is also of that type! Then it is just a question of defining "close".

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 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.
  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