The Majorana equation is a relativistic wave equation that describes particles known as Majorana fermions. These particles are unique in that they are their own antiparticles, meaning that they possess the same quantum numbers as their antiparticles, unlike traditional fermions (like electrons), which have distinct antiparticles (such as positrons).
C-symmetry, also known as charge conjugation symmetry, refers to a fundamental symmetry in particle physics concerning the transformation of particles into their corresponding antiparticles. Specifically, it involves changing a particle into its antiparticle, which has the opposite electric charge and other quantum numbers. In terms of mathematical representation, charge conjugation transforms a particle state \(| \psi \rangle\) into its charge-conjugated state \(| \psi^C \rangle\).
Fock space by Ciro Santilli 40 Updated 2025-07-16
Yup, this one Focks you up.
Video 1.
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:
Video 2. Source. 2 hour talk at the Kavli Institute for Theoretical Physics. Too mathematical, 2021 Ciro can't make much out of it.
Video 3.
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.
Modular exponentiation by Ciro Santilli 40 Updated 2025-10-14
Can be calculated efficiently with the Extended Euclidean algorithm.
The beauty of this algorithm is that because exponentiation grows really fast, there is no hope that we can ever learn all the digits of an exponential, as there is simply not enough time or memory for that. Therefore, a natural sub-question is if we can know some part of that number, and knowing the smallest digits is the most natural version of that question.
A **conical combination** is a mathematical concept primarily used in linear algebra and geometry. It refers to a specific type of linear combination of points (or vectors) that satisfies certain constraints, particularly in relation to convexity.
Conscious automatism refers to a psychological phenomenon where individuals perform actions or produce thoughts without conscious awareness or intentional control, yet they remain aware of the process. It is often associated with surrealism and certain artistic and literary movements, where creators aim to tap into the subconscious mind to generate spontaneous and uninhibited expressions.
math.stackexchange.com/questions/2382011/computational-complexity-of-modular-exponentiation-from-rosens-discrete-mathem mentions:
can be calculated in:
Remember that and are the lengths in bits of and , so in terms of the length in bits and we'd get:
The "Proceedings of the American Mathematical Society" (Proc. Amer. Math. Soc.) is a prestigious mathematical journal published by the American Mathematical Society (AMS). It serves as a venue for the publication of high-quality research articles in all areas of pure and applied mathematics. The journal is known for its rigorous peer review process and aims to disseminate significant mathematical findings and developments. The proceedings typically include original research papers that are often of broad interest to the mathematical community.
As of my last knowledge update in October 2023, there is no widely recognized public figure or significant entity known as "Alan Astbury." It's possible that this could refer to a private individual or a specific context that is not well-documented.
Bidimensionality is primarily a concept used in the field of computational complexity theory, specifically in the study of algorithm design and graph theory. It typically refers to a property of certain types of problems or structures that can be analyzed more effectively due to their two-dimensional characteristics. In a computational context, bidimensional problems often involve graphs or other structures that can be embedded or represented in two dimensions.

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