Ciro Santilli very aggressively aggressively people in social media.
There are basically 3 categories:
  • are you Ciro's parents or children or brothers: OK, keep following, unless you are truly truly very noise.
  • does Ciro really really like or respect you? OK, he can take some useless (i.e. non-technical/scientific) posts
  • otherwise: one bad post and unfollow
React by Ciro Santilli 37 Updated 2025-07-16
React officially recommends that you use Next.js[ref], so just do it. It just sets up obvious missing functionality from raw React.
React feels like a good. But it also feels impossible to use/learn sometimes.
Its main design goal is to reduce DOM changes to improve rendering times.
And an important side effect of that is that it becomes easier to do stuff of the type:
  • user creates a new comment that appears on screen without page reload
  • comment has a delete button, which is JavaScript callback activated
and then the new comment easily gets the callback attached to it.
And it also ends up naturally doubling as a template engine.
But React can also be extremely hard to use. It can be very hard to know what you can and cannot do sometimes, then you have to stop and try to understand how react works things better:The biggest problem is that it is hard to automatically detect such errors, but perhaps this is the same for other frontend stuff. Though when doing server-side rendering, the setup should really tell you about such errors, so you don't just discover them in production later on.
Is is also very difficult to understand precisely why hooks run a certain number of times.
Examples under: react.
Video 1.
React for the Haters in 100 Seconds by Fireship (2022)
Source.
You start with a very small list of:
Using those rules, you choose a target string that you want to reach, and then try to reach it. Before the target string is reached, mathematicians call it a "conjecture".
Mathematicians call the list of transformation rules used to reach a string a "proof".
Since every step of the proof is very simple and can be verified by a computer automatically, the entire proof can also be automatically verified by a computer very easily.
Finding proofs however is undoubtedly an uncomputable problem.
Most mathematicians can't code or deal with the real world in general however, so they haven't created the obviously necessary: website front-end for a mathematical formal proof system.
The fact that Mathematics happens to be the best way to describe physics and that humans can use physical intuition heuristics to reach the NP-hard proofs of mathematics is one of the great miracles of the universe.
Once we have mathematics formally modelled, one of the coolest results is Gödel's incompleteness theorems, which states that for any reasonable proof system, there are necessarily theorems that cannot be proven neither true nor false starting from any given set of axioms: those theorems are independent from those axioms. Therefore, there are three possible outcomes for any hypothesis: true, false or independent!
Some famous theorems have even been proven to be independent of some famous axioms. One of the most notable is that the Continuum Hypothesis is independent from Zermelo-Fraenkel set theory! Such independence proofs rely on modelling the proof system inside another proof system, and forcing is one of the main techniques used for this.
Figure 1.
The landscape of modern Mathematics comic by Abstruse Goose
. Source. This comic shows that Mathematics is one of the most diversified areas of useless human knowledge.
The Social Network by Ciro Santilli 37 Updated 2025-07-16
Video 1.
The Social Network: Winklevii pitch to Zuckerberg
. Source.
Video 2.
The Social Network: Eduardo Saverin tells the hearing how he was trapped into the shares dilution
. Source.
Video 3.
The Social Network: dinner with Sean Parker
. Source.
Video 4.
The Social Network: Eduardo Saverin tells the hearing how his shares were diluted
. Source.
Video 5.
The Social Network: I'm Not a Bad Guy
. Source.
The Klein-Gordon equation directly uses a more naive relativistic energy guess of squared.
But since this is quantum mechanics, we feel like making into the "momentum operator", just like in the Schrödinger equation.
But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...
So we just cheat and try to use the laplace operator instead because there's some squares on it:
But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.
So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.
Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:
taking the Hamiltonian twice leads to:
We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.
Instruction pipelining by Ciro Santilli 37 Updated 2025-07-16
The first thing you must understand is the Classic RISC pipeline with a concrete example.

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