Nothing phenomenally new on the early days to add on top of Video "Nerds 2.0.1 excerpt about Cisco (1998)", but a few new good points:
Sandy Lerner by Ciro Santilli 40 Updated 2025-07-16
This chick is hardcore.
Ainan Celeste Cawley by Ciro Santilli 40 Updated 2025-07-16
His father fought a lot with the stupid educational system to try and move his son to his full potential and move to more advanced subjects early.
A crime of society to try and prevent it. They actually moved the family from Singapore to Malaysia for a learning opportunity for the son. Amazing.
This is the perfect illustration of one of Ciro Santilli's most important complaints about the 2020 educational system:and why Ciro created OurBigBook.com to try and help fix the issue.
Video 1.
The Most Talented Children And Adults On The Planet by Our Life (2008)
Source. Has some good mentions of Ainan and others.
Video 2.
Ainan Cawley: Child prodigy (2013)
Source.
This was the first infinite family of simple groups discovered after the simple cyclic groups and alternating groups. The first case discovered was by Galois. You should understand that one first.
Very interesting story! A predecessor to microwave transmission for trading.
Video 1.
How The First Ever Telecoms Scam Worked by Tom Scott (2018)
Source. Amazing how they used control signals to hide the information from officials on either side.
Functional by Ciro Santilli 40 Updated 2025-07-16
A function that takes input function and outputs a real number.
Let's start with the one dimensional case. Let the and a Functional defined by a function of three variables :
Then, the Euler-Lagrange equation gives the maxima and minima of the that type of functional. Note that this type of functional is just one very specific type of functional amongst all possible functionals that one might come up with. However, it turns out to be enough to do most of physics, so we are happy with with it.
Given , the Euler-Lagrange equations are a system of ordinary differential equations constructed from that such that the solutions to that system are the maxima/minima.
In the one dimensional case, the system has a single ordinary differential equation:
By and we simply mean "the partial derivative of with respect to its second and third arguments". The notation is a bit confusing at first, but that's all it means.
Therefore, that expression ends up being at most a second order ordinary differential equation where is the unknown, since:
  • the term is a function of
  • the term is a function of . And so it's derivative with respect to time will contain only up to
Now let's think about the multi-dimensional case. Instead of having , we now have . Think about the Lagrangian mechanics motivation of a double pendulum where for a given time we have two angles.
Let's do the 2-dimensional case then. In that case, is going to be a function of 5 variables rather than 3 as in the one dimensional case, and the functional looks like:
This time, the Euler-Lagrange equations are going to be a system of two ordinary differential equations on two unknown functions and of order up to 2 in both variables:
At this point, notation is getting a bit clunky, so people will often condense the vector
or just omit the arguments of entirely:
Video 1.
Calculus of Variations ft. Flammable Maths by vcubingx (2020)
Source.
Their website, and in particular the recruitment section, are so creepy.
There's not mention of bombs. No photos of atomic explosions. The words "atomic" and "weapon" do not even show up in the front page!!! The acronym AWE is instead used everywhere as an euphemism.
In the recruitment section we can see a bunch of people smiling: web.archive.org/web/20211007213222/https://www.awe.co.uk/careers/working-at-awe/, suggesting:
We make nukes, and we do it with a smile!
There's even children outreach!!!
Ciro Santilli is not against storing a few nukes to be ready against dictatorships. But don't be such a pussy! Just say what the fuck you are doing more clearly! You are making weapons to kill people and destroy things in order to maintain the Balance of power. If the public can't handle such facts, then shut down the fucking program.
Video 1.
Keeping the peace: A history of AWE
. Source. By AWE, 2005.
Nature (journal) by Ciro Santilli 40 Updated 2025-07-16
Ended up under Springer in 2015 after a massive merger.
Planck's law by Ciro Santilli 40 Updated 2025-07-16
Used to explain the black-body radiation experiment.
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Video 1. Source. Contains a good explanation of how discretization + energy increases with frequency explains the black-body radiation experiment curve: you need more and more energy for small wavelengths, each time higher above the average energy available.

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