Formal language Updated 2025-07-16
Formal proof is useless Updated 2025-07-16
The only cases where formal proof of theorems seem to have had actual mathematical value is for theorems that require checking a very large number of case, so much so that no human can be fully certain that no mistakes were made. Some examples:
Form (mathematics) Updated 2025-07-16
Forward secrecy Updated 2025-07-16
Four Gentlemen Updated 2025-07-16
Plum, orchid, bamboo, chrysanthemum Chinese painting by Zheng Xie
. Source. This is an example of bird-and-flower painting, of which the Four Gentlemen are a common theme. TODO date. Fourier basis is complete for Updated 2025-07-16
Riesz-Fischer theorem is a norm version of it, and Carleson's theorem is stronger pointwise almost everywhere version.
Note that the Riesz-Fischer theorem is weaker because the pointwise limit could not exist just according to it: norm sequence convergence does not imply pointwise convergence.
Freeman Dyson Updated 2025-09-09
Ciro Santilli's admiration for Dyson goes beyond his "unify all the things approach", which Ciro loves, but also extends to the way he talks and the things he says. Dyson is one of Ciro's favorite physicist.
Besides this, he was also very idealistic compassionate, and supported a peaceful resolution until World War II with United Kingdom was basically inevitable. Note that this was a strategic mistake.
Dyson is "hawk nosed" as mentioned in Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Dyson". But he wasn't when he was young, see e.g. i2.wp.com/www.brainpickings.org/wp-content/uploads/2016/03/freemandyson_child-1.jpg?resize=768%2C1064&ssl=1 It seems that his nose just never stopped growing after puberty.
He also has some fun stories, like him practicing night climbing while at Cambridge University, and having walked from Cambridge to London (~86km!) in a day with his wheelchair bound friend.
Ciro Santilli feels that the label child prodigy applies even more so to him than to Feynman and Julian Schwinger.
Bibliography:
- QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 9 Freeman Dyson and the Structure of Quantum Field Theory
Freely licensed Bibles Updated 2025-07-16
How can you make a translation of the Bible and not put it in the public domain???? You tell me, you tell me.
With Falun Gong it's even more fun: the words of God Himself are will be copyrighted for a while after Li Hongzhi dies!!!
Frequency modulation Updated 2025-07-16
Front-end web framework Updated 2025-07-16
You need those because it is hard to do the following:
- client JavaScript sends a request to server
- server sends back data
- client updates what the user sees
This is hard to do notably because when the update happens, several things might need to change on the webpage at the same time.
Notably, new elements might need to be added to the webpage, which in turn means that new bindings such as button clicks have to be added to those, in a way that keeps the page working.
The only way to do this basically is to have a functional dependency graph that keeps everything in the page in working state as updates come.
Fusion power Updated 2025-07-16
Most promising approaches as of 2020:
Why Private Billions Are Flowing Into Fusion by Bloomberg (2022)
Source. - Joint European Torus
- General Fusion: compress with liquid metal. Intends to demo in JET site.
- Helion Energy: direct fusion to electricity conversion without steam, direct from magnetic field movements
- First Light: shootjobs.lever.co/proximafusion/23aab9a8-34ec-40d2-bb14-440f1130021c microscopic objct at a target to crush it so much that fusion happens
Fullerene Updated 2025-07-16
Buckyballs (C60) by Periodic Videos (2010)
Source. Actually shows them in a lab!- youtu.be/ljF5QhD5hnI?t=167 has a photo of the first effective production method, which passes a large current between two carbon rods
- youtu.be/ljF5QhD5hnI?t=245 and forward cuts (their editing is very annoying) shows how fullerene dissolves in an organic solvent TODO name, sounds like thodium? and produces a violet solution, while graphite doesn't. A Ultrasonic bath is needed for the solution to form however.
- youtu.be/ljF5QhD5hnI?t=501 fullerene is not a good lubricant despite being a little ball, because it is reactive and polymerises under pressure
Functional Analysis I course of the University of Oxford 2023-2024 Updated 2025-07-16
Open access with solutions: courses.maths.ox.ac.uk/course/view.php?id=4988
Lecturer: Luc Nguyen
Functional function Updated 2025-07-16
This is about functions that take functions as input or output.
Function (mathematics) Updated 2025-07-16
Set of ordered pairs. That's it! This is illustrated at: math.stackexchange.com/questions/1480651/is-fx-x-1-x-2-a-function/1481099#1481099
Fundação Estudar Updated 2025-07-16
You don't learn the Harvard experience, you absorb it.
- This one does have bias danger though. But detecting greatness, is as type of bias arguably.
Being amongst excellent people makes you learn what excelent people are like, just like only by tasting many different types of wine can you know what good wine is like.
Fusion power could be the next big thing Updated 2025-07-16
Main section: fusion power.
Gallatin School of Individualized Study Updated 2025-07-16
Gallium arsenide Updated 2025-07-16
This is apparently the most important III-V semiconductor, it seems to actually have some applications, see also: gallium arsenide vs silicon.
Gallium arsenide vs silicon Updated 2025-07-16
Trying to use gallium arsenide was Seymour Cray's fatal last flaw as mentioned at The Supermen: The Story of Seymour Cray by Charles J. Murray (1997).
The Supermen: The Story of Seymour Cray by Charles J. Murray (1997) page 4 mentions:
Cray wanted his new machine to employ circuits made from a material called gallium arsenide. Gallium arsenide had achieved limited success, particularly in satellite communications and military electronics. But no one had succeeded with it in anything so complicated as a computer. In the computer industry, engineers had developed a saying: "Gallium arsenide is the technology of the future," they would say. "And it always will be."
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