Ciro Santilli @cirosantilli 35

A theorem is said to be independent from a set of axioms if it cannot be proven neither true nor false from those axioms.

It or its negation could therefore be arbitrarily added to the set of axioms.

See: math.stackexchange.com/questions/579453/real-world-application-of-fourier-series/3729366#3729366 from heat equation solution with Fourier series.

Separation of variables of certain equations like the heat equation and wave equation are solved immediately by calculating the Fourier series of initial conditions!

Other basis besides the Fourier series show up for other equations, e.g.:

The dominating meme database as of 2020.

This was the pre-Internet precursor of wikis. This program was likely venerable, shame it predates Ciro Santilli's era.

But the thing was much more bloated it seems, and also included visual programming elements, and WYSISYG UI creation.

This is obviously the most efficient investment any non-English speaking country must do, because you need to know English to be able to learn from rich countries and innovate.

Further discussion at: Section "Having more than one natural language is bad for the world".

Website: xkcd.com/

This webcomic is venerated by software engineers as of 2020.

Being able to quote the right one at the right time is considered a fundamental shibboleth of the profession.

And with reason.

Licensed under Creative Commons license CC-BY-NC, amazing!!!

A meta breaking glitch of a video game is a glitch that when discovered significantly breaks the meta.

In non-video game-game, it does sometimes happen that a meta is broken as well, but these events tend to be rarer and less dramatic than meta-breaking due to computer program glitches.

In PvP games, those glitches are generally forbidden by existing rules, and quickly patched after discovered.

In speedrunning however, they are either incorporated in the existing strategy, or may lead to the creation of a new run category for particularly significant glitches.

Non-technical skills were moved to: Ciro Santilli's skills.

This has not been updated since 2016 after Ciro got a job, because it is too hard to put a number on any skill.

What really matters are the most important projects done by Ciro Santilli.

We map each point and a small enough neighbourhood of it to ${\mathbb{R}}^n$, so we can talk about the manifold points in terms of coordinates.

Does not require any further structure besides a consistent topological map. Notably, does not require metric nor an addition operation to make a vector space.

Manifolds are cool. Especially differentiable manifolds which we can do calculus on.

A notable example of a Non-Euclidean geometry manifold is the space of generalized coordinates of a Lagrangian. For example, in a problem such as the double pendulum, some of those generalized coordinates could be angles, which wrap around and thus are not euclidean.

Great chemistry content. Well detailed setups, notably substance extraction from off-the-shelf products.