Baker-Campbell-Hausdorff formula Updated 2025-07-16
Solution for given and of:
where is the exponential map.
If we consider just real number, , but when X and Y are non-commutative, things are not so simple.
Furthermore, TODO confirm it is possible that a solution does not exist at all if and aren't sufficiently small.
This formula is likely the basis for the Lie group-Lie algebra correspondence. With it, we express the actual group operation in terms of the Lie algebra operations.
Notably, remember that a algebra over a field is just a vector space with one extra product operation defined.
Since a group is basically defined by what the group operation does to two arbitrary elements, once we have that defined via the Baker-Campbell-Hausdorff formula, we are basically done defining the group in terms of the algebra.
Bank Updated 2025-07-16
Binance Updated 2025-07-16
Bare metal Updated 2025-07-16
Bare metal programming is to run a program without an operating system below it.
Or in other words, it is basically implementing an operating system/firmware yourself ad hoc, together with your actual program.
Baryon vs meson vs lepton Updated 2025-07-16
"Barys" means "heavy" in Greek, because protons and neutrons was what made most of the mass of known ordinary matter, as opposed notably to electrons.
Baryons can be contrasted with:
Base calling Updated 2025-07-16
Based God Updated 2025-07-16
Someone who is not a pussy.
Someone once called Ciro Santilli that: archive.is/W1ocv. It's an overstatement, considering that Ciro's parents have some money. Not infinite. But still. Changes everything. A real Based God is someone like Charles Bukowski, who had to work decades at the post office.
Bash (Unix shell) Updated 2025-07-16
The more heavily a project relies on it, the more you start to regret it.
Battle of Algiers (1966) Updated 2025-07-16
There's nothing like seeing the hypocrisy of the "Liberté, Égalité, Fraternité" people destroyed.
Interesting how Algeria now supports China's Xinjiang policy in 2019. But of course, dictatorships tend to work together
Ciro Santilli's father, an avid history reader, and in particular interested in the military dictatorship in Brazil through which he lived, once told Ciro how the French torture doctrine was directly adopted by Brazillian military, e.g. then even invited general Paul Aussaresses who had served in Algeria, to help them out with intelligence operations and give courses. Bro, fuck that.
BB(5) Updated 2025-07-16
The last value we will likely every know for the busy beaver function! BB(6) is likely completely out of reach forever.
By 2023, it had basically been decided by the The Busy Beaver Challenge as mentioned at: discuss.bbchallenge.org/t/the-30-to-34-ctl-holdouts-from-bb-5/141, pending only further verification. It is going to be one of those highly computational proofs that will be needed to be formally verified for people to finally settle.
As that project beautifully puts it, as of 2023 prior to full resolution, this can be considered the:
simplest open problem in mathematics
on the Busy beaver scale.

There are unlisted articles, also show them or only show them.