Ciro Santilli @cirosantilli 37

"Dojo" is the japanese version of the word that unfortunately came to dominate in the West, the original is of course Chinese Dao4 chang3 (道場) which means:

dao4 (道): Taoism, the Enlightned Path to something
chang3 (場): suffix indicating "a place where you do something"

 Read the full article

Fable by

Ciro Santilli 37 Updated 2025-07-16

 Read the full article

Millennium Prize Problems by

Ciro Santilli 37 Updated 2025-07-16

 View more

Ciro Santilli would like to fully understand the statements and motivations of each the problems!

Easy to understand the motivation:

Navier-Stokes existence and smoothness is basically the only problem that is really easy to understand the statement and motivation :-)
p versus NP problem

Hard to understand the motivation!

Riemann hypothesis: a bunch of results on prime numbers, and therefore possible applications to cryptography
Of course, everything of interest has already been proved conditionally on it, and the likely "true" result will in itself not have any immediate applications.
As is often the case, the only usefulness would be possible new ideas from the proof technique, and people being more willing to prove stuff based on it without the risk of the hypothesis being false.
Yang-Mills existence and mass gap: this one has to do with finding/proving the existence of a more decent formalization of quantum field theory that does not resort to tricks like perturbation theory and effective field theory with a random cutoff value
This is important because the best theory of light and electrons (and therefore chemistry and material science) that we have today, quantum electrodynamics, is a quantum field theory.

 Read the full article

Hunting by

Ciro Santilli 37 Updated 2025-07-16

 Read the full article

Alexander Grothendieck by

Ciro Santilli 37 Updated 2025-07-16

 View more

This dude looks like a God. Ciro Santilli does not understand his stuff, but just based on the names of his theories, e.g. "Yoga of anabelian algebraic geometry", and on his eccentric lifestyle, it is obvious that he was in fact a God.

 Read the full article

Henri Poincaré by

Ciro Santilli 37 Updated 2025-07-16

 Read the full article

Indo-European language by

Ciro Santilli 37 Updated 2025-07-16

 Read the full article

Linear function by

Ciro Santilli 37 Updated 2025-07-16

 View more

The term is not very clear, as it could either mean:

a real number function whose graph is a line, i.e.:
$f (x) = a x + b$
(1)
or for higher dimensions, a hyperplane:
$f (x_{1}, x_{2}, \dots, x_{n}) = c_{1} x_{1} + c_{2} x_{2} + \dots + c_{n} x_{n} + b$
(2)
a linear map. Note that the above linear functions are not linear maps unless $b = 0$ (known as the homogeneous case), because e.g.:
$f (x + y) = a x + a y + b$
(3)
but
$f (x) + f (y) = a x + b + a y + b$
(4)
For this reason, it is better never to refer to linear maps as linear functions.