Islam has some really nice things in it.
Ciro Santilli especially appreciates the ideas of
Most commonly refers to: exponential map.
An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) shows that this is a tensor that represents the volume of a parallelepiped.
It takes as input three vectors, and outputs one real number, the volume. And it is linear on each vector. This perfectly satisfied the definition of a tensor of order (3,0).
Lie Algebras In Particle Physics by Howard Georgi (1999) Updated 2025-07-01 +Created 1970-01-01
Integrable functions to the power , usually and in this text assumed under the Lebesgue integral because: Lebesgue integral of is complete but Riemann isn't
The dude was brutal. Ron Maimon praises that at youtu.be/ObXbKbpkSjQ?t=944 from Video "Ron Maimon interview with Jeff Meverson (2014)".
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 cryptographyOf 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 valueThis 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.
There are unlisted articles, also show them or only show them.