Ciro Santilli @cirosantilli 37

Two symmetric matrices $A$ and $B$ are defined to be congruent if there exists an $S$ in $GL(n)$ such that:

One of the most simply classification algorithm one can think of: just see whatever kind of point your new point seems to be closer to, and say it is also of that type! Then it is just a question of defining "close".

Scikit-learn implementation scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html at python/sklearn/knn.py

This idea also comes up in other sources of course.

Calculus of variations is the field that searches for maxima and minima of Functionals, rather than the more elementary case of functions from $\mathbb{R}$ to $\mathbb{R}$.

Contains the first sporadic groups discovered by far: 11 and 12 in 1861, and 22, 23 and 24 in 1973. And therefore presumably the simplest! The next sporadic ones discovered were the Janko groups, only in 1965!

Each $M_n$ is a permutation group on $n$ elements. There isn't an obvious algorithmic relationship between $n$ and the actual group.

TODO initial motivation? Why did Mathieu care about k-transitive groups?

Their; k-transitive group properties seem to be the main characterization, according to Wikipedia:Looking at the classification of k-transitive groups we see that the Mathieu groups are the only families of 4 and 5 transitive groups other than symmetric groups and alternating groups. 3-transitive is not as nice, so let's just say it is the stabilizer of $M_{23}$ and be done with it.

One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.

This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.

Published as On the Relative Motion of the Earth and the Luminiferous Ether.

A 4D gradient with some small special relativity specifics added in (the light of speed and sign change for the time).

scholarworks.sjsu.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=5051&context=etd_theses proves that the Mathieu group $M_{24}$ is simple in just 200 pages. Nice.

Examples:

Server run on the current machine. That's how all websites are developed and born!

Open source driver/hardware interface specification??? E.g. on Ubuntu, a large part of the nastiest UI breaking bugs Ciro Santilli encountered over the years have been GPU related. Do you think that is a coincidence??? E.g. ubuntu 21.10 does not wake up from suspend.