Ciro Santilli @cirosantilli 35

26 parameters of the Standard model on the blackboard. If one of those parameters should happen to be erased, 25 parameters of the Standard model on the blackboard....

But certainly, mathematics is not a part of.

In mathematics, a "classification" means making a list of all possible objects of a given type.

Classification results are some of Ciro Santilli's favorite: Section "The beauty of mathematics".

Examples:

As shown in Video "Simple Groups - Abstract Algebra by Socratica (2018)", this can be split up into two steps:This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the jordan-Holder Theorem.

Good lists to start playing with:

History: math.stackexchange.com/questions/1587387/historical-notes-on-the-jordan-h%C3%B6lder-program

It is generally believed that no such classification is possible in general beyond the simple groups.

Bibliography:

$M_n({\mathbb{F}}_q)$ accounts for them all, which we know how to do due to the classification of finite fields.

So we see that the classification is quite simple, much like the classification of finite fields, and in strict opposition to the classification of finite simple groups (not to mention the 2023 lack of classification for non simple finite groups!)

If you are a pussy and work a soul crushing job, this is one way to lie to yourself that your life is still worth living: do one cool thing every day.

Find a time in which your mind hasn't yet been destroyed by useless work, usually in the morning before work, and do one thing you actually like in life.

Work a little less well for you boss, and a little better for yourself. Ross Ulbricht:Selling drugs online is not advisable however.

Even better, try to reach an official agreement with your employer to work 20% less than the standard work week. For example, you could work one day less every week, and do whatever you want on that day. It is not possible to push your passion to weekends, because your brain is too tired. "You keep all non-company-related IP you develop on that time" is a key clause obviously.

On a related note, good employers must allow employees to do whichever the fuck "crazy projects", "needed refactorings or other efficiency gains" and "learn things deeply" at least 20% of their time if employees want that: en.wikipedia.org/wiki/20%25_Project. Employees must choose if they want to do it one day a week or two hours per day. One day per month initiatives are bullshit. Another related name: genius hour.

Highly relevant on this topic: Video "What Predicts Academic Ability? by Jordan B Peterson (2017)".

Maybe you will be fired, but long term, having tried, or even succeeded your dream, or a one of its side effects, will be infinitely more satisfying.

The same goes for school, and maybe even more so because your parents can still support you there. Some Gods who actually followed this advice and didn't end up living under a bridge:

Gandhi TODO source:

The only cases where formal proof of theorems seem to have had actual mathematical value is for theorems that require checking a very large number of case, so much so that no human can be fully certain that no mistakes were made. Some examples:

In the classification of finite simple groups, groups of Lie type are a set of infinite families of simple lie groups. These are the other infinite families besides te cyclic groups and alternating groups.

A decent list at: en.wikipedia.org/wiki/List_of_finite_simple_groups, en.wikipedia.org/wiki/Group_of_Lie_type is just too unclear. The groups of Lie type can be subdivided into:

The first in this family discovered were a subset of the Chevalley groups $A_n(q)$ by Galois: $PSL(2,p)$, so it might be a good first one to try and understand what it looks like.

TODO understand intuitively why they are called of Lie type. Their names $A_n$, $B_n$ seem to correspond to the members of the classification of simple Lie groups which are also named like that.

But they are of course related to Lie groups, and as suggested at Video "Yang-Mills 1 by David Metzler (2011)" part 2, the continuity actually simplifies things.

The following things come to mind when you look into research in this area, especially the search for BB(5) which was hard but doable:

Bibliography:

Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md

The most beautiful things in mathematics are results that are:

Good lists of such problems Lists of mathematical problems.

Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.