How useful is this? Not much that these things have in common beyond "results cited a lot".
Can't say that the subjects are chosen very precisely either -- the Fundamental Theorem of Algebra isn't actually a theorem of algebra; Tychonoff's theorem is fundamental only to the set-theoretical part of topology; the Fundamental Theorem of Counting is just a particular case of the "Fubini" interchange-of-summations formula, which I would call the real fundamental theorem of counting. The number of platonic solids is mostly a curiosity from a modern perspective; so are the transcendences of pi and e.
Also, the word "extended" in the Number systems section needs to be taken with some artistic license; the "extension" introduces new symbols (negatives) and new relations that can occasionally render some old elements identical (in the worst case, the whole monoid can collapse to a point). The most famous example of this is what happens if you divide by 0 (= extend the multiplicative monoid of real numbers to a group). This is not something the author should be blamed for; it's the only real error I've spotted at a quick skim, and it's rare for a collection as diverse as this to have this few errors. The real problem is: what's the point of such a survey if pretty much any of the results is given so little time and space that only those who already know it can understand it from the description?
Compact summaries are useful when revisiting something that was learnt before. Such a document might be more useful for mathematics than most subjects, since many have studied maths but stopped using it, and those teachings are generally still true and relevant.
The doc would be at least 20 % more useful to me if the pdf had a table of contents. Should be easy to include assuming that it was written with latex. Opinion: when writing a lengthy latex document, the extra 0.5 % of work required to add automated pdf metadata (table of contents, clickable references) has outsized usability effects.
I stumbled upon typos:
* "Basel problem formula": pi should be squared.
* The "more general" statement related to Bayes theorem lacks a right parenthesis.
Can't say that the subjects are chosen very precisely either -- the Fundamental Theorem of Algebra isn't actually a theorem of algebra; Tychonoff's theorem is fundamental only to the set-theoretical part of topology; the Fundamental Theorem of Counting is just a particular case of the "Fubini" interchange-of-summations formula, which I would call the real fundamental theorem of counting. The number of platonic solids is mostly a curiosity from a modern perspective; so are the transcendences of pi and e.
Also, the word "extended" in the Number systems section needs to be taken with some artistic license; the "extension" introduces new symbols (negatives) and new relations that can occasionally render some old elements identical (in the worst case, the whole monoid can collapse to a point). The most famous example of this is what happens if you divide by 0 (= extend the multiplicative monoid of real numbers to a group). This is not something the author should be blamed for; it's the only real error I've spotted at a quick skim, and it's rare for a collection as diverse as this to have this few errors. The real problem is: what's the point of such a survey if pretty much any of the results is given so little time and space that only those who already know it can understand it from the description?