I think someone said, "The more I learn the more I discover there is to learn." And today I discovered, in part, just how wide just my own chasm of ignorance is, and I consider myself an educated person.
The
American Mathematical Society, no less, has created a book 227 pages long, (
PDF here) and what it does is, lists is all of the
topics of mathematics, plus two pages on how to use the classification list, so that if you're writing an article for publication in their Journal, you put it in one (or more) of the
two thousand subject classifications. I mean, 227 pages and all it is is just the
list of subjects in mathematics; it doesn't even
begin to describe them.
There are more than 50 major topics, numbered from 00 to 97. Each major topic can have up to 27 sections, with -, or lettered A to Z. Then each section has up to 100 related subjects, numbered from 00 to 99, with 00, when used, for general works in that section, and 99, when present, reserved for "none of the above, but in this section."
Just for flavor, I'll pick 10 topics.
00 General and overarching topics; collections
03 Mathematical logic and foundations
19 K-theory
34 Ordinary differential equations
41 Approximations and expansions
42 Harmonic analysis on Euclidean spaces
43 Abstract harmonic analysis
68 Computer science
74 Mechanics of deformable solids
76 Fluid mechanics
Let's look at #68. Computer Science.
68-XX Computer science
- 68-04 Software, source code, etc. for problems pertaining to computer science
68Nxx Theory of software
-68N15 Theory of programming languages
68Pxx Theory of data
-68P05 Data structures
-68P10 Searching and sorting
You get the idea. This one topic has 10 sections, and a total of 110 subjects. Of these 110 my guess is I'm probably very familiar with 3 or 4, have some familiarity with 5 or 6, and maybe have heard of 10. That leaves 90 subjects in my own field I have neither knowledge nor understanding.
I think someone said, "The more I learn the more I discover there is to learn." And today I discovered, in part, just how wide just my own chasm of ignorance is, and I consider myself an educated person.
The [i]American Mathematical Society[/i], no less, has created a book 227 pages long, ([url=https://mathscinet.ams.org/mathscinet/msc/pdfs/classifications2020.pdf]PDF here[/url]) and what it does is, lists is all of the [i]topics[/i] of mathematics, plus two pages on how to use the classification list, so that if you're writing an article for publication in their Journal, you put it in one (or more) of the [i]two thousand subject classifications[/i]. I mean, 227 pages and all it is is just the [i]list[/i] of subjects in mathematics; it doesn't even [i]begin[/i] to describe them.
There are more than 50 major topics, numbered from 00 to 97. Each major topic can have up to 27 sections, with -, or lettered A to Z. Then each section has up to 100 related subjects, numbered from 00 to 99, with 00, when used, for general works in that section, and 99, when present, reserved for "none of the above, but in this section."
Just for flavor, I'll pick 10 topics.
00 General and overarching topics; collections
03 Mathematical logic and foundations
19 K-theory
34 Ordinary differential equations
41 Approximations and expansions
42 Harmonic analysis on Euclidean spaces
43 Abstract harmonic analysis
68 Computer science
74 Mechanics of deformable solids
76 Fluid mechanics
Let's look at #68. Computer Science.
68-XX Computer science
- 68-04 Software, source code, etc. for problems pertaining to computer science
68Nxx Theory of software
-68N15 Theory of programming languages
68Pxx Theory of data
-68P05 Data structures
-68P10 Searching and sorting
You get the idea. This one topic has 10 sections, and a total of 110 subjects. Of these 110 my guess is I'm probably very familiar with 3 or 4, have some familiarity with 5 or 6, and maybe have heard of 10. That leaves 90 subjects in my own field I have neither knowledge nor understanding.