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It appears to me most research in mathematics requires close studying of the work done by the previous generation, so this seems to rely on mathematicians keeping track of and recording the new knowledge which is discovered/created as well as there always being a new generation of people to carry on that task after the current mathematicians die. However from research online and questions like this one it appears there is maybe one mathematician per every 50,000 people on earth and in the United States alone probably no more then 9000 actual mathematicians that are engaged in research. Thus all of this seems very fragile/delicate, these people are already very rare so whose to say the number might not drop to half that in the next few decades?

Also given that people have contributed thousands and thousands of years of work to compiling all this information shouldn't there be some kind of mass archive to protect it? Like a seedbank or something? Sorry if this sounds stupid, but I guess my more pertinent question is where are these new people coming from who want to study mathematics? From looking online and talking with others, it seems that these people who go on to become mathematicians all overwhelming have experiences of being engaged in or encouraged to participate in STEM areas, so I'd guess a large component is childhood factors, which I suppose makes sense as in order to get engaged in mathematics it seems most have to study or work at it for a long time, it also seems a large number of the math undergraduates that I talked to had parents who were software engneers, teachers, etc. so thats likely a factor.

What are other variables correlated with perusing research in mathematics? I can't seem to find any studies, though I'd guess its just because they are so incredibly rare (to reiterate I'm talking about people engaged in research, not people in industry or teaching high school or something). Does anyone know of any studies or writings on this topic? How about on the stuff regarding some kind of "global archive" or "mass directory" like a seedbank to ensure all past and future work in math is not lost/forgotten/failed to be taught to new people? Again sorry if this all sounds stupid, I tagged this as "soft question".

user3865391
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    I study math because I like it. I have no profound reason to do so. Also, you may want to consider breaking this into paragraphs - a giant wall of text is a huge turn-off and makes it hard to read. – Sean Roberson Dec 21 '19 at 22:49
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    "When two mathematicians like each other very much..." – Ricardo Buring Dec 21 '19 at 22:51
  • Your numbers don't balance. If 1 in 50 thousand are mathematicians than one in 9 thousand mathematicians are engaged in research there is only 1 mathematician in America conducting research. – Doug M Dec 21 '19 at 22:51
  • @DougM 1 in 50,000 on Earth. The 1 in 9000 is for the United States. Though all of this is estimates. Sorry if I made it sound different. – user3865391 Dec 21 '19 at 22:52
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    In general, it is not a good idea to ask too many questions in one post: You seem to have asked at least 3. As for a "global archive", there are numerous libraries as well as arxiv doing exactly this. As for the question "so whose to say the number might not drop to half that in the next few decades?", the obvious answer is "nobody". A global nuclear war will cut the number not just in half... – Moishe Kohan Dec 21 '19 at 23:02
  • @MoisheKohan I thought that was just for new papers? Do they have an archive holding past work as well as books? I know very little but to me it looks like everything is spread out among books, papers, journals, blogs etc – user3865391 Dec 21 '19 at 23:04
  • @user3865391: The arxiv is active since 1992, almost all professional mathematicians post there. As for other online data banks, Google (or Alphabet) is copying pretty much everything it can get, also Gottingen Library is digitalizing everything which is not copyrighted. – Moishe Kohan Dec 21 '19 at 23:09
  • @MoisheKohan Wow thats good. But how long do they record stuff on servers? In fact how long can electronic storage even work for? I imagine for many decades, but don't the electric charges holding that data in place eventually dicipate? So is it all just relying on Google to "re-fresh" the charges or whatever on their servers (I imagine most electronic storage does this automatically)? Like hypothetically if you put your hard-drive in a box in the ground and left it there for 5000 years, and you came back to it, would all the stuff still be on there? – user3865391 Dec 21 '19 at 23:17
  • I am sure they are well aware of the "bit-rot", how do they deal with this, I do not know since I am not involved in this activity. See also Martin Sleziak's answer here. Basically, all reasonable math journals are actively digitalizing their old papers, to the point that I hardly ever now go to our university library to look even for 100-year old papers. – Moishe Kohan Dec 21 '19 at 23:22

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You asked at least three questions:

  1. What are digital databases of mathematical papers, journals and books?

There are many, see for instance the list maintained by the Library of the University of Bielefeld here. Most notable are:

  • DGZ at the University of Goettingen,

  • JSTOR

  • arXiv

  • numdam (primarily French).

    1. Why do people choose to do math?

This is highly variable, making an answer impossible. The reasons include the beauty and addictive nature of mathematics, security of employment (for those who have tenure), competitive nature of mathematics, collaborative nature of mathematics ...

  1. Who is to say that the number of mathematicians will not drop in half in the near future?

Nobody, of course. Having a reasonably large number of research mathematicians is a luxury that a civilized society can afford, but not a society struggling to survive. Just look at what happened to the science of Antiquity, much of which was lost.

Moishe Kohan
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