Is there any statistics/diagram that shows and compares the number of MO users in the course of time?
SEDE contains some data about users - so one should be able to find out at least some information. I have tried to create at least some queries - I hope that somebody with better knowledge of SQL might come up with some better suggestions.
Number of active users
I think that it is probably more interesting (and more useful) to look at active users rather than all users. Number of all users will, for example, include spambots or users who registered here and never did anything else. The question is, what does it mean that a user is active - I have tried using "posting at least one comment" or "creating at least one post" as a proxy.
I will reuse the queries from another answer:
- How many users created at least one post in the given month or in the given year.
- How many users posted at least one comment in the given month or in the given year.
It is worth mentioning that users with sufficient reputation have access to site analytics where they can see traffic - statistics about visits and page views. A screenshot from 2017 can be seen in another answer here on meta.
Number of all users
We probably want to see the total number of users who created their accounts until the given date.
- This query should show the total number of accounts created per month and per year.
- As another attempt I tried to take rene's query from an answer on Meta Stack Exchange and to modify it to count users: How can I get stats for the total number of questions and answers posted so far vs. time? This is what I get if I use 30 days and 365 days as the increment in that query.
- If users' ids were assigned consecutively from 1 to the most recent user, we could simply look at the maximum of userid. But this does not really work - as you can see in the queries showing the maxima and the minima per month and per year. I do not have some better explanation for the jumps in this graph other than they might be caused by merging accounts (where an older account might suddenly get higher user id if it was merged with a newer account.) For this reason, it might be better to look at the minima. Still, this will be an overestimate - as the id's are probably not necessarily consecutive. Here is a post mentioning this issue for the ids of posts: What are these mysterious gaps in the progression of post id?
Here are some related posts:
- The number of on line users at a given moment on MathOverflow Meta
- User retention rates on MathOverflow on MathOverflow Meta
- How to count the number of active users on SO or other SE communities? on Meta Stack Exchange