Are there any Mathematics SE users who have invested more reputation points in bounties than what they presently have? How can one find out?
As already mentioned in comments, SEDE can be used for such queries.
I took the query showing the users with most bounties awarded and I have sorted it based pm percentage of the reputation given away in bounties: Highest percentage of reputation offered as bounties.
One problem with the query is that all suspended users are in the database with reputation 1. Which means that for such user we'll get from that query much larger amount in bounties than their reputation. Similarly, you will get at the top many users who have never posted anything here and just spent their association on a bounty. So to get some sensible result, you probably want to show only users above some minimal reputation threshold. Here is what you get if you only look at users with reputation at least 50 and at least 50 reputation points in bounties. Or we can lower that even to 2 reputation points - as the main point is to remove users with reputation 1 for reasons mentioned above - and we end up with this list.
Notice that the query has three parameters. Using the parameter min you can restrict it to users which have more than
min reputation points. The parameter minbounties is a restriction on the amount offered in bounties. And the parameter num decides how many top users will be shown.
I will also mention that the query in the first comment only look at the bounties which were actually awarded (and not all offered bounties). If you are interested only in the awarded bounties, you can modify the query for percentage.
EDIT: I started thinking that there was a mistake in those queries after I noticed that one of the top users has different reputation spent on bounties shown in the queries and on the profile page. (And the difference was rather big, about 1000 reputation points.) Then I realized that this is caused by bounties on deleted questions: Users with most bounties on deleted questions. (Until now I did not know that SEDE stores bounties on deleted questions.) IIRC after the question is deleted, the offered bounty amount is refunded to the user.
I do not think that this will influence many users - and even for those users, differences will typically be rather small. Still, I have created a query which only counts reputation on questions that are not deleted: Highest percentage of rep in bounties - only counting questions which are not deleted.