Taking a very obvious example, you can't do much in the way of historical research without at least trying to establish which things happened before which other things. It's a serious problem in ancient history.

I'm pretty sure modern historians use a lot of mathematical tools: statistics, information science, digital archives, computer imaging, etc. It's very hard to search for this, though, because all of the results concern the history of mathematics. You have to examine the tools and methods used.

Pretty much every field in the social sciences and humanities requires their undergrads to take at least one course in statistics. Sure, these students may complain about it but they need to be trained to not make common statistical errors in their publications. Unfortunately, they still do, which highlights the importance of mathematical education even in these fields.