TITLE: Elementary problems that would've been hard for past mathematicians, but are easy to solve today?
QUESTION [12 upvotes]: I'm looking for problems that due to modern developments in mathematics would nowadays be reduced to a rote computation or at least an exercise in a textbook, but that past mathematicians (even famous and great ones such as Gauss or Riemann) would've had a difficult time with. 
Some examples that come to mind are group testing problems, which would be difficult to solve without a notion of error-correcting codes, and -- for even earlier mathematicians -- calculus questions such as calculating the area  of some $n$-dimensional body.
The questions have to be understandable to older mathematicians and elementary in some sense. That is, past mathematicians should be able to appreciate them just as well as we can.

REPLY [4 votes]: In the nineteenth century expressing the antiderivative of an elementary function as an elementary function was an open problem.
Nowadays, Risch algorithm, which can be run on machines, decides whether such operation can be done and, if so, yields a version of the correct result.
I cannot speak for past mathematicians, but I think this is a useful tool.
Added: @columbus8myhw made a very important technical remark in the comments, which is also explained in the last part of the wikipedia article.