It could plural or singular, I think. You can refer to the entire field of mathematics, or you can refer to the fields that make up mathematics. If that makes sense.
If I'm right in thinking that you're asking if it's possible to find the area of a circle without using pi at all, then the answer is "sort of". There are lots of methods of approximating it without using pi, but you can never get the exact answer without pi (and you can never get the exact value of pi, so you can never really know the exact area of a circle).