Does there exist applied mathematics research that involves primarily pencil-to-paper work, without the use of computers? Or, are computers quickly replacing everything that an applied mathematician can once do by hand / traditionally does by hand?
Anything in academia in applied math research that computers can't do?
For instance, do PDE theorists use computers or strictly pencil and paper / chalk and chalkboard -- and leave the numerics of PDEs to numerical analysts instead? Is there such a distinction, or is there instead always some sort of collaboration between the two types of applied mathematicians?
Another example that I can think of is the work of probability theorists.
Any insight to my very naive question would be greatly appreciated :)