From Mathematics without Apologies:

It’s conventional to classify mathematicians as “problem solvers” or “theory builders,” depending on temperament. My experiences and the sources I consulted in writing this book convince me that curiosity about problems guides the growth of theories, rather than the other way around. Alexander Grothendieck and Robert Langlands … count among the most ambitious of all builders of mathematical theories, but everything they built was addressed to specific problems with ancient roots.

**Related post**: Examples bring a subject to life

The client’s problem builds the consultant. The consultant can’t work on the same problem and continue to grow. When the work becomes replication, growth has stopped. Find new clients with new problems. Drive your vector of differentiation.

Another great example of this is the work of Donald Rubin. All his theoretical contributions started from his desire to solve applied problems in a general way.