I don't know about Grothendieck. But, Kontsevich's statement is telling:

For myself sometimes I work on one or two examples

Halmos (quoting Hilbert) captures this very well:

What mathematics is really all about is solving concrete problems. Hilbert once said (but I can't remember where) that the best way to understand a theory is to find, and then to study, a prototypal concrete example of that theory, a root example that illustrates everything that can happen. The biggest fault of many students, even good ones, is that although they might be able to spout correct statements of theorems, and remember correct proofs, they cannot give examples, construct counterexamples, and solve special problems.