Indeed every mathematician knows that a proof has not been "understood" if one has done nothing more than verify step by step the correctness of the deductions of which it is compose d and has not tried to gain a clear insight into the ideas which have led to the construction of this particular chain of deductions in preference to every other one.

Quoted in Douglas M. Campbell and John C. Higgins, Mathematics: People, Problems, Results (Volume 3), In Richard A. De Millo, Richard J. Lipton and Alan J. Perlos, Social Processes and Proofs of Theorems and Programs (p. 25)