I think that cogsci can help me to study a problem in philosophy of math. Consider this case (adapted from M. Detlefsen, *Brouwerian intuitionism*):

Lucy has the kind of understanding of a given math subject S that we typically associate with the master mathematician. John has a superb ability to manipulate the axioms for S according to logical means. 

Problem: is there a significant difference between Lucy's knowledge of S and John's knowledge of S? Is it true that the second kind of knowledge does not imply the first? Is it true that Lucy *understands* S to a certain significant degree), John does not understand S to a certain significant degree.

Are there works in cogsci that can help me to study this problem?

I have found a relatively old article (Arbib, *A piagetian perspective on mathematical constructions*), but nothing else. 

Thanks very much.