What does vice versa mean here? Clerks are turned into mathematicians by using a computer?

A clerk who once used a physical filing system but now uses a computer may naturally begin to bring the filing system to a higher level of abstraction. Think filing clerk -> database administrator -> relational algebra...

E.g. there would be enormous difficulty in replacing the Dewey Decimal System with something else, if only due to its physical inertia, but with a computer system a curious clerk can invent an alternative categorization and retrieval system which inevitably touches on mathematical topics.