Everything is pattern matching (or memorization). You can use this approach to half-automate the solution to a known existing class of problems, but how do you come up with anything new? How did Paul Cohen came up with the forcing technique? Who figured out probabilistic proofs as a possible vector of attack?

"Both these properties, predictability and stability, are special to integrable systems... Since classical mechanics has dealt exclusively with integrable systems for so many years, we have been left with wrong ideas about causality. The mathematical truth, coming from non-integrable systems, is that everything is the cause of everything else: to predict what will happen tomorrow, we must take into account everything that is happening today.

Except in very special cases, there is no clear-cut "causality chain," relating successive events, where each one is the (only) cause of the next in line. Integrable systems are such special cases, and they have led to a view of the world as a juxtaposition of causal chains, running parallel to each other with little or no interference."

- Ivar Ekeland