So would you say people who do master complex mathematical concepts too learn from examples, rather than a deductive approach of understanding pure theory?
https://gowers.wordpress.com/2007/10/19/my-favourite-pedagog...
https://gowers.wordpress.com/2007/10/24/examples-first-ii/
(There are also comments by those who disagree.)
I looked at a couple of instances to see how one of my favourite authors, Knuth, explains things. If you look at how he introduces BDDs (Binary Decision Diagrams), it is with an example first: http://www.cs.utsa.edu/~wagner/knuth/fasc1b.pdf#page=8
When he introduces an algorithm for generating all permutations (http://www.cs.utsa.edu/~wagner/knuth/fasc2b.pdf#page=5), he does not work through the entire algorithm on an example case. However, when he mentions “all permutations … in lexicographic order”, he immediately gives an example of what that means.
(In general Knuth is a big fan of the principle of saying everything twice, once informally and once formally; his literate programming paradigm is also an extension of this idea, where first you explain something informally and then write down the code which is supposed to be a precise version of it.)
Everyone learns better starting from examples. Humans are inductive learners. Makes sense, given our situation.
However, from our starting point some people meta-learn abstract reasoning i.e. mathematics, which doesn't come naturally. Maths is hard because it isn't the way we usually think.
Often those people claim to find purely theoretical approaches better for learning, although I'm personally sceptical from attending a decade of seminars and classes at many institutions; people presenting a purely theoretical introduction to a topic are immediately hit with requests for examples. And usually criticised for not starting with examples. But I do not usually attend lectures in maths departments (rather than related subjects, e.g. CS).