Before one can do advanced mathematics (I have too have done research in math) one needs to learn the basics. Reading Smullyan did not in any way help you learn advanced mathematics. It may have helped you to get motivated to learn math and want to learn advanced math but it didn’t help you accomplish this. There’s a reason just about every mathematics department teaches classes on how to do proofs and on basic set theory but almost none of them teach from Smullyan’s book.

The overwhelming empirical evidence is that having a course on proofs and basic set theory is much better preparation for advanced mathematics than reading Smulyan’s recreational math books. I guess you’d rather your students read Martin Gardner and then do Fraliegh’s Abstract Algebra book. No one does it that way but go with your so called empirical evidence.

Having a Ph.D. in math ought to have taught you to reason better than to use “actual research” as part of your reasoning when discussing learning topics that are not cutting edge. One doesn’t need to have done research in mathematics to know about Gorenstein rings or projective dimension or other such stuff. It also has nothing to do with teaching basic math.

I could be wrong in my opinion but attack it on its merits without using superfluous things like “actual research” when research has nothing to do with the topic.

Do you have any evidence that Euclid disagreed with me? Elements starts off with a list of postulates, definitons, and common notions. Then he proceeds to proposition 1. He does not motivate why one would want to come up with proposition 1 or why would should care about it. Have you read Elements?

How do you propose one do applications of point set topology without knowing about sets and mappings? Before the applications one must know the language. We don’t teach the quadratic formula and solving simple velocity problems before teaching students how do the basics of manipulating algebraic expressions.

One must first be a baby before being an adult.