Applied v. Pure mathematics

I used to be having this huge internal battle between whether I wanted to do pure or applied Mathematics.  And, a long while back I met a while by the name of Robert with whom I discussed this at length.  And, I gave a lot of arguments that Hardy would've been proud of, but in the end, he ended up convincing me by noting that, "All applied Mathematics today is pretty pure, anyways."

And given a lot of the theoretical considerations that goes on, and the historical fact that a lot of Mathematics comes from Physics, and not the other way around as mathematicians would have you believe, gives some credence to this idea.

Plus, I did read Hardy's "Apology for the Mathematician".  He makes a lot of good points intellectual curiosity, professional pride, ambition are the dominant incentives (but no mention of Poincaré's dictum, "Mathematics for Mathematics sake", or of Turán's motto, "Mathematics is a strong fortress.").  The majority of his points on the aesthetics of Mathematics relate to an analogy to the arts:  Artists -> patterns, Painter -> shapes, Poet -> words, Mathematician -> ideas (Hardy holds a very Platonic view of the world, things are of ideal forms, and uses this as a huge justification throughout the entire essay).  However, this does not seem to deny the capability of applied mathematicians.  Moreover, and finally, my main point of contention is Hardy famously saying pure Mathematics is 'useless'.  This to me seems to be the crux of the matter between pure and applied Mathematics.  In particular, Hardy uses this as justification that Mathematics can 'do no harm'.  And uses the Mathematics of number theory and relativity not yet having uses for warfare as examples.

Which, we all know what happened to those two examples (HINT:  CRYPTOGRAPHY AND THE ATOM BOMB GUISE).....