As an aside, it's amusing that this conversation is a re-statement of a main point in TFA:

> However, math problems are really there to solve a real world problem.

vs

> That theory might be inspired by the real world, but the problem itself is purely theoretical.

From TFA:

> In my essay The Two Cultures of Mathematics a quarter of a century ago, and which can be summarized by saying that there is a spectrum of attitudes in mathematics to the relationship between problem-solving and conceptual understanding.

The author thinks this letter was choosing only one of them as the "right" approach whereas the better stance is "porque no los dos?"