[red_trumpet]

I agree that pure mathematicians might not care about applications. That is simply not their job.

But successful applications of the real numbers are everywhere present in physics, engineering, statistics, and the other natural sciences. The funny thing is that many of those applications don't care either if real numbers represent an aspect of reality. They are a well-enough approximation, and that makes them work.

[xanderlewis]

The job of an academic is, one could say, to wonder about things (and then pursue them with scholarly rigour). So it seems strange to me that academics think of themselves as having such narrowly-defined roles even within their own subject. But I guess the (pragmatic) answer is that to be successful you must keep focused.

Of course, this is opening another whole can of worms that is perhaps starting to become off-topic.