Hersh is one of the premier popular explicators of mathematics of the 20th century. But interestingly, he and Martin Gardner (probably the more popular writer, but less-schooled in academic mathematics than Hersh) feuded over the years, with their opposing views of math's relationship to 'reality.'
Gardner was the adamant and traditional "Platonist" believing (as most intuitively do) that mathematics is a true reflection of the real world (outside the human mind). Seems obvious to many... but in fact a surprising number of professional mathematicians hold to a different view of mathematics, as just another creation of the human mind (not objectively discovered, but very much influenced and created by human culture, cognition, psychology, etc.). Remove humans (and their minds) from the Universe and there would be no mathematical laws, as we perceive them, operating.
I didn't realize, until reading his brief Wikipedia entry, that Hersh actually originally earned a B.A. degree in English Literature (Harvard), and worked as a machinist and writer for Scientific American, before eventually getting his Ph.D. in mathematics in 1962 (New York University).
Here is what Gardner had to say of Hersh in one of his many online interviews:
"Reuben Hersh is a marvelous example of a person who thinks that mathematics is entirely a human product and has no reality outside of human culture. He has written a whole book about this called "What Is Mathematics Really?" To Reuben Hersh, mathematics is no different from art or fashions in clothes. It’s a cultural phenomenon. The postmodernists in France have essentially this point of view. And it drives me up the wall. I like to say, 'If two dinosaurs met two other dinosaurs in a clearing, there would be four of them even though the animals would be too stupid to know that.' Of course, the argument as to whether the universe exists outside of the human mind goes back to the middle ages."(I suspect Hersh might object to at least part of this characterization.) The irreconcilable differences between these two pillars of 20th century math reporting/education is fascinating, and both views have very bright, significant supporters on their sides (if anything, the Hersh view may even have made gains in recent years, though the Platonist view still predominates).
This simple 2008 piece on the Web addresses the issue:
And Gardner himself has a wonderful 2005 essay (actually a book review), "A Defense of Platonic Realism," reprinted as chapter 9 in his volume "The Jinn From Hyperspace," if you have access to that.
Or, an earlier Gardner essay entitled "How Not To Talk About Mathematics" in his "The Night Is Large" book (chapter 24) covers much the same ground as well (with more specific reference to Hersh). It's a fascinating debate that won't end anytime soon, and that non-mathematicians often aren't even aware of.