About a year and a half ago, after reading Penrose's book "The Road to Reality" I started a thread The Platonic World. Real or a human construct? in which I tapped into a rich vein of opinion concerning the nature of mathematics. At the time I hadn't appreciated how strongly some mathematicians feel about this, so I trod on some toes, and also got diverted into posting about string theory. I've recently been enlightened by a new article that may be of interest in this forum. It's perhaps better to start a new thread about it than to revive the old one. The new article is Mathematical Platonism and its Opposites , by Barry Mazur. He holds a name chair at Harvard and the article is in my opinion worth reading, perhaps by philosophers especially. He discusses both Platonic and Anti-Platonic views about this question, which he says concern most dedicated mathematicians. Do folk in this forum have any further comments on what Mazur calls "The Question" that they might wish to express ?