For Plato mathematics was real, but not only that, the stuff we see around us was not. In the Republic he therefore complains about mathematicians "... always

For Plato mathematics was real, but not only that, the stuff we see around us was not. In the Republic he therefore complains about mathematicians "... always talking in a narrow and ridiculous manner, of "squaring" and "extending" and "applying" and the like - they confuse the ways of geometry with those of daily life; whereas knowledge is the real object of the whole science." I find it amazing that Plato wrote this 2000 years before it was taken up again (quite radically) by Brouwer's intuitionism, where "squaring", "extending", "applying" are the only way of doing mathematics (and proof by contradiction, one of Plato's favourite devices, is not admissible) The article's conclusion "Just about everything [except basic number theory] in mathematics is determined by the society in which you live" is rather disappointing, and not at all contradicts the reality of mathematics, as those societies might just have made different discovery journeys in Plato's realm of eternal mathematical truth.