Cartesian geometry emerged from the same social context as modern cartography. Alexandrian astronomy also precipitated a more decisive departure from the sterile tradition of Platonic geometry. From Euclid, the first teacher of Alexandrian mathematics, the Alexandrians had received Plato’s idealistic doctrine that mathematics should be cultivated as an aid to spiritual refinement. The first measurements of celestial distances sufficed to show the clumsiness of the Platonic methods. The stubborn realities of the material world forced them to refinements which resulted in cultivating new methods. Hipparchus compiled the first trigonometrical table — a table of sines. Thenceforth Plato’s geometry was an anachronism. With the aid of six or, at most twelve, of its propositions, we can build up the whole of trigonometry and the Cartesian methods. Unfortunately the curriculum of our grammar schools was designed by theologians and politicians who believed in Plato. So we continue to teach Euclidean geometry for the good of the soul. Since few normal people like what is good for them, this makes mathematics a most unpopular subject and effectually prevents the majority from ever finding out the immense usefulness of mathematics in man’s social life. One result of not understanding how mathematics can be usefully applied is that many people do not realize when it cannot be usefully applied. Hence the delusion that a subject is entitled to rank as a science when it contains formulae.

(From Science for the Citizen – Lancelot Hogben)