## Andreas Speiser and the teaching of mathematics

In his paper 'Symmetry in Science and Art',

*Daedalus***89**(1, The Visual Arts Today) (1960), 191-198, Andreas Speiser begins with a short section entitled "Why Is Mathematics So Unpopular?". We give this section below and encourage the interested reader to look at the whole of Speiser's article which also contains the sections: 'How Symmetry Acts'; 'Groups and the Visual Arts'; 'New Proportions for Art'; 'The Figure as a Plan for the Center of a City'; and 'The Use of the Plan for a Church or a Secular Building'.**Why Is Mathematics So Unpopular?**

Whoever in his youth enjoyed musical instruction, as in playing the piano or the violin, will recall the course of such a lesson: it began with finger exercises, scales, and arpeggios, followed by an etude, then by a short composition, and at the end came the classical sonata. Thus each lesson became an adventure with an increasing content. The fact that the student was by no means capable of understanding the full import of the classical composition made no difference, and it became his permanent property, which he enjoyed again and again. Instruction in mathematics, on the other hand, has for more than a century taken an entirely different course: often the student never passes beyond finger exercises and other boring, mindless gymnastics; while the same persons who enjoy card games, crossword puzzles, dancing, and drumming to the point of obsession regard mathematics merely as the very image of boredom. No subject of instruction in school is abused to such an extent as mathematics, and from this viewpoint it looks like a sterile desert. It is quite understandable that no pleasure can ever be derived from this science when one is under such interminable torture. Its instruction is aimed entirely at practical applications - whereas the art is never mentioned. It cannot be denied, however, that most games enjoyed by human beings owe their laws, even their very existence, to mathematics, or that within man's soul there dwells a spiritual nature that derives enjoyment from these geometric and arithmetic structures them selves, quite apart from intellectuality. This teaching concerning the mathematical nature of our soul is very ancient: it was formulated by Kepler, who in turn took it over from Proclus.