Brahmagupta’s problem[96] appears to be the earliest instance of a kind of joke which has been much used by mathematicians. For the sake of giving a certain picturesqueness to the data of problems, and so to excite that sort of interest which is partly expressed by a smile, mathematicians have got into the habit of talking, for example, of monkeys in the form of geometrical points climbing up massless ropes. Professor P. StÄckel[97] truly remarked that physiological mechanics—the mechanics of bones, muscles, and so on—is wholly different from this. There was once a lecturer on mathematics at Cambridge who used yearly to propound to his pupils a problem in rigid dynamics which related to the motion of a garden roller supposed to be without mass or friction, when a heavy and perfectly rough insect walked round the interior of it in the direction of normal rolling.

Hitherto this has been the only mathematical outlet for the humour of mathematicians; and those who really had the interests of mathematics at heart saw with alarm the growing tendency towards scholasticism in mathematical jokes. Fortunately the discovery of logic by some mathematicians has removed this danger. Still to many mathematicians logic is still unknown, and to them—to Professor A. Schoenflies for example—modern mathematics, owing to its alliance with logic, appears to be sinking into scholasticism. It is true that the word “scholasticism” is not used by Professor Schoenflies in any intentionally precise signification, but merely as a vague epithet of disapproval, as the word “socialism” is used by the ordinary philistine, and this would certainly serve as a sufficient excuse. But no excuse is needed: these opinions are themselves a source of mathematical jokes.

CHAPTER XXXVII