It might be asked: Was there any knowledge of Pythagoras' Theorems before Pythagoras gave us his proof? We should have to answer: It was in existence at least in the still dark field of vision of Pythagoras, which became illumined one day when he took such a view of the number-ratios 3--4--5 that an exact intuition could actually come about. It is erroneous to assume that a creative act suddenly called up before his soul as if by magic the figure with the three squares drawn externally on the sides of a triangle. Rather, he "took his stride" (as we know from Vitruvius) by considering a triangle whose sides were of a definite length; and the well-known proof, which is linked indissolubly in our minds with his work, is not his at all, but Euclid's. Yet our annals grow musty, centuries pass by, and the credit of being the creator rests with the man who first succeeded in getting a clear picture of such a triangle. It seems natural to test discoveries by experiments. The first result of doing this is a very remarkable increase in the rate at which the intuitive process has developed. In ancient times, intuition, it seems, scarcely felt the need of proving things by experiment; all that was discovered by Archimedes in mechanics, by the Pythagoreans in acoustics, by Euclid in optics, may be reduced practically to the formula "heureka," and it is probably scarcely an exaggeration to say that more and more fruitful experiments are performed in one week nowadays than in the whole of the classical age taken together.[3] [Footnote 3: Recently certain precisians in definition have been seeking to establish a fundamental difference between physicists of reality, experimental physicists, and "blackboard-physicists." The last term is given jeeringly to theoretical physicists because they, in the opinion of these critics, wish to found Nature entirely on formulæ argued out on the blackboard. The history of science does recognize this distinction, although it is, of course, quite possible for a physicist to arrive at important discoveries without making any experiments. One might be more justified in asserting that the great theorist need not necessarily be a great experimenter and vice versa. But I can quote no example of a physicist who confined himself obstinately to blackboard discussion, and on principle disowned all experimental work. I must add that Einstein himself is fond of experimenting, and has had much success in experimental work. The amount of advice and encouragement that he has given, and still gives, to many workers in this field is very considerable. But he does not practise experimental work regularly, and remarked that he is obliged to appeal to outside help for certain practical tests. There are specific experimental geniuses, whose activity assumes the happiest and most fruitful form when it supplements that of the theorist and fertilizes it.]