It would be foolish to pretend that we can penetrate the most obscure corners of Einstein’s theories without the aid of mathematics. I believe, however, that we can give in ordinary language—that is to say, by means of illustrations and analogies—a fairly satisfactory idea of these things, the intricacy of which is usually due to the infinitely subtle and supple play of mathematical formulæ and equations. After all, mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediæval slowness of the syllogisms expressed in our words. However paradoxical this may seem to people who regard mathematics as _of itself_ a means of discovery, the truth is that we can never get from it anything that was not implicitly inherent in the data which were thrust between the jaws of its equations. If I may use a somewhat trivial illustration, mathematical reasoning is very like certain machines which are seen in Chicago—so bold explorers in the United States tell us—into which one puts living animals that emerge at the other end in the shape of appetising prepared meats. No spectator could have, or would wish to have, eaten the animal alive, but in the form in which it issues from the machine it can at once be digested and assimilated. Yet the meat is merely the animal conveniently prepared. That is what mathematics does. By means of a marvellous machinery the mathematician extracts the valuable marrow from the _given facts_. It is a machinery that is particularly useful in cases where the wheels of verbal argument, the chain of syllogisms, would soon be brought to a halt. Does it follow that, properly speaking, mathematics is not a science? Does it follow at least that it is only a science in so far as it is based upon reality, and fed with experimental data, since “experience is the sole source of truth.” I refrain from answering the question, as I am one of those who believe that everything is material for science. Still, it was worth while to raise the question because many are too much disposed to regard a purely mathematical education as a scientific education. Nothing could be further from the truth. Pure mathematics is, in itself, merely an abbreviated form of language and of logical thought. It cannot, of its own nature, teach us anything about the external world; it can do so only in proportion as it enters into contact with the world. It is of mathematics in particular that we may say: _Naturæ non imperatur nisi parendo._