as a whole, which is independent of all systems of reference. When this independence is proved--and in Einstein's case it is so--the complicated aspect of the formula disappears entirely in the light of the higher simplicity and unity of the world-system that presents itself--a world-system that is directed in conformity with the one fundamental law of general relativity as well in the motion of the electrons as in motion of the most distant stars. With regard to the other postulate, that of completeness, _i.e._ absolute accuracy, we have been furnished with proofs that have rightly excited the wonder of the present generation. But are we then to recognize the Principle of Approximation in every direction? Is there then nothing that can be proved rigorously, nothing that is unconditionally valid in the form of knowledge that corresponds exactly to truth? We are led to think of mathematical theorems, which, when they have once been proved, are evident to the same degree as the axioms from which they have been derived, by virtue of logic which cannot be disputed since a contradiction leads to absurdity. It has been said that mathematics _est scientia eorum_, _qui per se clara sunt_, that is, is the science of what is self-evident. But here again doubts arise. If we should get to know only a single case, in which the self-evident came to grief, the road to further doubts becomes open. Such a case will now be quoted. As we know, a tangent is a straight line, which makes contact with a curve at two coincident (or infinitely near) points without actually cutting the curve. The simplest case of this is the perpendicular at the extremity of a radius of a circle. And it agrees fully with what our feeling leads us to expect when it is stated that every curved line that is "continuous," that is, which discloses no break and no sudden bend, has a tangent at every point. Analysis, which treats plane curves as equations in two variables, gives the direction of the tangent in terms of the differential coefficient, and declares accordingly that every continuous function has a differential coefficient, that is, may be differentiated, at every point. The one statement amounts to the same as the other, since there must be an equivalent graphical picture corresponding to every functional expression. But this apparently rudimentary theorem involves an error, which was not discovered before the year 1875. The theory of curves has been in existence for centuries, but it occurred to no one to doubt the general validity of this theorem of tangents. It was regarded as self-evident, as a mathematical intuition. And certainly neither Newton, nor Leibniz, nor Bernoulli, not to mention the mathematicians of olden times, even dreamed that a continuous curve without a tangent, or a continuous function without a differential coefficient, was possible.