A fact amazing in its simplicity here comes to light. Newton states the proposition: "According to whatever law an accelerating force acts from a centre on a body moving freely, the radius vector will always sweep out equal areas in equal lengths of time." Nothing is assumed except the law of inertia and a little elementary mathematics, namely, the theorem that triangles on the same base and of the same altitude are equal in area. The form in which this theorem occurs in Newton's simple drawing is certainly astonishing. One feels that there in a few strokes a cosmic problem is solved; the impression is ineffaceable. This theorem together with its proof is contained in Newton's chief work, _Philosophiæ naturalis principia mathematica_. The interfusion of philosophy and mathematics furnished him with the natural principles of knowledge.* Einstein made some illuminating remarks about Newton's famous phrase: "Hypotheses non fingo." I had said that Newton must have been aware that it is impossible to build up a science entirely free from hypotheses. Even geometry itself has arrived at that critical stage at which Gauss and Riemann discovered its hypothetical foundations. Einstein replied: "Accentuate the words correctly and the true sense will reveal itself!" It is the last word that is to be stressed and not the first. Newton did not want to feel himself free from hypotheses, but rather from the assumption that he invented them, except when this was absolutely necessary. Newton, then, wished to express that he did not go further back in his analysis of causes than was absolutely inevitable. Perhaps, I allowed myself to interject, a more violent suspicion against the word "hypotheses" was prevalent with scholars in Newton's time than now. Newton's emphatic defence would then appear a shade more intelligible. Or did he cherish the belief that his world-law was the only possible one in Nature? Einstein again referred to the universality of Newton's genius, saying that Newton was doubtless aware of the range within which his law was valid: this law applies to the realm of observation and experience, but is not given _a priori_, no more than Galilei's Law of Inertia. It is certainly conceivable that beyond the domain of human experience there may be an undiscoverable universe in which a different fundamental law holds, and one which, nevertheless, does not contradict the principle of sufficient reason. The antithesis: Simplicity--Complexity, led the conversation into a short bypath; it arose out of an example which I quoted and that I shall repeat here even if it may seem irrelevant.