Jan Arnoldus Schouten

"In 1905 "LEnseignement Mathématique" started an inquiry into the methods of working of mathematicians. The results of this inquiry augmented and developed later by several authors, for instance Carmichael and Hadamard, can be expressed shortly as follows. The faculty of deduction belongs to the conscious mind, the subconscious being in general only able to perform very simple and trivial deductions. On the contrary the faculty of rearranging is typical of the work of the subconscious and is described by Carmichael as consisting of an extremely rapid passing over of innumerable useless combinations till a vital one or some vital ones rise to consciousness, to bring, after a severe control of the conscious mind, new truth to light."

"I certainly learned a great deal from him; especially the combination of algebraic and geometric thinking typical of Klein and Darboux. Our first common publication appeared in 1918; it investigated the connection between geometry and mechanics in the static problems of general relativity. Thus it accounted for the perihelion movement of Mercury, then a crucial test for Einsteins theory, by the change of the metric corresponding to a corrective force."

"In differential geometry conditions of integrability frequently occur, but in the cases usually investigated only the first of these conditions has to be considered. In 1922 ... Eisenhart and Veblen gave a necessary and sufficient condition that a geometry of paths be a Riemann geometry by using a new method of treating the conditions of integrability of higher order."

"Tensor calculus would not exist in its modern form if there had never been a theory of relativity. The ties between these two branches of mathematics and physics are so many that they would fill a big textbook. ... Although the affine invariant form of the electromagnetic equations was not unknown to preceding authors, ... van Dantzig was the first to develop in a long series of publications a consistent theory of relativity which was independent of metrical geometry."