Lecture XII

Thus in the case of these two personalities one is led back to a period when their lives ran together. I would never have found Byron in this earlier life if I had not found this geometry teacher of mine at his side. Byron was a genius. My geometry teacher was not even a genius in his own way. He was not a genius at all, but he was an excellent geometrician, quite the best I have ever come across, because he was a genuine geometrician and nothing else. In the case of a painter or a musician, you know that you are dealing with a one-sided man. For as a matter of fact, people are significant only when they are one-sided. As a rule, however, a geometrician in our time is not one-sided. A geometrician knows the whole of mathematics; when he constructs something in geometry, he always knows how to state the equations for it. He knows the mathematical, calculating side of it all. But this geometry teacher, though an excellent geometrician, was properly speaking no mathematician at all. He understood, for example, nothing whatever of analytical geometry. He knew nothing of the geometry that has to do with calculating and equations; in that respect he sometimes did the most childish things. On one occasion it was really very humorous. The man was so entirely a constructive geometrician and nothing else that he arrived by means of constructive geometry at the fact that the circle is the locus of the constant quotient. He found it out by construction, and since no one had found it before by construction, he regarded himself as its discoverer. We boys, who were as yet unsophisticated and had a good store of high spirits left in us, knew that in our book of analytical geometry it is shown how one sets up such and such an equation and the circle comes. We took the occasion to change the name of the circle and to start calling it by the name of our geometry teacher. The “N.N. line” we called it (I won't give his real name). This man had in fact the one-sidedness of the constructive geometrician to the point of genius. That was what was so significant about him; his character and talents were so clearly defined. People of the present day are not like that at all; you cannot get hold of them; they are like slippery eels! My teacher was anything but a slippery eel; he was a man with sharp corners, and that even in his external appearance. He had a face shaped like this—quite square, a most interesting head, absolutely four-angled, nowhere round. Really, you could study in the face of the man the right-angled nature of his peculiar constructive talent. It was most interesting.