cont’d in Gass, READING RILKE
After training,… after an education, comes practice. Intense. Extended. Mindful. Careful. While continuing to read, to imitate if necessary, to learn. Rilke’s easy way with words led him astray, and he was late in his mastery of Goethe, Hölderlin, and many others. Rilke’s salad days were followed by arid stretches, by doubts, difficulties of all kinds, and these were painful for him, but no doubt necessary. Meanwhile, he was trying to understand his own conflicted nature. It is important to remember that the body fuels the mind. And that character controls both. The creative life of the mathematician is usually over by age forty. Perhaps the emotional problems the scholar is fleeing, by working in a world of total abstraction, no longer exert the same fearful pressures. Rilke needed his neuroses, he thought, and he refused, for that reason, to undergo psychoanalysis, although it was suggested to him.
Once one has become a mathematician, a physicist, a poet, then what one knows, what one feels and thinks, can be focused upon a particular problem. “For fifteen days,” Poincaré tells us, “I strove to prove that there could not be any functions like those I have since called Fuchsian functions.” Despite his own denials, a sleepless night full of colliding ideas allowed him to establish the existence of such a class. Next, he wished to represent these new functions through the quotient of two series. This was a conscious choice. And the choice was made by an analogy with solutions achieved in other areas. Meanwhile, Poincaré had agreed to go by bus on a geologic excursion. Mathematical issues were far from his thoughts. “At the moment when I put my foot on the step [of the bus] the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.”
As in Rilke’s case, the ultimate solution to this complex problem was achieved in stages. Work. Blockage. Insight. Verification. Followed by the orderly development of the new idea.
Poincaré then turned his attention to what appeared to be quite a different set of problems in arithmetic, but he had a signal lack of success. Giving up in disgust, he took a few days off to visit the seaside. Then, for him, the Rilke-like moment arrived: “One morning, walking on the bluff, the idea came to me, with just the same characteristics of brevity, suddenness and immediate certainty, that the arithmetic transformations of indeterminate ternary quadratic forms were identical with those of non-Euclidean geometry.” Further verifications follow. That is to say: proofs. “Naturally I set myself to form all these functions. I made a systematic attack upon them and carried all the outworks, one after another. There was one however that still held out, whose fall would involve that of the whole place.” One more blockage. Now he has to leave his work to go through military service (Poincaré is no exception to the rule of youth). While he was walking down the street one seemingly ordinary day, “the solution of the difficulty which had stopped me suddenly appeared to me.” He had to delay writing down this solution for some time, but time was no longer a factor. Eventually, he did it with dispatch.
In each stage of Poincaré’s amazing discovery, there are the same factors: initial talent, life preparation, focus, failure, distraction, revelation. In Rilke’s case, we can be considerably more detailed in our description. And the delays are sometimes years rather than weeks or days. Not only is the inspirational moment preceded by a lifetime of practice, but its environmental conditions must be fully met—in effect, the gun must be loaded and cocked before the trigger is pulled. However, since one is never sure what all these conditions are, they are realized by luck as much as plan.