But her brother did not take notice of this and gave an example: “When I became a mathematician,” he said, “I wanted to achieve scientific success and applied all my energy to that end, even though I regarded it only as a preliminary to something else. And even though my first papers were of course imperfect, as beginnings always are, they really did contain ideas that were new at the time and either remained unnoticed or even met with resistance, even though my other work was well received. Now I suppose one could call it ‘fate’ that I lost patience with having to go on driving that wedge with all my strength.”

“Wedge?” Agathe interrupted him, as if the mere sound of this industriously masculine word connoted something that could not fail to be unpleasant. “Why do you call it a wedge?”

“Because that was all I wanted to do in the beginning: I wanted to keep driving the investigation further and deeper like a wedge, and then I simply lost patience. And today, when I finished what may be the last work reaching back to that period, I realized that I probably might have been not entirely unjustified in regarding myself as the leader of a movement, if at the time I had been luckier or shown more persistence.”

“You could still make up for lost time!” Agathe said. “After all, a man isn’t as likely to get too old for something as a woman is.”

“No,” Ulrich replied, “I don’t want to do that. Because it is surprising, but true, that objectively—in the course of things, in the development of mathematical science itself—nothing would have changed. I may have been about ten years ahead of my time, but others, moving more slowly and along different paths, got there without me. The most I could have done was lead them there more quickly; and it’s an open question whether such a change in my life would have quickened my imagination enough to give me a new lead and carry me across the finish line. So there you have a piece of what is called personal fate, but it amounts to something remarkably impersonal.

“Anyway, it happens more and more often the older I get,” he continued, “that something I used to hate subsequently and in a roundabout way takes the same direction as my own path, so that suddenly I can no longer deny its right to exist; or else it will happen that ideas or events that once brought out my greatest enthusiasm turn out to be faulty. So in the long run it seems to make no difference if one gets excited, nor does it matter what meaning one has invested one’s excitement in. It all comes to the same thing in the end. Everything serves a development that is impenetrable and unfailing.”