Too Much Happiness

“My goodness,” said Clara, whose speculations were the more lively, “my goodness, we thought, what have we here, is it a Charlotte Corday?”

This was all told to Sophia later, when she had become their friend. And Elisa added drily, “Fortunately our brother was not in his bath. And we could not get up to protect him because we were all wrapped up in those endless mufflers.”

They had been knitting mufflers for the soldiers at the front. It was 1870, before Sophia and Vladimir took what they meant to be their study trip to Paris. So deep they were then in other dimensions, past centuries, so scant their attention to the world they lived in, that they had scarcely heard of a contemporary war.

Weierstrass had no more idea than his sisters of Sophia’s age or mission. He told her afterwards that he had thought her some misguided governess who wanted to use his name, claiming mathematics among her credentials. He was thinking he must scold the maid, and his sisters, for letting her break in on him. But he was a courteous and kindly man, so instead of sending her away at once, he explained that he took only advanced students, with recognized degrees, and that he had at the moment as many of those as he could handle. Then, as she remained standing-and trembling-in front of him, with that ridiculous hat shading her face and her hands clutching her shawl, he remembered the method, or trick, he had used once or twice before, to discourage an inadequate student.

“What I am able to do in your case,” he said, “is to set you a series of problems, and ask you to solve them and bring them back to me one week from today. If they are done to my satisfaction, we will talk again.”

A week from that day he had forgotten all about her. He had expected, of course, never to see her again. When she came into his study he did not recognize her, perhaps because she had cast off the cloak that had disguised her slender figure. She must have felt bolder, or perhaps the weather had changed. He had not remembered the hat-his sisters had-but he had not much of an eye for female accessories. But when she pulled the papers out of her bag and set them down on his desk, he remembered, and sighed, and put on his spectacles.

Great was his surprise-he told her this too at a later time-to see that every one of the problems had been solved, and sometimes in an entirely original way. But he suspected her still, thinking now that she must be presenting the work of someone else, perhaps a brother or lover who was in hiding for political reasons.

“Sit down,” he said. “And now explain to me each of these solutions, every step taken.”

She began to talk, leaning forward, and the floppy hat fell over her eyes, so she pulled it off and let it lie on the floor. Her curls were revealed, her bright eyes, her youth, and her shivering excitement.

“Yes,” he said. “Yes. Yes. Yes.” He spoke with ponderous consideration, hiding as well as he could his astonishment, especially at the solutions whose method diverged most brilliantly from his own.

She was a shock to him in many ways. She was so slight and young and eager. He felt that he must soothe her, hold her carefully, letting her learn how to manage the fireworks in her own brain.

All his life-he had difficulty saying this, as he admitted, being always wary of too much enthusiasm-all his life he had been waiting for such a student to come into this room. A student who would challenge him completely, who was not only capable of following the strivings of his own mind but perhaps of flying beyond them. He had to be careful about saying what he really believed-that there must be something like intuition in a first-rate mathematician’s mind, some lightning flare to uncover what has been there all along. Rigorous, meticulous, one must be, but so must the great poet.

When he finally brought himself to say all this to Sophia, he also said that there were those who would bridle at the very word, “poet,” in co

As she had expected, there was deeper and deeper snow outside the train windows as they travelled east. This was a second-class train, quite spartan in comparison with the train she had taken from Ca

Every time she lifted her eyes to the window it seemed that the snow fell more thickly, and sometimes the train slowed, almost stopping. They would be lucky at this rate to reach Berlin by midnight. She wished that she had not let herself be talked out of going to a hotel, instead of to the house on Potsdam Street.

“It will do poor Karl so much good just to have you for one night under the same roof. He still thinks of you as the little girl on our doorstep, even though he gives great credit to your achievements and takes pride in your great success.”

It was in fact after midnight when she rang the bell. Clara came, in her wrapper, having sent the servant to bed. Her brother-she said this in a half whisper-had been wakened by the noise of the cab and Elisa had gone to settle him down and to assure him that he would see Sophia in the morning.

The word “settle” sounded ominous to Sophia. The sisters’ letters had mentioned nothing but a certain fatigue. And Weierstrass’s own letters had held no personal news, being full of Poincaré and his-Weierstrass’s-duty to mathematics in making matters clear to the king of Sweden.

Now hearing the old woman’s voice take that little pious or fearful drop as she mentioned her brother, now smelling the once-familiar and reassuring but tonight faintly stale and dreary odors of that house, Sophia felt that teasing was not perhaps so much in order as it used to be, that she herself had brought not only the cold fresh air, but some bustle of success, an edge of energy, of which she had been quite unaware, and which might be a little daunting and disturbing. She who used to be welcomed with hugs and robust pleasure (one of the surprises about the sisters was how jolly they could be yet how conventional) was still hugged, but with tears standing in faded eyes, with old arms trembling.

But there was warm water in the jug in her room, there was bread and butter on her night table.

As she undressed she could hear faintly agitated whispering out in the upper hall. It might have been about their brother’s state or about herself or about the absence of a cover on the bread and butter, which maybe had not been noticed until Clara ushered her into her room.

When she worked with Weierstrass, Sophia had lived in a small dark apartment, most of the time with her friend Julia, who was studying chemistry. They did not go to concerts or plays-they had limited funds and were absorbed by their work. Julia did go out to a private laboratory where she had obtained privileges hard for a woman to get. Sophia spent day after day at her writing table, not rising from her chair sometimes till the lamp had to be lit. Then she would stretch and walk, quickly, quickly, from one end of the apartment to the other-a short enough distance-sometimes breaking into a run and talking aloud, bursting into nonsense, so that anybody who did not know her as well as Julia did would wonder if she was sane.

Weierstrass’s thoughts, and now hers, were concerned with elliptic and Abelian functions, and the theory of analytic functions based on their representation as an infinite series. The theory named for him contended that every bounded infinite sequence of real numbers has a convergent subsequence. In this she followed him and later challenged him and even for a time jumped ahead of him, so that they progressed from being teacher and pupil to being fellow mathematicians, she being often the catalyst to his investigations. But this relationship took time to develop, and at the Sunday suppers-to which she was invited readily because he had given up his Sunday afternoons to her-she was like a young relation, an eager protégée.