1There was a small town in the German lands called Göttingen, with a wall round it and geese in its market, and in those days it was the first city of the world for the science of number.
2In the second year of the great war the two chief masters of that town, Hilbert and Klein, were stuck. They were working at the new law of the bent Weave, and there was a hole in it. In every law of nature known till then, the fire of the world, which the learned call energy, is never made and never lost; it only changes its coat. In the new law this seemed to fail. The sums would not close.
3So they sent for the one person who knew the craft that could mend it.
4Her name was Emmy Noether. She was thirty-three, the daughter of a master of number in a southern town. When she was a girl, a woman could not enter the lessons there as a student at all. She had sat at the back by leave of each teacher, one at a time, a guest in the room. Later the rule was changed, and she took the highest degree. Then for seven years she taught at her father's school and was paid nothing, because there was no rule under which a woman could be paid.
5She came to Göttingen, and the masters of number wished to make her one of the teachers. The other masters of the town, the men of history and of old tongues, rose against it. A woman had never taught there. What would our soldiers think, they asked, when they come home from the ditches and find they must sit at the feet of a woman?
6It is told that Hilbert lost his temper in the meeting. He said he could not see what the candidate's being a man or a woman had to do with the matter; they were a university, after all, and not a bath-house.
7They refused her all the same. So Hilbert did a sly thing. He put up the notice of his own lessons, in his own name, and then let her stand up and give them. For four years the students of Göttingen went to hear Professor Hilbert, and were taught by Emmy Noether, who had no title, no desk and no wage.
8She mended the hole in the law within three years. And in mending it she found something far larger than the thing she had been sent for.
9Listen now, for this is one of the deep things, and it can be said simply.
10Take any law of nature, and ask of it: is there some way I can shift the whole world, and find that this law has not changed? If I do my work today or tomorrow, will the law be the same? If I do it here or a mile off? If I face north or face east?
11For every such sameness, she showed, there is a treasure that is never lost. Because the laws are the same tomorrow as today, the fire of the world is kept: not one spark of it is ever made or destroyed. Because the laws are the same here as there, the push of moving things is kept. Because they are the same whichever way you face, the turning of turning things is kept.
12It was not three facts. It was one fact, with three faces, and more beyond those. Every evenness in the Weave is a promise, and every promise the Weave keeps is an evenness seen from the other side.
13Men had known for a hundred years that the fire of the world is kept. Carnot's heirs had built their engines on it. No one had known why. Now a woman without a wage had written down why.
14The clerk of Bern read her proof in Berlin and wrote to Hilbert that he was struck by it, and that the old guard of Göttingen might learn a thing or two from Fräulein Noether.
15After the war the rule was changed and she was let in, on the lowest step. Some years later they gave her a small wage. She never rose higher. She did not seem to notice.
16Now hear what she was like, from one who knew her.
17A girl named Marta Lenz came to Göttingen from a town in the east, in the last good years. She had been the best at number in her school and had never met anyone who was better. On her first day she went to find the famous Fräulein Noether, expecting a tall cold lady.
18She found a short, stout, untidy woman in a loose dress, with thick spectacles and her hair coming down, talking at the top of her voice in the middle of the street. A string of young men walked with her, and she was drawing in the air with both hands. A cart had to go round them.
19"You are new," said Emmy Noether. "Good. Come along. We are going to the hills. What do you say a number is?"
20Marta said what she had been taught. Emmy Noether laughed, not unkindly, and by the time they reached the hills Marta understood that everything she knew was a few leaves, and here was the tree.
21That was her way of teaching. She did not stand at a desk. She walked, and argued, and ate pudding with her students at her own table under the roof, and washed the bowls herself still talking. Her thoughts came too fast for her tongue. She gave them away with both hands. A student would bring her a small idea; she would give back a great one, and tell him to print it under his own name, and forget she had done so.
22They came to her from Russia and Holland and Japan. In the town they were called the Noether boys, though some were girls. She cared nothing for her dress, her dinner or her rank. She cared for the thing itself, and for whoever would look at it with her.
23Marta asked her once whether it did not make her bitter: the years without pay, the title that never came.
24"It would take a great deal of time to be bitter," said Emmy Noether. "And look how much there is to do." That was all the answer Marta ever got.
25Then came the thirty-third year of the century.
26A new master had risen in the German lands, a man who shouted. He taught that the household of man was not one but many, and that some of its rooms should be emptied. Chief among those he hated were the Jews. He had been in power ten weeks when the law went out: no one of that people may hold a post in the schools of the state.
27Emmy Noether was a Jew. The telegram came to Göttingen in April with six names on it. Hers was one.
28Marta ran to the house under the roof and found her packing books into piles, and not for herself. "Sit down, child, and help me. These are for the young ones; I will not need them. Now, who is to look after the seminar? And where can we send those who have lost their places?"
29"They have thrown you out," said Marta. "Twenty years, and they have thrown you out in one line."
30"They have thrown out many who are worse placed than I am. Some have small children. Let us think where they can go."
31The lessons went on. They went on in her kitchen, with the students sitting on the bed and the floor. It was forbidden. Any neighbour might have told.
32And on a certain evening one of her best pupils came up the stairs wearing the brown shirt of the shouting man's fighters, with the crooked cross on the arm.
33Marta was there. She saw the room go still. The others looked at the floor. That shirt, in those weeks, was beating Jews in the street below.
34Emmy Noether looked at him over her spectacles. She did not send him away. She did not make a speech. She said, "You are late. We were at the third step. Sit there." And she turned back to the board she had propped against the stove, and went on.
35Marta was angry with her afterward, in the stairwell. "How could you let him in? Wearing that?"
36"He came to learn," said Emmy Noether. "While he is at my table, he is learning. That is one evening he is not somewhere else. What would you have me teach him by shutting my door? That is what they do."
37Marta did not agree with her then. She was not certain, even long after, that it had been wise. But she never forgot that in the one room in Göttingen where the hated woman was master, no one was put out.
38A friend of hers, a great man of number, wrote of those months that her courage, her frankness and her unconcern for her own fate were a comfort to everyone, in the middle of all the hatred and the meanness.
39By autumn it was plain that she could not stay. A college for women in America, a place called Bryn Mawr among green fields, found the money for one year, and then another. Her brother Fritz, a master of number also, went east instead, to the Russian lands. She went to the ship with two trunks. At the station in Göttingen her students stood on the platform, and some were in tears, and she leaned from the window to finish an argument until the train moved.
40In America she was happy, which surprised everyone but those who knew her. She had four young women to teach, and she walked them over the hills in all weathers. Once a week she rode the train to Princeton to lecture, where the clerk of Bern now lived, an exile as she was. For the first time in her life she had a proper wage. She was fifty-one.
41She had a little less than two years of it.
42In the spring of the second year the doctors found a growth in her and said it must be cut out. She told almost no one. She set her papers in order, and wrote careful notes for her pupils on what each should work at next. The cutting went well. For three days she mended. On the fourth a fever took her, suddenly, and within hours she was gone. She was fifty-three.
43Marta heard of it in a letter that took three weeks to cross the sea. By then she was teaching children their sums in a village, for the high schools of the new Germany had no place for a pupil of Emmy Noether's.
44The clerk of Bern wrote to the great newspaper of New York, so that her passing should not go unmarked. He wrote: "In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."
45It was meant as high praise, and it was. But those who had walked with her in the hills thought it said too little. They did not think of her as the greatest among women. They thought of her as one of the few, among all who have lived, who saw into the grain of things.
46Her brother Fritz did not find safety in the east. The master of that land was hunting through his own people, and Fritz was taken away in the night on a false charge, and some years later he was shot. So the two children of the old master of Erlangen were lost, one to each of the two great tyrannies of that age.
47Now count what was done to her, and what she did.
48Every door of her life was closed against her, or opened a hand's breadth and no further. As a girl she was not to learn. As a woman she was not to teach. As a teacher she was not to be paid. As a Jew she was not to remain. Four times the short horizon of other people was laid across her way.
49And she did not close one door in return. Not to the faculty that mocked her, nor to the students who took her ideas, nor even to a boy in a brown shirt. She left behind no wealth and no children. She left a way of seeing that every student of number in the world now uses without knowing whose it is, and a room full of people who had been made larger.
50Remember her law, for it has a second meaning that she did not write down. Where there is sameness, something is kept. She proved it of the stars. She lived it at her kitchen table. She was the same to the great and the small, the same in honour and in exile, the same on the last day as on the first. And so something in her was never lost, and could not be taken by any telegram.
51On the hills above Göttingen the paths are still there. It is said that if you walk them with a hard question, and talk aloud, and wave your hands, you will be doing her honour in the only way she would have understood.