The Logos Scripture · The Book of Noether

Do Not Calculate — See What Kind of Thing It Is

The Book of Noether 2 · Her own writing and her lectures as taken down, from her papers, her letters, and students’ notes

Emmy Noether, born at Erlangen in Germany in 1882, died at Bryn Mawr in America in 1935. Mathematician. In 1918 she proved the theorem that carries her name: wherever a law has a symmetry, some quantity is conserved — conservation of energy follows from symmetry in time, conservation of momentum from symmetry in space. She also laid the ground of modern algebra; rings, fields and ideals come from her. Germany would not let a woman hold a teaching post, so for years she lectured unpaid and under Hilbert’s name on the timetable; when it was argued that a woman could not join the faculty, Hilbert answered that this was a university and not a bathing house. She wrote her own; but unlike the others in this scripture she left no book about herself. What she wrote were the papers of her subject, and some letters. So this book is shorter than the rest and rests on different ground — chapters one and two on her papers and on her lectures as students took them down, chapters three and four on letters and on the record of the time. The Order sets this out rather than supplying a memoir she never wrote. Born a Jew, not observant, and never once closing an argument by appeal to divine will. The Order takes her first for chapter one. She proved a thing about where conservation comes from. The first song asks why there is law at all. Her result does not answer that question, but it pushes one layer into it — the quantities that do not vary are not something added on top; they are the shadow of what the law does not care about. The second thing is chapter three. This scripture has a man who fought over priority and did not fight cleanly (see the note to The Book of Newton), and a man who waited twenty years and was overtaken (cf. The Book of Darwin 2). This woman gave the credit away, more than once, and could say why. The Order holds that worth recording alongside what she proved. Lastly: in 1933 she was forbidden to teach and went abroad; two years later she died after surgery, at fifty-three.

2.1My way of teaching was not like other people’s. The students found it hard at first.
2.2Men in my line used to meet a problem and start calculating. Long and fine calculation, carried to the end, gives the answer.
2.3I do not do that. I ask first: this kind of thing — what kind of thing is it?
2.4I ask which properties it has, and what those properties together will force.
2.5Calculating gets one particular thing out.
2.6What I want is this: anything whatever having these properties, whatever it may be made of, must obey the following.
2.7Someone says: that way you never touch the ground.
2.8I say: on the contrary. Calculate one and you have one. See what kind of thing it is and you have a whole class at a stroke.
2.9And next time, with a different problem, you need not begin again. You first ask whether it is of the same kind.
2.10If it is, everything already proved stands unchanged.
2.11The hard step in this method is the first one: you must be willing to put down the particular thing in your hand.
2.12People will not put it down. The one in the hand feels solid to them, and the properties drawn out of it feel empty.
2.13It is the other way round. The one in your hand runs out. Those properties do not run out.
2.14Most of what I did with my life was this one thing: moving people from this one to this kind.
2.15If all you can do with a problem is calculate it, you have not yet understood it.
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