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Emmy Noether (Beihefte zur Zeitschrift "Elemente der Mathematik", 13)
In 1964 at the World's Fair in New York I City one room was dedicated solely to mathematics. The display included a very at tractive and informative mural, about 13 feet long, sponsored by one of the largest com puter manufacturing companies and present ing a brief survey of the history of mathemat ics. Entitled, "Men of Modern Mathematics," it gives an outline of the development of that science from approximately 1000 B. C. to the year of the exhibition. The first centuries of this time span are illustrated by pictures from the history of art and, in particular, architec ture; the period since 1500 is illuminated by portraits of mathematicians, including brief descriptions of their lives and professional achievements. Close to eighty portraits are crowded into a space of about fourteen square feet; among them, only one is of a woman. Her face-mature, intelligent, neither pretty nor handsome-may suggest her love of sci- 1 Emmy Noether ence and creative gift, but certainly reveals a likeable personality and a genuine kindness of heart. It is the portrait of Emmy Noether ( 1882 - 1935), surrounded by the likenesses of such famous men as Joseph Liouville (1809-1882), Georg Cantor (1845-1918), and David Hilbert (1862 -1943). It is accom panied by the following text: Emmy Noether, daughter of the mathemati cian Max, was often called "Der Noether," as if she were a man.
72 pages, Paperback
First published January 1, 1970
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Displaying 1 - 6 of 6 reviews
April 1, 2015
It is hard to explain why I found this simple and unassuming little book so affecting, and yet I did. I have an important deadline, and I've promised to get something written by Friday. I'd been intending to spend yesterday evening working on it. But in fact, once I'd picked up Dick's biography of Emmy Noether, I couldn't put it down. I finished it a little after midnight and retired guiltily to bed. I will have to write my piece today.
If you search for Noether on the web, you'll find many pages telling you that she was the greatest woman mathematician who has ever lived. This is inaccurate. As the book makes clear, she was one of the greatest mathematicians who has ever lived, and she also happened to be a woman. I had understood that she'd made important contributions to the subject, but I hadn't understood quite how important they were. One of the things that initially perplexed me was that there was very little mention of Noether's Theorem, widely considered to be fundamental to modern theoretical physics. After a while, the reason became clear: it just wasn't one of the bigger things she did. Her contributions to pure mathematics were far more significant, and she spent most of her life working on them. Noether's Theorem was something she happened to dash off in passing. What she was really interested in was transforming the way in which people did abstract algebra, and she was rather successful: the "Noether school" has conquered the world. In many cases without realizing it, pure mathematicians are by now all Noetherians.
She effected these momentous changes to two separate disciplines without ever, really, having a proper paid job. She never got a full professorship, and struggled by on various hand-outs and temporary posts. She never received any kind of public recognition; only a few people at the very top of the mathematical hierarchy were aware of how important she was. She was forced to leave Germany in 1933 when Hitler came to power (she was Jewish as well as female). With some difficulty, she obtained a temporary visiting professorship at Bryn Mawr. She died unexpectedly a year and a half later, at the age of 52, as a result of complications following what was thought to be a routine operation. Some of the greatest mathematicians of the time - van der Waerden, Weyl, Alexandroff, Einstein - published tributes to her; they are reproduced here.
So what did she actually do? That's the problem: if you're not an expert, it's almost impossible to explain it. A couple of weeks ago, we watched The Tribe , a stunning movie that's entirely in Ukrainian sign language with no subtitles. It sounds ridiculous, but against all expectation it works: it picked up three prizes at Cannes and has been playing to packed houses all across Europe. Reading this book was a similar experience. It's a glimpse of a completely alien universe that can only be explained in its own terms, and somehow it also works. It's a unique story.
We think we understand how the world is, and really we understand nothing at all. All around us, there are dramas playing out so strange that we wouldn't be able to grasp what was happening even if we did somehow notice them. Some of these dramas end up changing everyone's lives - Noether's ideas soon found their way into quantum mechanics, and then into nuclear physics - and we still have no idea that they ever happened. This book is one of the most striking examples I've seen.
Now I must return to everyday life and get my document finished.
________________________________
As Elham pointed out, there's a good PDF available for free download here. Though debap says that this version is better suited to e-book readers.
________________________________
[23 March 2015]
Naomi just pointed out to me that Noether's 133rd birthday is celebrated today on the Google Doodle. You can among other things see pictures of the ascending chain condition, the intersection of prime ideals, symmetries, topological invariants, and a non-trivial conserved quantity in a mechanical system.
If you search for Noether on the web, you'll find many pages telling you that she was the greatest woman mathematician who has ever lived. This is inaccurate. As the book makes clear, she was one of the greatest mathematicians who has ever lived, and she also happened to be a woman. I had understood that she'd made important contributions to the subject, but I hadn't understood quite how important they were. One of the things that initially perplexed me was that there was very little mention of Noether's Theorem, widely considered to be fundamental to modern theoretical physics. After a while, the reason became clear: it just wasn't one of the bigger things she did. Her contributions to pure mathematics were far more significant, and she spent most of her life working on them. Noether's Theorem was something she happened to dash off in passing. What she was really interested in was transforming the way in which people did abstract algebra, and she was rather successful: the "Noether school" has conquered the world. In many cases without realizing it, pure mathematicians are by now all Noetherians.
She effected these momentous changes to two separate disciplines without ever, really, having a proper paid job. She never got a full professorship, and struggled by on various hand-outs and temporary posts. She never received any kind of public recognition; only a few people at the very top of the mathematical hierarchy were aware of how important she was. She was forced to leave Germany in 1933 when Hitler came to power (she was Jewish as well as female). With some difficulty, she obtained a temporary visiting professorship at Bryn Mawr. She died unexpectedly a year and a half later, at the age of 52, as a result of complications following what was thought to be a routine operation. Some of the greatest mathematicians of the time - van der Waerden, Weyl, Alexandroff, Einstein - published tributes to her; they are reproduced here.
So what did she actually do? That's the problem: if you're not an expert, it's almost impossible to explain it. A couple of weeks ago, we watched The Tribe , a stunning movie that's entirely in Ukrainian sign language with no subtitles. It sounds ridiculous, but against all expectation it works: it picked up three prizes at Cannes and has been playing to packed houses all across Europe. Reading this book was a similar experience. It's a glimpse of a completely alien universe that can only be explained in its own terms, and somehow it also works. It's a unique story.
We think we understand how the world is, and really we understand nothing at all. All around us, there are dramas playing out so strange that we wouldn't be able to grasp what was happening even if we did somehow notice them. Some of these dramas end up changing everyone's lives - Noether's ideas soon found their way into quantum mechanics, and then into nuclear physics - and we still have no idea that they ever happened. This book is one of the most striking examples I've seen.
Now I must return to everyday life and get my document finished.
________________________________
As Elham pointed out, there's a good PDF available for free download here. Though debap says that this version is better suited to e-book readers.
________________________________
[23 March 2015]
Naomi just pointed out to me that Noether's 133rd birthday is celebrated today on the Google Doodle. You can among other things see pictures of the ascending chain condition, the intersection of prime ideals, symmetries, topological invariants, and a non-trivial conserved quantity in a mechanical system.
November 15, 2018
Emmy Noether was one of the greatest mathematicians of the 20th Century and the greatest algebraist (except, maybe, Andrew Wiles?). She revolutionised the approach to her field and, entirely by accident, proved a connection between symmetry laws and conservation laws which has profound consequences for physics. Despite this, she is much less famous than many of her contemporaries, such as Hilbert, Weyl and Klein. Proper recognition of her talents and acheivements, outside the abstract algebra community is only just beginning.
She lived at a time of widespread institutional and individual sexism and anti-Semetism and at that point in history, in the worst possible country for a female Jew - Germany. Anybody who came into close acquaintance with her realised her unique genius but, despite their best efforts, she was never able to obtain a proper, permanent academic post and, with the rise of the Nazis, she had to emigrate to the USA in order to carry on working in any academic capacity.
She died suddenly and unexpectedly of complications from what should have been a routine surgical procedure at the height of her mathematical powers, a very unusual state of affiars as most mathematicians do their best work before they are 30.
This biography seems to be written by a mathematician for other mathematicians. The details of Noether's life are sketchy, because there isn't much documentary evidence and there is no attempt to explain what Noether's acheivements were to people without a very advanced education in algebra. There are, however, reprints of three obituaries appended to the main text and one of these (Weyl's) takes on the task with moderate success - but still probably unintelligible to people without a significant mathematical background.
I think people should read this book regradless of their level of mathematical education and just skim the technical stuff if it seems like gibberish in order to understand what an extraordinary talent Noether had and what she, with unfailing positivity, had to put up with in order to do her lastingly influential, pioneering work.
She lived at a time of widespread institutional and individual sexism and anti-Semetism and at that point in history, in the worst possible country for a female Jew - Germany. Anybody who came into close acquaintance with her realised her unique genius but, despite their best efforts, she was never able to obtain a proper, permanent academic post and, with the rise of the Nazis, she had to emigrate to the USA in order to carry on working in any academic capacity.
She died suddenly and unexpectedly of complications from what should have been a routine surgical procedure at the height of her mathematical powers, a very unusual state of affiars as most mathematicians do their best work before they are 30.
This biography seems to be written by a mathematician for other mathematicians. The details of Noether's life are sketchy, because there isn't much documentary evidence and there is no attempt to explain what Noether's acheivements were to people without a very advanced education in algebra. There are, however, reprints of three obituaries appended to the main text and one of these (Weyl's) takes on the task with moderate success - but still probably unintelligible to people without a significant mathematical background.
I think people should read this book regradless of their level of mathematical education and just skim the technical stuff if it seems like gibberish in order to understand what an extraordinary talent Noether had and what she, with unfailing positivity, had to put up with in order to do her lastingly influential, pioneering work.
April 28, 2015
I wasn't as moved by this book as Manny was, but I did find it highly interesting. Emmy Noether is someone who I would have liked to get to know.
March 28, 2016
I read this book upon seeing Manny's review, a number of which have led me down new literary paths. While I wasn't as powerfully affected as he was (probably my attentions were diverted while foolishly trying to grapple with the descriptions of her mathematical work, which still went over my head), I very much appreciated her story and the personal and scientific impact she had.
Most noticeably, I felt frustrated by the social and political constraints placed on her—for being a woman, for being a Jew. To say nothing of the destruction of the preeminent, centuries-old mathematics department at Göttingen University in just the space of a year, after the rise of National Socialism. How far we've come (and yet how far to go).
Most noticeably, I felt frustrated by the social and political constraints placed on her—for being a woman, for being a Jew. To say nothing of the destruction of the preeminent, centuries-old mathematics department at Göttingen University in just the space of a year, after the rise of National Socialism. How far we've come (and yet how far to go).
April 13, 2018
Really nice insight into her life but it is extremely mathematically heavy which whilst interesting broke up the flow of the book and made it a bit of a struggle to read. Incredible woman though and worth reading if you're interested in mathematics/sciences.
September 4, 2018
The most thorough and authoritative text on Noether. Which is sad, since this is very short and not a very thorough biography at all.
Displaying 1 - 6 of 6 reviews