Google Doodles these days to be concentrating on the contributions of women in science and technology, and today’s features Emmy Noether, a mathematician born on this day in 1882 (died 1935). If you click on the screenshot below, it will take you to the Google page, and there clicking on the picture itself takes you to a page of references about Noether.
I’m not a mathematician and hence hadn’t heard of her, but Wikipedia describes her as a big macher:
an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, Norbert Wiener and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Noether’s theorem explains the fundamental connection between symmetry and conservation laws.
I’m sure we have some math-y readers who can explain more in the comments. Noether was in the math department at Göttingen until 1933, when the Nazis expelled her because she was Jewish:
The following year [1933], Germany’s Nazi government dismissed Jews from university positions, and Noether moved to the United States to take up a position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery for an ovarian cyst and, despite signs of a recovery, died four days later at the age of 53.
How many people (and how much talent) did we lose that modern medicine could have saved?
Noether:
Over at Google, the artist Sophie Diao describes how she put this together:
When I first started tackling this doodle, I originally drew several concepts attempting to visualize Noether’s Theorem due to it’s [JAC: the unfortunate “artist’s apostrophe”!] revolutionary impact on the way people approach physics. But after discussing my ideas with a few professionals in the field, I decided that the doodle should include references to her mathematical work too. Noether was passionate about math, despite living in an era where women were often excluded from these subjects. While studying at the University of Erlangen as just one of two women at the school, Noether was only allowed to audit classes and needed to obtain permission from her professors in order to attend. After passing her graduation exam, she taught at the school’s Mathematical Institute for seven years without pay, frequently covering her father’s classes when he was out sick and publishing her own papers.
But there weren’t any obstacles that would stop Noether from her studies. In this doodle, each circle symbolizes a branch of math or physics that Noether devoted her illustrious career to. From left to right, you can see topology (the donut and coffee mug), ascending/descending chains, Noetherian rings (represented in the doodle by the Lasker-Noether theorem), time, group theory, conservation of angular momentum, and continuous symmetries–and the list keeps going on and on from there! Noether’s advancements not only reflect her brilliance but also her determination in the face of adversity.
That brings about reminiscences of my Math studies – as an Algebraic, Noether was omnipresent in my studies.
Also famous David Hilbert’s remark when the University of Göttingen tried to refuse her Habilitation (on the grounds that women shouldn’t do that in general): “This is a University, not a bathing facility!” Hilbert appealed to some Prussian Minister but Noether was refused entry to the University anyway. In the end, Noether had to teach using Hilbert’s name …that was 1917. After WW1, the law was changed and Noether became the first female Professor in the Weimar Republic.
The first professor in Math, anyway.
A well deserved Doodle. Emmy Noether was responsible for one of the most profound insights in fundamental physics.
Why is energy conserved? Because the laws of physics are the same at different times.
Why is momentum conserved? Because the laws of physics are the same at different places.
Why is angular momentum conserved? Because the laws of physics are the same regardless of angle.
Noether’s theorem formally proves that for any such symmetry principle (= laws of physics being invariant) there is a corresponding conserved quantity.
And this was a “throwaway” result that she did because David Hilbert asked her to look at the question. It was her only paper on Physics.
I was amazed when I would read advanced Physics books that would quote the result without naming Noether. (Talking about you, Lev Landau!)
In line with my theme of showing the lack of dividing line between physics and metaphysics, I regard the Noether theorems (above) as a profound contribution to the latter as well. (She and Turing I regard as mathematicians who inadvertently did philosophy. :))
They’ve been generalized as well – we now also know about gauge symmetry and its conservation law, for example.
Very profound work indeed. It makes me wonder if dissipative systems (non-Lagrangian) are really just labeled that way because we do not have the complete knowledge of a system to predict future states of a dissipative system.
I have heard this argued – that entropy is actually an “objective measure of ignorance”, or the like.
Sadly we don’t get that doodle in the UK, which is a pity.
Even in my day, women were discouraged from math. A high school friend’s mother was not allowed to take math in school simply because she was female. My math issues were not addressed because “girls can’t do math anyway”.
And left handed people were discouraged from writing. My mother had to learn how to write with her non-dominant hand.
That is great for ambidexterity, but not so great for knowing right from left. She grabs a scissor, and then have to change to the hand that it is supposed to work with. Or she says “go right” and means left, which is terrible in a co-driver.
Now it is feminism and ageism that are the new frontiers…
I seem to recall some recent news reports that suggests a milder version of this continue with girls receiving lower marks from teachers for identical work in maths/science(a working paper from the National Bureau of Economic Research reporting research carried out in Israel so Google reveals).
While having nothing to do with maths/science education I do like to chuck names of women scientists into my law problem questions and offer the usual chocolate fish prize to anyone who knows who they were- long pause while google warms up and then an answer.
I don’t know about the marks difference, but it wouldn’t surprise me. I recall a study that sent out false resumes (I can’t remember if it was to universities or to companies offering jobs, though), randomly assigning them male and female genders. Shamefully, the females were less likely to be received as applicants, despite being equally as qualified.
Topologically, (is that a word?) a coffee mug is a doughnut, or rather, a torus. I remember in the dark ages seeing an article in Scientific American about how turn a sphere inside out without leaving a crease. I found an animation about this. It was very interesting.
Yes I saw that too – it’s mind-boggling.
Is a coffee mug a torus though? I thought the stipulation was any transformation was possible but no tears or rips of the manifold(?) are allowed. How can you turn a coffee mug into a ring without violating those rules? I’m assuming you’re not counting the handle…or maybe you are. Actually, thinking about it you probably are. D’oh.
It took me a moment to realize it, but the handle makes a partial torus. The cup that is continuous with it is the rest of the torus with a big dent in it.
Yes, that’s what I thought.
It’s very beautiful. I never really understood what mathematicians and physicists meant when they spoke about the beauty of their subjects until I fell for science and started immersing myself in physics. It’s not subjective, aesthetic beauty, although there’s plenty of that in the scientific world, in the Hubble’s photographs, particle trails in cloud chambers, and so on – it’s a kind of austere, disturbingly callous elegance, and it’s objectively definable to a certain extent too, in that the more beautiful ideas are free of informational redundancy, are hard to vary without making them malfunction and exhibit many of the symmetric properties that Noether, insofar as I understand it, explored.
It’s a very strange, bracing, chilly beauty – like listening to Steve Reich after a lifetime of Mozart and Bach. Thinking about it now, an appreciation of scientific beauty might have opened my mind up to artists like Steve Reich and, in another direction, Suicide without my even realising it. Discovering science at 25 really was a philosophically jarring experience for me. The world was transformed. A bit like a coffee cup:)
How eloquent!
Very nice! But, how did you not “discover” science at school?
To a first approximation (ignore ENT), we’re toruses (tori?) too!
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Here’s an animation of the homotopy between a mug and a doughnut from the Wiki entry for Emmy Noether.
She should be as famous as Einstein. She was able to resolve a problem with conservation of energy in the General Theory that others hadn’t and made a favourable impression on Einstein.
Big macher is almost an understatement.
As I’m sure I have mentioned here before, Noether is among my scientific heroes, since she succeeded to study at the university by prying open access to math “in the face of adversity”. And of course here two theorems are pivotal in order to understand lawfulness of nature and hence science.
While I’m not hip to the math, I think Noether’s theorems presage the modern view of action as a field entity that tells a field particle how to move locally, expressed in “principal bundles” of gauge theory. [ http://en.wikipedia.org/wiki/Principal_bundle ] But I am no expert, haven’t studied the theorems yet, and can be wrong.
As I understand it though, in Noether’s case the action preserves the laws of physics (as realized in the action) in the analogous way to a (quantum) field. As a result it pops out a preserved quantity analogous to the electron of the EM field, therefore generically called a “charge”. As Coel describes, the “charge” of translation is the classical conjugate variable of position*, namely momentum. And so on.
As I remember it the reason why there are two theorems is that the energy “charge” of time is a different beast and it is an expression of a global rather than a local symmetry…
*So the underlying relation runs deep, at least in retrospect. But Noether was the first to grok exactly why.
“her” theorems.
Without knowledge of the requisite, technical mathematical concepts I can understand her work only in a pretty basic way but I love the mathematics of symmetry – I devoured Marcus Du Sautoy’s fantastic book on the subject, as well as a few others, and I’m a big fan of proto-hipster Evariste Gallois, whose mathematical brilliance was curtailed in a duel at a very early age.
I’d love to go back and study maths, or theoretical physics, now that I’m actually interested in these things but I’ve not got the necessary precision and multi-tasking mental abilities I don’t think. I can understand it only insofar as philosophers can understand it, which is to say very badly, but I can see that Noether’s ideas are about as deep as physics gets, and they are fabulously elegant.
Galois is one of those guys I’d like to know more about – I did a double take when I found a street named for him in the RDP area of Montreal.
I have a friend (as well as know of several others in the field) who has done work in the history and philosophy of algebra who might know where to start.
There’s an excellent take on his story in the Marcus Du Sautoy book I mentioned – Finding Moonshine it’s called. It’s terrific, one of the best popular science books I’ve ever read, as is his book on prime numbers.
“As I’m sure I have mentioned here before, Noether is among my scientific heroes…”
You have — so I was expecting you to be the first commenter! 😃
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PS. Jerry: “I’m not a mathematician and hence hadn’t heard of her…”
So, Jerry’s not been reading your comments, Torbjörn! 😁
I read Torbjörn’s comments and I don’t remember her either. But I do have a bad habit of skipping over names.
Ha! Torbjörn’s mentioning her seems to me to be as much a WEIT thing as Ben’s abhorrence of the trolley problem.
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I am chagrined! CHAGRINED!
Being an experimentalist, I only mildly comprehend mathematics, however Noether’s theorems are very rich in developing ideas concerning thermodynamics, heating, cooling, sympathetic interactions…just a whole bunch of ideas can come from a simple premise. Thank you Emmy.
People are mostly talking about her single (but so important) result linking continuous symmetries to conserved quantities.
But Noether (together with Emil Artin) also helped create modern graduate level Algebra. Every advanced mathematics student learns the Noether isomorphism theorems and learns about Noetherian rings and modules.
She demonstrated the power of her abstract approach by taking results that had been previously proven only for polynomials (and generally via arduous calculations) and generalizing them to much broader classes of objects, with much clearer proofs. (Famous examples are the generalizations of Hilbert’s Basis Theorem and Lasker’s results on primary decomposition.)
As van der Waerden himself said, his very influential two volume book on Algebra was his way of educating generations of mathematicians about what he learned from Noether and Artin.
By the way, Emmy Noether’s father, Max, was no slouch either. He proved several important results in classical Algebraic Geometry.
Having learned about symmetry in physics and chemistry in the latter part of the 20th century, it remains unclear to me the extent to which Noether just formalized what physicists were already doing. In classical mechanics, constants of the motion were already paramount in the Lagrangian and Hamiltonian formulations of Newtonian mechanics, for example. This is so central to way physics is taught now that I have a hard time seeing whether Noether’s contributions mostly provided a shoring up (or providing a rigorous justification for) the way physicists were already thinking, or whether she helped shift everyone’s approach.
As a regular teacher of a course in symmetry and group theory in chemistry, I really should look more into the historical evolution of the subject! Steven Weinberg clearly thinks that symmetry is pretty much everything:
*Steven Weinberg, Sheldon Glashow, and Abdus Salam were awarded the 1979 Nobel Prize in Physics for their incorporation of the weak and electromagnetic ‘forces’ into a single theory.
As far as I know the rigorous *equivalence* was due to Noether, and the fact that one can then see that all future conservation laws will have a symmetry.
(I’m going from memory of the discussions at a Society for Exact Philosophy meeting and a book I read about matters at the time, so that might be a bit shaky. I have yet to read the original paper.)
I know it’s Emmy Noether’s special day, but I just have to give a shout out to the “Lasker” name that keeps popping up in relation to her theorem… this refers to Emanuel Lasker, world chess champion from 1894-1921. Lasker occupies a special place in the pantheon of chess greats, and to see his name associated with this doodle makes me feel just how intertwined the history of ideas actually is.
Even at the distance of 80 years, the appalling damage that the Nazis did to the German academic system beggars belief. I would say that Göttingen was the centre of the physics world in the 1920’s and first couple of years of the 1930’s.
“When Hitler arrived in 1933, the tradition of scholarship in Germany was destroyed, almost overnight.” Bronoswki
In many cases Germany’s loss was America’s gain!
And the UK’s. Just look at the number of German refugees who so enriched British science in the 40’s and beyond. Popper, Krebs, Chain, Kornberg, Perutz, Bondi, Peierls ……….
And the aged “grandfather”, Hilbert, actually told off the Nazi hack that came to some dinner or other and had the ignorance to ask about how the state of the department.
I was hoping you’d note today’s doodle! A lovely piece commemorating a beautiful woman.
See? Something good already happened this week and it’s not even lunchtime (in the US) yet!
As I understand it, Noether’s Theorem basically expresses mathematically the idea that, if something changes, then something has to change.
Though superficially trivial, it’s actually the whole reason why anything ever happens at all. Science is, in a very real sense, simply the endeavor of discovering what does and doesn’t change. This can be expressed as symmetries, which can in turn be expressed as conservations, which is often expressed as laws of nature.
It’s one of those “obvious once you notice it” things…save it takes a genius to notice it….
b&
Take that, Larry Summers.
😉