Emmy Noether Quotes

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.

Cada simetría de la acción lleva asociada una cantidad conservada —dijo Sebas a modo de conclusión—. Este teorema se lo debemos a una de las mujeres más importantes de la historia de las Matemáticas; Emmy Noether.

When Einstein calls you the most significant and creative woman in the history of mathematics, you can probably call it a day and go home. Unless you're Emmy Noether, whose pursuit of game-changing innovation in the field of numbers was, in a word, tenacious.

My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.

Grothendieck transformed modern mathematics. However, much of the credit for this transformation should go to a lesser-known forerunner of his, Emmy Noether. It was Noether, born in Bavaria in 1882, who largely created the abstract approach that inspired category theory.1 Yet as a woman in a male academic world, she was barred from holding a professorship in Göttingen, and the classicists and historians on the faculty even tried to block her from giving unpaid lectures—leading David Hilbert, the dean of German mathematics, to comment, “I see no reason why her sex should be an impediment to her appointment. After all, we are a university, not a bathhouse.” Noether, who was Jewish, fled to the United States when the Nazis took power, teaching at Bryn Mawr until her death from a sudden infection in 1935.

Perhaps we are being a bit presumptuous in calling our species “intelligent.” After all, this species has waged numerous inane wars where millions of their own were slaughtered. As a whole, this species spends trillions of hours a year watching insipid television shows. And “intelligent” is not the right name for a species that invented spam e-mails and encourages narcissistic pastimes like Facebook. Nevertheless, over the millennia, this species produced many shining lights that make us worthy of the lofty title: Blaise Pascal, Isaac Newton, David Hume, Marie Curie, Albert Einstein, Arthur Stanley Eddington, Emmy Noether, Andrew Lloyd Webber, Meryl Streep, and, of course, tiramisu.

The German mathematician Emmy Noether proved in 1915 that each continuous symmetry of our mathematical structure leads to a so-called conservation law of physics, whereby some quantity is guaranteed to stay constant-and thereby has the sort of permanence that might make self-aware observers take note of it and give it a "baggage" name. All the conserved quantities that we discussed in Chapter 7 correspond to such symmetries: for example, energy corresponds to time-translation symmetry (that our laws of physics stay the same for all time), momentum corresponds to space-translation symmetry (that the laws are the same everywhere), angular momentum corresponds to rotation symmetry (that empty space has no special "up" direction) and electric charge corresponds to a certain symmetry of quantum mechanics. The Hungarian physicist Eugene Wigner went on to show that these symmetries also dictated all the quantum properties that particles can have, including mass and spin. In other words, between the two of them, Noether and Wigner showed that, at least in our own mathematical structure, studying the symmetries reveals what sort of "stuff" can exist in it.

The task Gordan gave her was a truly daunting one: to develop the complete invariant theory for ternary forms of degree four. Whether Gordan had ever attempted this is hard to say, but one can safely say that Emmy Noether's work was the last word with regard to this problem. She was able to construct 331 associated covariants. After finishing this ambitious work and publishing it in Crelle, she passed her oral exam "summa cum laude", but later dismissed her dissertation as a piece of juvenalia (she once called it "dung").

The first law is essentially based on the conservation of energy, the fact that energy can be neither created nor destroyed. Conservation laws—laws that state that a certain property does not change—have a very deep origin, which is one reason why scientists, and thermodynamicists in particular, get so excited when nothing happens. There is a celebrated theorem, Noether’s theorem, proposed by the German mathematician Emmy Noether (1882–1935), which states that to every conservation law there corresponds a symmetry. Thus, conservation laws are based on various aspects of the shape of the universe we inhabit. In the particular case of the conservation of energy, the symmetry is that of the shape of time. Energy is conserved because time is uniform: time flows steadily, it does not bunch up and run faster then spread out and run slowly. Time is a uniformly structured coordinate. If time were to bunch up and spread out, energy would not be conserved. Thus, the first law of thermodynamics is based on a very deep aspect of our universe and the early thermodynamicists were unwittingly probing its shape.