If anything, the article probably understates her importance (and doesn't really explain why she is so important). You do get an idea when you start at her bibliography; not many scientists have their papers subdivided into epochs [1].

To begin with, Einstein didn't describe Emmy Noether (in his obituary of her, sent to the New York Times) as "the most 'significant and 'creative' female mathematician of all time". The exact quote is instead: "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." [2]

In essence, he is describing her as the greatest mathematician of the past decades, male or female. That may have been a slight exaggeration (she was a friend of his and visited frequently at Princeton during her time at Bryn Mawr), but not much: she was definitely one of the most influential mathematicians of the 1920s and early 1930s. Many mathematicians and physicists visited Göttingen specifically to interact with her.

What made her so important were not just her contributions to abstract algebra (groundbreaking as they were, essentially redefining the field), but probably most of all her axiomatic "method of abstraction", pioneered in several papers starting with 1921's "Idealtheorie in Ringbereichen". For non-mathematicians, it is roughly the same concept as abstract data types; instead of proving theorems about very specific mathematical constructs (such as integers and polynomials), you prove them for more general constructs, abstractly defined through operations over them and axioms connecting those operations. It is one of those things that seem blindingly obvious in retrospect, but the approach was actually hotly debated in the 1920s; these days, it's foundational for much of mathematics.

A good example of this is the so-called Lasker-Noether theorem, which was initially proven by Emanuel Lasker for a couple of specific rings, a result that Emmy Noether later generalized for a wide class of rings (rings that we now call, for other reasons, Noetherian rings).

Another reason why she is little known these days even among mathematicians is probably that she didn't care much about getting credit for her ideas (even though she was painstakingly careful about giving others credit in her own papers). Her own publications, numerous as they were [1], are probably only the tip of the iceberg; it is known, for example, that volume 2 of van der Waerden's "Modern Algebra" (the standard textbook for abstract algebra for decades) was essentially her work (van der Waerden never made a secret of it). A lot of her other work was likewise published under the name of her students and colleagues. (Unlike what the article states, she never published under a man's name.)

This is the final way in which she influenced mathematics -- as a teacher. She never was a very good teacher when it came to actual lecturing (being too much of an absent-minded professor), but she was generous with sharing her ideas and an inspiring influence for her students on colleagues (her first Ph.D. student, Grete Hermann, went on to lay the foundations for Computer Algebra, for example).

As van der Waerden wrote, "Each of her lecture series was a paper. And nobody was happier than herself when such a paper was completed by her students. Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all."

[1] http://en.wikipedia.org/wiki/Emmy_Noether_bibliography

[2] http://www-history.mcs.st-andrews.ac.uk/Obits2/Noether_Emmy_...