If you wanted a list of 10 mathematicians you might not have heard of, but should, Amalie Emmy Noether would be near the top of the list. She lived March 23, 1882 to April 14, 1935. She made huge contributions to algebra and theoretical physics (e.g. Noether’s Theorem). In fact, if you’ve studied commutative rings and ideals, then you’ve definitely learned mathematics invented (discovered?) by Noether. So much so that one of the most fundamental concepts of commutative algebra, noetherian ring, is named after her.
Part of what makes her so interesting is that she did all this great mathematics despite the obstacles she faced as a woman in a field which thought of itself as a man’s world. She earned her Ph.D. in 1907 at the University of Erlangen in Germany. This was already a big deal as there was only two female students at the University and the faculty senate of the university had recently determined that allowing female students would “overthrow all academic order”. After getting her degree, Noether worked without pay for 7 years at the Mathematical Institute of Erlange.
Recognizing her abilities, two of the greatest mathematicians of the day, David Hilbert and Felix Klein, invited Noether to teach at the University of Göttingen in Germany. However, some of the faculty there objected and for a years she had to teach for free as the University wouldn’t give her an offical position. Objecting to the narrowmindedness of his colleagues, Hilbert said “I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bath house.”!
In the end Noether was at Gottingen until 1933 doing lots of great mathematics and advising students. And of course now Noether is world famous and all those idiots who thought a woman couldn’t be worthy of being a math professor are long forgotten (or, rather, are remembered only for being idiots!).
As if being a woman wasn’t enough of a complication, Noether was also Jewish. As you can imagine, Germany in the 1930′s was a difficult place to be if you were a Jewish professor. One of the first things which Hilter’s government did was order the removal of most Jews and other politically suspicious individuals from government positions (including professors). Based on this law Noether was fired in 1933. Fortunately she was able to accept a position at Bryn Mawr College in Pennsylvania. She was there for two years before passing away due to complications from cancer.
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. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians.
On 2 January 1935, a few months before her death, mathematician Norbert Wiener wrote that:
Miss Noether is … the greatest woman mathematician who has ever lived; and the greatest woman scientist of any sort now living, and a scholar at least on the plane of Madame Curie.
Nowadays most any mathematician would say Emmy Noether is one of the greatest mathematicians of the 20th century, woman or man.