Like most people, I end up having dinner with my family every so often. Unlike most people, our family conversations always seem to include math or physics. Generally we end up trying to stump each other with various questions. It’s like a game to us.
A few nights ago we had one of those dinners. I found a lull in the conversation and I fired off, “Hey dad, do you know any significant female mathematicians?” His jaw went a little loose and he gave me a blank stare. It was the same look people give me when they find out I talk about math at the dinner table.
My crippling question had developed from a classroom discussion about an influential female mathematician, Sophie Germain. I’d realized in that discussion that I could name several influential female scientists. For whatever reason, I’d never heard of any women known for their mathematics.
As the feeling of triumph settled in, a smile developed across my face. Sophie and I were about to taste victory. I watched confidently as my father’s eyes slowly rolled back into his head. Gradually his eyes came back down and his smile met mine. I knew I was in trouble when he said, “Well, the oldest one I can think of is Hypatia”.
He went on to tell us the story of the daughter of Theon of Alexandria. Theon was a known scholar and professor of mathematics at the University of Alexandria. His daughter, Hypatia, was given all the best. In particular, her education was second to none. With such great influences, many historians believe she was able to eclipse her father’s knowledge at an early age. In time, people would come from distant cities to learn from her.
Sadly, none of her original work has survived to this day. As a mathematician we remember her largely for her editing and insightful comments on other great works of the time. Some of the more important works included the Arithmetica by Diophantus and Conics of Apollonius. The book on conics was particularly significant. It contained progressive information about cutting cones with planes that helped develop ellipses, hyperbolas and parabolas.
Unfortunately, Hypatia is possibly better known for the way she died than the way she lived. During her lifetime, the quality of life in Alexandria was on the decline. Fighting had developed among the different religious factions and it threatened to destroy the city. At one point, the Roman emperor ordered the destruction of all pagan temples. As an educated pagan that often spoke about non-Christian philosophy, Hypatia was a likely target. Ultimately her end came when a group of Christians pulled her from her carriage, drug her into a church, stripped her, beat her to death, tore her to pieces, burned the pieces and disgracefully scattered her remains.
At this point my mother had made it to the other side of the table. She began slapping my father’s arm while muttering something through clenched teeth. “Ok, Ok”, he conceded and continued, “My favorite was Emmy Noether anyway”. “She died of natural causes!” he taunted my mother as she wandered into the kitchen. By this time my smile was long gone. He’d already won the game and was just showing off.
Much like Hypatia, Noether was the daughter of a successful professor of mathematics. Her German family was quite wealthy and provided all her needs. Unfortunately, sometimes society isn’t as helpful.
Noether found herself suffering from restricted access to the University of Erlangen. Her father was on faculty there and I expect it felt like home. Fortunately, she was able to audit classes until they started accepting female students. I’m just speculating here, but I’d like to think she helped drive the decision. A brief four years later she was awarded her Ph.D. summa cum laude.
In spite of her obvious achievement, society still wasn’t quite ready for Noether. She spent the next several years working with David Hilbert and other prominent mathematicians at Göttingen University. Due to a lack of insight, much of the faculty refused to allow a female member. As a result, she worked for free.
As the years went by at Göttingen she worked on incredible theories and taught classes in Hilbert’s name. Eventually her situation improved when she was allowed to become a licensed lecturer. The university wasn’t paying her yet, but at least she could collect student fees. Years later she was finally granted a position as an adjunct teacher.
It’s worth mentioning she was considered a remarkable instructor. More than a few of her students went on to make significant contributions to mathematics. If all things were equal, it would be hard to imagine her without tenure.
While Noether may not be well known to the general public, great minds have given her enormous respect. Einstein referred to her as a “significant creative mathematical genius”. This may well be due to her contributions to general relativity.
Her major mathematical contribution was in a 1921. It was a groundbreaking paper on the theory of ideal rings. She was able to think of things in an extremely abstract way. Many consider her the mother of modern algebra.
One of the more easily understandable ideas she developed involved creating ascending or descending chains. Imagine a set A1 is contained in a set A2, which is contained in a set A3, etc. Sometimes you can see that after a certain point, the rest are the same. For example we might notice that A10, A11, A12, etc are all the same. On the surface it may not seem like a big deal. But techniques like these are frequently exploited in proofs.
Quite honestly, the scope of her contribution is breathtaking. It warms my heart to know people have been making such impressive advances in the last hundred years. It’s even more rewarding to see remarkable individuals like Emmy Noether push through an unjust barrier. In spite of never being treated equally, she emerge a champion with the landscape changed behind her.
By the time my father had finished his glowing praise of Emmy Noether, my face was in my palm. I had clearly lost my challenge. I thought we had him, Sophie.