The Obscure Mathematician

Born in Germany 130 years ago,Amalie Noether invented important theorems that form the backbone of modern physics

Scientists are a famously anonymous lot,but few can match in the depths of her perverse and unmerited obscurity the 20th-century mathematical genius Amalie Noether.

Albert Einstein called her the most significant and creative female mathematician of all time,and others of her contemporaries were inclined to drop the modification by sex. She invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation. Some consider Noethers theorem,as it is now called,as important as Einsteins theory of relativity; it undergirds much of todays vanguard research in physics,including the hunt for the almighty Higgs boson. Yet Noether herself remains utterly unknown,not only to the general public,but to many members of the scientific community as well.

When Dave Goldberg,a physicist at Drexel University who has written about her work,recently took a little Noether poll of several dozen colleagues,students and online followers,he was taken aback by the results. Surprisingly few could say exactly who she was or why she was important, he said. A few others knew her name but couldnt recall what shed done,and the majority had never heard of her.

Noether was born in Erlangen,Germany,130 years ago. She was a brilliant theorist at a time when most German universities didnt accept female students or hire female professors,and then a Jewish pacifist in the midst of the Nazis rise to power. Through it all,Noether was a highly prolific mathematician,publishing groundbreaking papers,sometimes under a mans name,in rarefied fields of abstract algebra and ring theory. And when she applied her equations to the universe around her,she discovered some of its basic rules,like how time and energy are related,and why it is,as the physicist Lee Smolin of the Perimeter Institute put it,that riding a bicycle is safe.

Ransom Stephens,a physicist and novelist who has lectured widely on Noether,said,You can make a strong case that her theorem is the backbone on which all of modern physics is built.

Noether came from a mathematical family. Her father was a distinguished math professor at the universities of Heidelberg and Erlangen,and her brother Fritz won some renown as an applied mathematician. Emmy,as she was known throughout her life,started out studying English,French and pianosubjects more socially acceptable for a girlbut her interests soon turned to math. Barred from matriculating formally at the University of Erlangen,Emmy simply audited all the courses,and she ended up doing so well on her final exams that she was granted the equivalent of a bachelors degree.

She went on to graduate school at the University of Goettingen,where she earned her doctorate summa cum laude and met many of the leading mathematicians of the day,including David Hilbert and Felix Klein,who did for the bottle what August Ferdinand Moebius had done for the strip. Noethers brilliance was obvious to all who worked with her,and her male mentors repeatedly took up her cause,seeking to find her a teaching position that paid.

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At Goettingen,she pursued her passion for mathematical invariance,the study of numbers that can be manipulated in various ways and still remain constant. In the relationship between a star and its planet,for example,the shape and radius of the planetary orbit may change,but the gravitational attraction conjoining one to the other remains the sameand theres your invariance.

In 1915 Einstein published his general theory of relativity. The Goettingen math department fell head over ear with it,in the words of one observer,and Noether began applying her invariance work to some of the complexities of the theory. That exercise eventually inspired her to formulate what is now called Noethers theorem,an expression of the deep tie between the underlying geometry of the universe and the behaviour of the mass and energy that call the universe home.

What the revolutionary theorem says,in cartoon essence,is the following: Wherever you find some sort of symmetry in nature,some predictability or homogeneity of parts,youll find lurking in the background a corresponding conservationof momentum,electric charge,energy or the like. If a bicycle wheel is radially symmetric,if you can spin it on its axis and it still looks the same in all directions,well,then,that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noethers theorem,youll see its angular momentum,the Newtonian impulse that keeps bicyclists upright and on the move.

Some of the relationships to pop out of the theorem are startling,the most profound one linking time and energy. Noethers theorem shows that a symmetry of timelike the fact that whether you throw a ball in the air tomorrow or make the same toss next week will have no effect on the balls trajectoryis directly related to the conservation of energy,our old homily that energy can be neither created nor destroyed but merely changes form.

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Noether left little record of how she felt about the difficulties she faced as a woman,or of her personal and emotional life generally. She never married,and if she had love affairs she didnt trumpet them. Noether was one of the first Jewish scientists to be fired from her post and forced to flee Germany. In 1933,with the help of Einstein,she was given a job at Bryn Mawr College,where she said she felt deeply appreciated as she never had been in Germany. But only 18 months after her arrival in the United States,at the age of 53,Noether was operated on for an ovarian cyst,and died within days.