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Monday, March 23, 2015

Emmy Noether revolutionized mathematics — and still faced sexism all her life

Brad Plumer, Senior Editor writes, "Emmy Noether was one of the most brilliant and important mathematicians of the 20th century. She altered the course of modern physics. Einstein called her a genius. Yet today, almost nobody knows who she is."

Painting of Emmy Noether by Jennifer Mondfrans from her series, "At Least I Have You, To Remember Me" (Maia Weinstock/Flickr)

In 1915, Noether uncovered one of science's most extraordinary ideas, proving that every symmetry found in nature has a corresponding law of conservation. So, for example, the fact that physical laws work the same today as they did yesterday turns out to be related to the notion that energy can neither be created nor destroyed. Noether's theorem is a deep insight that underpins much of modern-day physics and things like the search for the Higgs boson.

Even so, as one of the very few female mathematicians working in Germany in her day, Noether faced rampant sexism. As a young woman, she wasn't allowed to formally attend university. Even after proving herself a first-rate mathematician, male faculties were reluctant to hire her. If that wasn't enough, in 1933, the Nazis ousted her for being Jewish. Even today, she remains all-too obscure.
That should change. So it’s welcome news that Google is honoring Noether today with a Google Doodle on her 133rd birthday. To celebrate, here's an introduction to the life and work of a woman Albert Einstein once called "the most significant creative mathematical genius thus far produced."

Noether was brilliant — yet universities wouldn't hire her

Photo: Wikipedia, the free encyclopedia

Amalie Emmy Noether was born in 1882 in Erlangen, Germany, to a family of mathematicians. Her father, Max Noether, was a professor at the University of Erlangen. Her brother Fritz later proved worthy in the field of applied math.
Despite this fertile background, it wasn't obvious that Emmy could become a mathematician too. German universities rarely accepted female students at the time. She had to beg the faculty at Erlangen to let her audit math courses. It was only after she dominated her exams that the school relented, giving her a degree and letting her pursue graduate studies.
Her early work focused on invariants in algebra, looking at which aspects of mathematical functions stay unchanged if you apply certain transformations to them. (To give a very basic example of an invariant, the ratio of a circle's circumference to its diameter is always the same — it's always πno matter how big or small you make the circle.) Noether studied invariants for polynomial functions and made some impressive advances.**

Her work got noticed, and, in 1915, the renowned mathematician David Hilbert lobbied for the University of Göttingen to hire her. But other male faculty members blocked the move, with one arguing: "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?" So Hilbert had to take Noether on as a guest lecturer for four years. She wasn't paid, and her lectures were often billed under Hilbert's name. She didn't get a full-time position until 1919.
That didn't stop Noether from doing trail-blazing work in a number of areas, especially abstract algebra. Rather than focusing on real numbers and polynomials — the algebraic equations we learn in high school — Noether was interested in abstract structures, like rings or groups, that obey certain rules. Abstract algebra was one of the big mathematical innovations of the 20th century, and Noether was hugely influential in shaping it.
But perhaps Noether’s most consequential work came in another field: physics. In 1915, Einstein published his general theory of relativity, showing that gravity was a property of space and time, and the University of Göttingen was all abuzz with the the discovery. Hilbert asked Noether to apply her work on algebraic invariants to the equations in Einstein's theory.
In the process, Noether made a startling discovery of her own.
Read more... 

Related link 
Emmy Noether (From Wikipedia, the free encyclopedia)

** In her 1907 dissertation, for instance, Noether studied degree-four polynomials with three variables. She found that these polynomials had 331 independent invariants, and all other invariants depended on these. This was a mind-numbing feat of calculation — she later described it as "a jungle of formulas." She soon moved on to bigger, conceptual insights.

Source: Vox