Emmy Noether: Magic Mathematician

Remarkable story of mathematical genius whose work continues to impact today's research.

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A postcard sent by Emmy Noether to a colleague Ernst Fischer with dicussion on abstract algebra.

Emmy Noether, the first child of the mathematician Max Noether, was born on March 23, 1882, in Erlangen in Southern Germany. She was destined to change our perception of the universe with her profound, paradigm shifting fundamental theory of physics, besides her prominent contributions in the field of abstract algebra.

As a child, she was not very exceptional; however, since an early age, she was identified as being clever and friendly, these being the qualities that she was recognized with till the very last of her days. She did not show any exceptional talent or fervor in household activities either, or at any ladylike skill for that matter. But she was passionate about dancing.

“As a child, she was not very exceptional; however, since an early age, she was identified as being clever and friendly.”

An early childhood incident recounted by her peer proves as a testimony to her wits, who recalls Emmy being very quick at solving what we call a “combination problem” in mathematics, posed as a teaser at children’s birthday party. She managed to crack with quick maneuvering the puzzle that stymied every other child of her age.

By the age of eighteen, she was an accomplished linguist with above average grade in French and English and was qualified to be a teacher of modern languages in a Bavarian girls college. But at this point in history, her apparently ordinary life took an interesting turn, with her decision of pursuit of higher education in mathematics over the safe course and the economically promising but rather dull option of teaching languages to girls.

At that time, the certified teachers who selected “continued education” as the purpose of their studies, were not permitted to enroll as regular students and were only admitted as auditors, without access to examinations. So, for the winter semester of 1900-01 in Erlangen, she registered herself as female auditor. On July 14, 1903, she took graduation exams at the Royal College for Semi Classical Education in Nuremberg.

After graduation, she registered herself as auditor for the winter semester 1903-04 in Gottingen but returned to pursue her doctoral in Erlangen, her hometown. Meanwhile, at Gottingen, she attended the lectures of Hermann Minkowaski, Otto Blumenthal, Felix Klein, and David Hilbert. And thus, she exploited the opportunity of getting acquainted with prominent 20th century mathematicians and being where the action was happening.

“For every conservation law, there is an accompanying invariant and conversely for every invariant there exists a conservation law.”

In the following years, under the guidance of a family friend and ‘The Master of Invariance’, Paul Gordan, Noether wrote her doctoral dissertation in the field of invariance. She was the first German woman to earn a Ph.D. in Mathematics and also had the honor of being the only female doctoral student of Gordan.

Later, this asset of hers proved of great utility to the development of Einstein’s Theory of Relativity. When Hilbert, who was responsible for the mathematics of Theory of Relativity, asked Noether for her insights regarding the energy conservation issue, the Noether’s Theorem of profound implications in physics was born. The theorem would centuries later still open doors to realms of newer possibilities. One of the towering achievements of the 20th century was the famously known General Theory of Relativity that offers a new perception of gravity, with the introduction of fabric of space and time. But little is known of the person who justified the final conflicts and incoherencies arising in the validation of the theory.

Emmy Noether was the first German woman to earn a PhD in Mathematics.

Since Einstein’s theory of relativity apparently defied conservation of energy, Noether proposed a simple idea that revolutionized the understanding of the laws of the universe. The statement of the theorem is succinctly put as follows:

“For every conservation law, there is an accompanying invariant and conversely for every invariant there exists a conservation law.”

Thus, the energy conservation problems occurred since time in-variance was failed to be brought into account, which was implicit and thus irrelevant in the classical physics.

A century later, Noether Teorem is still influencing major discoveries in the field of physics and revealing the mysteries of the universe.

Einstein remarked in the recognition of her genius in these words; “In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education women began”.

A century later, Noether Teorem is still influencing major discoveries in the field of physics and revealing the mysteries of the universe. The theorem was fundamental in establishing the theoretical existence of Higgs Boson, the elementary particle in the Standard Model of Physics that explains the existence of all mass.

Although Noether revolutionized physics, her major contributions remain to be in the discipline of pure mathematics. In this discipline, she was one of the principle architects of abstract algebra. Her name is remembered in many of its concepts, structures and objects, such as: Noetherian, Noetherian group, Noetherian induction, Noether normalization, Noether problem, Noetherian ring, Noetherian module, Noetherian scheme, Noetherian space, Albert–Brauer–Hasse Noether theorem, Lasker Noether theorem, and Skolem–Noether theorem.

She lived to witness the Nazi era of Germany. As the fascist government rose to power in Germany, all the Jews were stripped of their official titles and services, and many were forced to exile. Inevitably, Noether was subjected to the consequences of anti-Semitic persecution. And she lost her hard-won job of a lecturer at Gottingen. Not just Noether but two-third of German mathematicians fell victim to this ethnic screening and Germany never managed to recover its revered place of ‘center of mathematics of the world’ again. Luckily, Noether managed to restore purpose to her life by acquiring a teaching position at Bryn Mawr, Pennsylvania, USA. She served there for two years before her accidental death in 1935.

CORRECTION: An earlier version of this article incorrectly reported that Emmy Noether was first German woman to attain a doctorate. We have since learnt that first German to attain a PhD Dorothea Erxleben who attained her PhD in 1754.

This article was written in collaboration with Maliha Amin. 

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