amalie (emmy) noether (1882 -...

Amalie (Emmy) Noether (1882 - 1935)

Mairi Sakellariadou

King’s College London

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Emmy Noether was born in Erlangen, Germany on March 23, 1882

She was named Amalie, but always called "Emmy"

Emmy Noether 10th February 2016 Zakopane Mairi Sakellariadou

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The family

The father: Max Noether

(1844 Mannheim– 1921 Erlangen)

From a Jewish family of wealthy wholesale hardware dealers.

At 14, Max contracted polio and was afflicted by its effects for the rest of his life.

Through self-study, he learned advanced mathematics and entered the University of

Heidelberg in 1865.

He moved to the University of Erlagen in 1888. While there, he helped to found the field

of algebraic geometry.

In 1880 he married Ida Amalia Kaufmann, the daughter of another wealthy Jewish

merchant family.

Two years later they had their first child, named Amalia (“ Emmy “) after her mother.


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The family

The mother: Ida Amalia Kaufmann

(1852 Koln – 1951 Erlagen)

From a wealthy Jewish merchant family.

Ida had a brother who was a professor at the University of Berlin.

In 1880 she married Max Noether ; they had four children.

Ida was a skilled pianist.


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Emmy 1882 – 1935

Professor of Mathematics in

Erlagen, Gottingen, and Bryn

Mawr (USA)

Alfred 1883 – 1918

Chemist

Fritz 1884 – 1937

Professor of Mathematics in

Breslavia (Germany) and in Tomsk

(Russia)

Gustav Robert 1889 -- 1928

The family


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The family a bit before the first world war


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The Erlagen period (1882 – 1915)

Emmy's childhood was unexceptional, going to school, learning

domestic skills, and taking piano lessons. Her passion was dancing.

Since girls were not eligible to enroll in the gymnasium, she

attended the Municipal School for Higher Education of Daughters

in Erlangen, where she studied arithmetic and languages.

Emmy also loved mathematics, but she knew that the rules of the time meant

she would not be allowed to follow in her father’s footsteps to become a

University academic.

At age18, she was qualified to teach

English and French in girls’ schools.


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Although a career in teaching offered her financial security, her love

of mathematics proved to be too strong.

Emmy decided to abandon teaching and apply to the University of

Erlangen to observe mathematics lectures.

She could only observe lectures, because women were not permitted

to enroll officially at the University.

Between 1900 and 1902 Emmy

studied mathematics at Erlangen.

In July 1903 she went to Nürnberg

and passed the matriculation

examination allowing her to study

mathematics (but not officially enroll)

at any German University.

Emmy was one of the two female students sitting in on courses at Erlangen.


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Emmy chose to go for a semester to the University of Göttingen. She attended lectures given by:

Minkowski

Hilbert

Schwarzschild Blumenthal

Klein

Again she was not allowed to be a

properly matriculated student but

was only allowed to sit in on lectures.

After one semester at Göttingen,

Emmy returned to Erlangen.



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At this point the rules were changed and women students were allowed

to matriculate on an equal basis to the men.

On 24 October 1904 Emmy matriculated at Erlangen and in 1907, at the age of 25,

she was granted a doctorate after working under Paul Gordan,.

Her thesis was entitled “On the construction of the system of forms of a ternary

biquadratic form “ (the search for the invariants of a homogeneous polynomial of

degree 4 in 3 variables).

Emmy was the only student Gordan ever accepted as a Ph.D. candidate.

“.. her dissertation with Gordan pursued a huge calculation that had stumped Gordan forty years before and which Noether could not complete either. So far as I know no one has ever completed it or even checked it as far as she went. “

Colin McLarty (2011)



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Research and teaching at Erlagen University (1908-1915)

Having completed her doctorate the normal progression to an academic post

would have been the habilitation.

However this route was not open to women so Emmy remained at Erlangen,

helping her father who, particularly because of his own disabilities, was grateful for

his daughter's help.

Emmy also worked on her own research; she was influenced by Ernst Fischer who

had succeeded Gordan to the chair of mathematics when he retired in 1911.

Emmy wrote about Fischer's influence:

“Above all I am indebted to Mr E Fischer from whom I received the decisive impulse to study abstract algebra from an arithmetical viewpoint, and this remained the governing idea for all my later work. “


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Research and teaching at Erlagen University (1908-1915)

Dr. Noether, Mathematics Lecturer

In 1908 Emmy was appointed to the position of mathematics lecturer at

Erlangen. Unfortunately, it was an unpaid position.

Emmy’s parents supported her as much as they could through this time.

Nevertheless, her life was a struggle financially.

While working as a lecturer, Emmy became fascinated by work Hilbert had

done in Göttingen.

1908: member of the Mathematical Circle of Palermo

1909: member of the Mathematical German Society


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The Göttingen period (1915 –1933)

Felix Klein 1849 – 1925 David Hilbert: 1862 – 1943

Hilbert was working on physics, in particular on ideas on the theory

of relativity close to those of Albert Einstein.

He decided that he needed the help of an expert on invariant

theory and, after discussions with Klein, they issued the invitation.


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In 1915 Hilbert invited her to become a lecturer in Göttingen.

This provoked a storm of protest from philologists and historians among the

faculty. One faculty member protested: ‘’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? ‘’

Hilbert responded with indignation, stating, “ I do not see that the sex of the candidate is an argument against her admission ... After all, we are a university, not a bath house. ‘’

Emmy was so eager to join Hilbert’s department

in Göttingen that, to overcome Hilbert’s

opponents, she agreed not to be formally

appointed as a lecturer and to receive no pay.

Her father continued supporting her financially

(her mother died in 1915) and the lectures she

gave were advertised as lectures by Professor

Hilbert, with assistance from Dr. E. Noether.



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Soon after arriving at Göttingen, Noether proved her two theorems in

1915, published in 1918, under the title Invariante Variationsprobleme



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in Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu

Gottingen, Mathematisch-physikalische Klasse, 1918, pp. 235-257.

.


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Every differentiable symmetry of the action of a physical system has a corresponding conservation law.

Among the most important mathematical

theorems ever proved in guiding the

development of modern physics.


Emmy’s theorems relate symmetry groups

of a variational integral to properties of its

associated Euler-Lagrange equations.



in Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu

Gottingen, Mathematisch-physikalische Klasse, 1918, pp. 235-257.

.


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Emmy submitted the “invariant Variationsprobleme” for her

Habilitation, finally obtained in 1919.

She never referred to her article in her subsequent publications.

In Göttingen, Emmy had only one immediate follower, Erich Bessel-Hagen

(1898-1946), who was Klein’s student.

He formulated the two Noether theorems slightly more general than they

had been formulated in her article, and added “I owe these to an oral communication by Miss Emmy Noether herself “.


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November 1915

Albert Einstein publishes his theory of General Relativity.

David Hilbert states the Variational Principle.

Albert Einstein: 1879-1955 David Hilbert: 1862 – 1943

The contribution of Emmy’s

work was fundamental.


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Although Noether's theorem had a profound effect upon physics,

among mathematicians she is best remembered for her seminal

contributions to Abstract Algebra.

In 1924 B. L. van der Waerden, arrived at the University of Göttingen.

van der Waerden later said that her originality was “absolute beyond comparison “.

In 1931 van der Waerden published Modern Algebra, a central text in the field;

its second volume borrowed heavily from Emmy's work.

“ ... The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her – in published papers, in lectures, and in personal influence on her contemporaries. .."

Nathan Jacobson

in his introduction to Nother’s collected papers


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Assistant professor in 1922

During her time at the University of Gottingen, she accumulated a small

following of students known as Noether's boys.

Emmy as Assistant. Professor was teaching Group Theory and Hypercomplex Numbers Hypercomplex Quantities and Representation Theory Noncommutative Algebra Noncommutative Arithmetic Algebra of Hypercomplex Quantities

but during the first few years she was not receiving a salary.

She was living in a student pension, until she was thrown out after student

leaders complained of living with "a Marxist-leaning Jewess" . She was taking

her meals in a canteen for poor people.


“ Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all.‘’

van der Waerden


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In the twenties, Göttingen gathered the best mathematicians.

Apart Hilbert and Klein, there were also Hermann Weyl, Richard Courant,

Constantin Caathéodory, and many more.

Many visitors were also spending long periods, like for instance André Weil,

Solomon Lefschetz, and Claude Chevalley.

Emmy was playing a protagonist role in this golden period of mathematics.



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In the winter of 1928–29 Emmy accepted an invitation to Moscow State

University, where she continued working with P. S. Alexandrov.

In addition to carrying on with her research, she taught classes in Abstract Algebra and Algebraic Geometry.

She worked with the topologists, Lev Pontryagin and Nikolai Chebotaryov,

who later praised her contributions to the development of Galois theory.


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Recognition

In 1932 Emmy Noether and Emil Artin received the

Ackermann–Teubner Memorial Award for their contributions to mathematics.

In November 1932 Emmy delivered a plenary address on "Hyper-complex

systems in their relations to commutative algebra and to number theory" at

the International Congress of Mathematicians in Zürich. The congress was

attended by 800 people.

But she was not elected to the Göttingen Academy of Sciences and was

never promoted to the position of Full Professor.

For her fiftieth birthday (1932) Helmut Hasse dedicated an article to her in

the Mathematische Annalen, wherein he confirmed her suspicion that

some aspects of noncommutative algebra are simpler than those of

commutative algebra by proving a noncommutative reciprocity law.


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In January 1933 Adolf Hitler becomes the German Reichskanzle

At the University of Göttingen the German Student

Association led the attack on the "un-German spirit" attributed

to Jews and was aided by a Werner Weber, a former Emmy’s

student.

In April 1933 Emmy received a notice from the Prussian Ministry for Sciences, Art,

and Public Education which read:

"On the basis of paragraph 3 of the Civil Service Code of 7 April 1933, I hereby withdraw from you the right to teach at the University of Göttingen.”

Emmy accepted the decision calmly, providing

support for others during this difficult time.

She remained focused on mathematics, gathering

students in her apartment to discuss class field theory.

When one of her students appeared in the uniform

of the Nazi, she showed no sign of agitation.


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Albert Einstein and Hermann Weyl were appointed by the

Institute for Advanced Study in Princeton, while others

worked to find a sponsor required for legal immigration.

Emmy was contacted by representatives of two educational

institutions, the Bryn Mawr College for female students in

Philadephia (USA) and the Somerville College at the

University of Oxford in England.

After a series of negotiations with the Rockefeller Foundation,

a grant to Bryn Mawr was approved for Emmy and she took

a position there, starting in late 1933.

Bryn Mawr: 1933 - 1935


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At Bryn Mawr, Emmy worked with Anna Wheeler, who had studied at

Göttingen just before Emmy arrived there.

Another source of support was the Bryn Mawr president, Marion Edwards Park,

who enthusiastically invited mathematicians in the area to "see Dr. Noether in action !“.

Emmy and a small team of students worked through van der Waerden's book

Modern Algebra I and parts of Erich Hecke's Theory of algebraic numbers.

In 1934, Emmy began lecturing at the Institute for Advanced Study in Princeton..

However, she remarked about Princeton University that she was not welcome at

the "men's University, where nothing female is admitted “.

Bryn Mawr: 1933 - 1935


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Bryn Mawr: 1935

In April 1935 doctors discovered that she had a tumour.

Two days later they operated, finding further tumours

which they believed to be benign and did not remove.

The operation seemed a success and for three days her

condition improved.

However, on the fourth day, 14th April 1935, Emmy

suddenly collapsed and developed a very high

temperature. She died later that day.

Her body was cremated and the ashes interred under the walkway

around the cloisters of the M. Carey Thomas Library at Bryn Mawr.


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“ 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... "

Albert Einstein

New York Times (1935)


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“ E. Noether’s famous 1918 paper, “Invariant variational problems” crystallised essential mathematical relationships among symmetries, conservation laws, and identities for the variational or `action’ principles of physics... Thus, Noether’s abstract analysis continues to be relevant to contemporary physics, as well as to applied mathematics. “

Gregg Zuckerman

(1987)


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Emmy Noether: 1882 - 1935


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