Amalie (Emmy) Noether (1882

Amalie (Emmy) Noether (1882 - 1935)
Mairi Sakellariadou
King’s College London
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
2
Mairi Sakellariadou
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.
Emmy Noether
10th February 2016 Zakopane
3
Mairi Sakellariadou
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.
Emmy Noether
10th February 2016 Zakopane
4
Mairi Sakellariadou
The family
 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
Emmy Noether
10th February 2016 Zakopane
5
Mairi Sakellariadou
The family a bit before the first world war
Emmy Noether
10th February 2016 Zakopane
6
Mairi Sakellariadou
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.
Emmy Noether
10th February 2016 Zakopane
7
Mairi Sakellariadou
The Erlagen period (1882 – 1915)
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.
Emmy was one of the two female students sitting in on courses at Erlangen.
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 Noether
10th February 2016 Zakopane
8
Mairi Sakellariadou
The Erlagen period (1882 – 1915)
Emmy chose to go for a semester to the University of Göttingen.
She attended lectures given by:
Schwarzschild
Minkowski
Blumenthal
Again she was not allowed to be a
properly matriculated student but
was only allowed to sit in on lectures.
Klein
Emmy Noether
Hilbert
After one semester at Göttingen,
Emmy returned to Erlangen.
10th February 2016 Zakopane
9
Mairi Sakellariadou
The Erlagen period (1882 – 1915)
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)
Emmy Noether
10th February 2016 Zakopane
10
Mairi Sakellariadou
The Erlagen period (1882 – 1915)
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. “
Emmy Noether
10th February 2016 Zakopane
11
Mairi Sakellariadou
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
Emmy Noether
10th February 2016 Zakopane
12
Mairi Sakellariadou
The Göttingen period (1915 –1933)
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.
Felix Klein 1849 – 1925
Emmy Noether
David Hilbert: 1862 – 1943
10th February 2016 Zakopane
13
Mairi Sakellariadou
The Göttingen period (1915 –1933)
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.
Emmy Noether
10th February 2016 Zakopane
14
Mairi Sakellariadou
The Göttingen period (1915 –1933)
Soon after arriving at Göttingen, Noether proved her two theorems in
1915, published in 1918, under the title Invariante Variationsprobleme
Emmy Noether
10th February 2016 Zakopane
15
Mairi Sakellariadou
The Göttingen period (1915 –1933)
Soon after arriving at Göttingen, Noether proved her two theorems in
1915, published in 1918, under the title Invariante Variationsprobleme
in Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu
Gottingen, Mathematisch-physikalische Klasse, 1918, pp. 235-257.
.
Emmy Noether
10th February 2016 Zakopane
16
Mairi Sakellariadou
The Göttingen period (1915 –1933)
Soon after arriving at Göttingen, Noether proved her two theorems in
1915, published in 1918, under the title Invariante Variationsprobleme
in Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu
Gottingen, Mathematisch-physikalische Klasse, 1918, pp. 235-257.
.
Emmy’s theorems relate symmetry groups
of a variational integral to properties of its
associated Euler-Lagrange equations.
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 Noether
10th February 2016 Zakopane
17
Mairi Sakellariadou
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 “.
Emmy Noether
10th February 2016 Zakopane
18
Mairi Sakellariadou
The Göttingen period (1915 –1933)
November 1915
Albert Einstein publishes his theory of General Relativity.
David Hilbert states the Variational Principle.
The contribution of Emmy’s
work was fundamental.
Albert Einstein: 1879-1955
Emmy Noether
David Hilbert: 1862 – 1943
10th February 2016 Zakopane
19
Mairi Sakellariadou
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
Emmy Noether
10th February 2016 Zakopane
20
Mairi Sakellariadou
The Göttingen period (1922 –1933)
Assistant professor in 1922
During her time at the University of Gottingen, she accumulated a small
following of students known as Noether's boys.
“ Completely unegotistical and free of vanity, she never claimed anything
for herself, but promoted the works of her students above all.‘’
Emmy as Assistant. Professor was teaching
van der Waerden
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.
Emmy Noether
10th February 2016 Zakopane
21
Mairi Sakellariadou
The Göttingen period (1922 –1933)
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.
Emmy Noether
10th February 2016 Zakopane
22
Mairi Sakellariadou
The Göttingen period (1922 –1933)
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.
Emmy Noether
10th February 2016 Zakopane
23
Mairi Sakellariadou
The Göttingen period (1922 –1933)
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.
Emmy Noether
10th February 2016 Zakopane
24
Mairi Sakellariadou
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.
Emmy Noether
10th February 2016 Zakopane
25
Mairi Sakellariadou
Bryn Mawr: 1933 - 1935
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.
Emmy Noether
10th February 2016 Zakopane
26
Mairi Sakellariadou
Bryn Mawr: 1933 - 1935
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 “.
Emmy Noether
10th February 2016 Zakopane
27
Mairi Sakellariadou
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.
Emmy Noether
10th February 2016 Zakopane
28
Mairi Sakellariadou
“ 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)
Emmy Noether
10th February 2016 Zakopane
29
Mairi Sakellariadou
“ 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)
Emmy Noether
10th February 2016 Zakopane
30
Mairi Sakellariadou
Emmy Noether: 1882 - 1935
Emmy Noether
10th February 2016 Zakopane
31
Mairi Sakellariadou