Emmy Noether: Her story in sketches

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Under the twitter banner of #Noethember, initiated by Constanza Rojas-Molina, an international drawing challenge themed around mathematician Emmy Noether was organised in November, 2018. The project resulted in a huge number of drawings and a warm feeling among those who participated. For 30 days, people across Twitter shared their sketches illustrating facts about Noether’s life and work.

Day 1: Emmy Noether was born on 23 March 1882 in Erlangen, Germany to Max Noether (mathematician) and Ida Kaufmann. — **Day 1:** Emmy Noether was born on 23 March 1882 in Erlangen, Germany to Max Noether (mathematician) and Ida Kaufmann.

Day 2: From 1889 to 1897 Noether attended Höhere Töchter Schule in Erlangen (girls school). She studied German, arithmetic, French and English, and learned the piano. — **Day 2:** From 1889 to 1897 Noether attended Höhere Töchter Schule in Erlangen (girls school). She studied German, arithmetic, French and English, and learned the piano.

Day 3: When she was young, she loved dancing and “used to look forward to family parties”. — **Day 3:** When she was young, she loved dancing and “used to look forward to family parties”.

Day 4: “As a child, Emmy gave no sign of precociousness or extraordinary ability and was indistinguishable from all the other young girls in Erlangen”. — **Day 4:** “As a child, Emmy gave no sign of precociousness or extraordinary ability and was indistinguishable from all the other young girls in Erlangen”.

Day 5: Emmy Noether’s father Max was also famously a mathematician, and so was her younger brother Fritz. — **Day 5:** Emmy Noether’s father Max was also famously a mathematician, and so was her younger brother Fritz.

Day 6: In 1900 she decided to attend university in Erlangen – but as girls were not trained to prepare for the entrance exam at school, Emmy had to spend 3 years preparing for the exam independently. — **Day 6:** In 1900 she decided to attend university in Erlangen – but as girls were not trained to prepare for the entrance exam at school, Emmy had to spend 3 years preparing for the exam independently.

Day 7: At Erlangen , Noether was one of only two women in a university of 986 students, and was only allowed to audit classes rather than participate fully. She required the permission of individual professors whose lectures she wished to attend. — **Day 7:** At Erlangen, Noether was one of only two women in a university of 986 students, and was only allowed to audit classes rather than participate fully. She required the permission of individual professors whose lectures she wished to attend.

Day 8: Although it had been well received, Noether later described her thesis and a number of subsequent similar papers she produced as “crap”. — **Day 8:** Although it had been well received, Noether later described her thesis and a number of subsequent similar papers she produced as “crap”.

Day 9: After completing her dissertation in 1907, she worked at the Mathematical Institute of Erlangen without pay for seven years, since at the time, women were largely excluded from academic positions. — **Day 9:** After completing her dissertation in 1907, she worked at the Mathematical Institute of Erlangen without pay for seven years, since at the time, women were largely excluded from academic positions.

Day 10: In 1908 she was elected member of the Circolo Matematico di Palermo. In 1909 she was elected member of the German Mathematical Society, and started giving lectures at their meetings. — **Day 10:** In 1908 she was elected member of the Circolo Matematico di Palermo. In 1909 she was elected member of the German Mathematical Society, and started giving lectures at their meetings.

Day 11: She moved to Göttingen on the invitation of David Hilbert and Felix Klein. Hilbert and Klein asked for a position for Emmy, and for her to be able to pass the Habilitation and become “Privatdozent” (person who has permission to lecture at university). For this, the whole philosophy faculty had to agree, which included philosophers, historians, and philologists, who refused. Hilbert solved this by having her lecture in his stead. — **Day 11:** She moved to Göttingen on the invitation of David Hilbert and Felix Klein. Hilbert and Klein asked for a position for Emmy, and for her to be able to pass the Habilitation and become “Privatdozent” (person who has permission to lecture at university). For this, the whole philosophy faculty had to agree, which included philosophers, historians, and philologists, who refused. Hilbert solved this by having her lecture in his stead.

Day 12: “I do not see that the sex of the candidate is an argument against her admission as Privatdozent [teaching assistant]. After all, we are a university and not a bathing establishment.” David Hilbert. — **Day 12:** “I do not see that the sex of the candidate is an argument against her admission as Privatdozent [teaching assistant]. After all, we are a university and not a bathing establishment.” David Hilbert.

{Day 13:} \FiraSansLight “I have completely forgotten formal calculus.” Emmy Noether, Letter to Helmut Hasse (April 14, 1932). } — **Day 13:** “I have completely forgotten formal calculus.” Emmy Noether, Letter to Helmut Hasse (April 14, 1932).

Day 14: In 1932 she received the Alfred Ackermann-Teubner Memorial Prize for the Advancement of Mathematical Knowledge, and was the first woman to be a Plenary speaker at the International Congress of Mathematicians. — **Day 14:** In 1932 she received the Alfred Ackermann-Teubner Memorial Prize for the Advancement of Mathematical Knowledge, and was the first woman to be a Plenary speaker at the International Congress of Mathematicians.

Day 15: In 1933, Nazis forced the retirement of Jews and all civil servants with at least one Jewish grandparent. This included university staff, and Emmy left her post at Göttingen. — **Day 15:** In 1933, Nazis forced the retirement of Jews and all civil servants with at least one Jewish grandparent. This included university staff, and Emmy left her post at Göttingen.

Day 16: Bryn Mawr University invited Emmy to move to the US as a guest professor, thanks to a grant from the Rockefeller Foundation. Many other displaced German academics also found places to work in the USA during this time. — **Day 16:** Bryn Mawr University invited Emmy to move to the US as a guest professor, thanks to a grant from the Rockefeller Foundation. Many other displaced German academics also found places to work in the USA during this time.

Day 17: In 1934 Noether also later lectured at the Institute for Advanced Studies at Princeton, but she found it less welcoming, calling it “the men’s university, where nothing female is admitted”. — **Day 17:** In 1934 Noether also later lectured at the Institute for Advanced Study at Princeton, but she found it less welcoming, calling it “the men’s university, where nothing female is admitted”.

Day 18:} \FiraSansLight She continually advised her students to read and re-read Dedekind’s works, in which she saw an inexhaustible source of inspiration. When praised for her own innovations, she used to repeat: “Es steht alles schon bei Dedekind.” (All of this is already in Dedekind). — **Day 18:** She continually advised her students to read and re-read Dedekind’s works, in which she saw an inexhaustible source of inspiration. When praised for her own innovations, she used to repeat: “Es steht alles schon bei Dedekind.” (All of this is already in Dedekind).

Day 19: Much of Noether’s work in abstract algebra was studying rings – sets of objects with two different ways to combine them – such as the ring of integers with addition and multiplication. Of particular interest are ideals, which are particular subsets of a ring. — **Day 19:** Much of Noether’s work in abstract algebra was studying rings – sets of objects with two different ways to combine them – such as the ring of integers with addition and multiplication. Of particular interest are ideals, which are particular subsets of a ring.

Day 20: A Noetherian ring is a ring with some extra properties – in particular, one that satisfies the ascending chain condition on left and right ideals. This means a sequence of nested ideals, each of which sits inside the previous, cannot continue getting smaller forever. If a ring has this property, it immediately follows that it has many other useful properties. Rational numbers, real numbers and complex numbers (and in fact all fields) are examples of Noetherian rings. — **Day 20:** A Noetherian ring is a ring with some extra properties – in particular, one that satisfies the ascending chain condition on left and right ideals. This means a sequence of nested ideals, each of which sits inside the previous, cannot continue getting smaller forever. If a ring has this property, it immediately follows that it has many other useful properties. Rational numbers, real numbers and complex numbers (and in fact all fields) are examples of Noetherian rings.

Day 21: The Lasker–Noether theorem states that every Noetherian ring is a Lasker ring – it can be considered an extension of Fundamental Theorem of Arithmetic, in that it shows algebraic sets can be decomposed in the same way numbers decompose into primes. — **Day 21:** The Lasker–Noether theorem states that every Noetherian ring is a Lasker ring – it can be considered an extension of Fundamental Theorem of Arithmetic, in that it shows algebraic sets can be decomposed in the same way numbers decompose into primes.

Day 22: Noether’s (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. It explains the mathematical origin of conservation of energy and momentum in physics. — **Day 22:** Noether’s (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. It explains the mathematical origin of conservation of energy and momentum in physics.

Day 23: “If one proves the equality of two numbers <span class="wp-katex-eq" data-display="false">A</span> and <span class="wp-katex-eq" data-display="false">B</span> by showing first that <span class="wp-katex-eq" data-display="false">A\leq B</span> and then that <span class="wp-katex-eq" data-display="false">B\leq A</span> it is unfair; one should instead show that they are really equal by disclosing the inner ground for their equality.” – Emmy Noether — **Day 23:** “If one proves the equality of two numbers A and B by showing first that A ≤ B and then that B ≤A it is unfair; one should instead show that they are really equal by disclosing the inner ground for their equality.” – Emmy Noether

Day 24: In 1958 the University of Erlangen organised a meeting, inviting her former students and their students, to commemorate the 50th anniversary of her degree and discuss her work, applications and influence. — **Day 24:** In 1958 the University of Erlangen organised a meeting, inviting her former students and their students, to commemorate the 50th anniversary of her degree and discuss her work, applications and influence.

Day 25: Noether was featured at an exhibition at the 1964 World’s Fair devoted to Modern Mathematicians – and was the only woman represented there. — **Day 25:** Noether was featured at an exhibition at the 1964 World’s Fair devoted to Modern Mathematicians – and was the only woman represented there.

Day 26: A street in her hometown of Erlangen is named after Emmy and her father; Emmy-Noether-Weg (Emmy Noether Way) in Göttingen is also named after her, and in Unterschleissheim, near Munich, a ring-road is cleverly named Emmy-Noether-Ring. — **Day 26:** A street in her hometown of Erlangen is named after Emmy and her father; Emmy-Noether-Weg (Emmy Noether Way) in Göttingen is also named after her, and in Unterschleissheim, near Munich, a ring-road is cleverly named Emmy-Noether-Ring.

Day 27: Many other things have been named or renamed after Noether, including her former high school, a crater on the moon and a minor planet, and many other awards, scholarship programmes and university buildings. — **Day 27:** Many other things have been named or renamed after Noether, including her former high school, a crater on the moon and a minor planet, and many other awards, scholarship programmes and university buildings.

Day 28: LEGO have now released several Women in Science sets, featuring famous female scientists – but not Emmy Noether yet. What should it look like? What other toys could celebrate her life? — **Day 28:** LEGO have now released several Women in Science sets, featuring famous female scientists – but not Emmy Noether yet. What should it look like? What other toys could celebrate her life?

Day 29: For Emmy Noether’s birthday in 2015, Google celebrated with a Google Doodle, which displayed many of the areas to which she contributed, including topology, ascending/descending chains, Noetherian rings, time, group theory, conservation of angular momentum, and continuous symmetries. — **Day 29:** For Emmy Noether’s birthday in 2015, Google celebrated with a Google Doodle, which displayed many of the areas to which she contributed, including topology, ascending/descending chains, Noetherian rings, time, group theory, conservation of angular momentum, and continuous symmetries.

Day 30: “It surely is not much of an exaggeration to call her the mother of modern algebra.”–-Irving Kaplansky — **Day 30:** “It surely is not much of an exaggeration to call her the mother of modern algebra.”–-Irving Kaplansky

Acknowledgement: Thanks to Constanza Rojas-Molina, Katie Steckles and aperiodical.com for the list of Emmy Noether highlights. Many thanks to Constanza Rojas-Molina for the initiative, her wonderful sketches and the kind permission to reproduce them here. And thanks to Bruno Duchesne for his article in Images des Mathematiques, and for help facilitating the production of this article.

Constanza Rojas-Molina is a mathematician at the CY Cergy Paris Université in France, passionate about illustration, graphic narrative, and about transforming complex ideas and thought processes into visual language.

French edition of this article was originally published in Images des Mathématiques with the title “Noethember” https://images.math.cnrs.fr/Noethember.html, and is published here, in English translation, with permission.