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Emmy Noether, German mathematician and physicist (Germany, 1882- USA, 1935) is considered to be the mother of abstract algebra. She made very important contributions to the formulation of the theory of general relativity, explaining the origin of problems found in it. Her famous Noether's Theorem is the basis of the most important results in theoretical physics.

Despite being a world-renowned figure, she did not get a teaching position at a German University, although she did teach, not only because of the prejudice against women at the time, but also because she was Jewish, a social democrat and pacifist. In 1933 she had to go into exile in the USA.

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Justificacions

• Ph.D in Mathematics.
• She is considered the mother of abstract algebra.
• Noether's theorem is the fundamental piece of current theoretical physics.
• She made important contributions to the theory of relativity by Einstein. She explained how some of the problems scientists found in the theory of relativity were not problems, but that it was only necessary to study these concepts locally.
• She considered teaching to be essential. She did everything for her students and fought for them
• She was a reference for future generations.
• She was denied a dignified and recognized position at the German university despite being n internationally renowned figure for her contributions to mathematics.

Biografia

Emmy Noether was born in 1882 in the German city of Erlangen. There she was a student of Paul Gordan (1837-1912). Under his guidance she wrote a thesis on the formal theory of Gordan's computational invariants, which she defended in 1907. At Hilbert's invitation, in 1916 Noether moved to Göttingen, where she lived until 1933, when, forced to leave Germany (Emmy Noether was Jewish), she accepted a teaching position at Bryn Mawr College for Women in the United States, where she lived for the last year and a half of her life, commuting constantly to the Princeton Graduate Institute to teach seminars and carry out her research work.

Emmy was the daughter of the renowned mathematician Max Noether, a friend of Gordan's, and the mathematical conversations between the two friends were a fundamental ingredient of the atmosphere in the house she grew up in, where studying mathematics was not an obligation, but a free activity and regarded as a pleasure. As a child, Emmy danced and played the piano. At the age of 18 she got the official certificates to be an English and French teacher, and that same year she enrolled at the University of Erlangent. Then, as one of only two women among a thousand students, she chose courses in history and modern languages. In 1904, it is not known why, she switched to mathematics. She made her decision freely, as an adult and knowing what she was doing. Years of living with her father had given her more than enough information about how difficult mathematics are, the pleasure they give, and the many hours it takes to reach those moments of pleasure. On the other hand, before opting for maths, she studied other things and she always led a very politically-committed life. Both are important: she had the information and was allowed to choose.

In the field of algebra and topology, Noether was able to transfer the structures that had been built up over the years to study the factorization of integers to other, much more general mathematical objects, directly connected with the study of curves, surfaces and varieties in general. This made the arithmetization of geometry and topology possible.

In 1908 she was selected for the Circolo Matematico di Palermo. In 1909 she was invited to become a member of the Deutsche Mathematiker-Vereinigung and, in the same year, was invited to address the Society's annual meeting in Salzburg.

In 1915, Hillbert invited Emmy Noether to be a part of a mathematical team he was creating at the University of Göttingen. In June and July 1915, a few months after Noether's arrival, Albert Einstein (1879-1955) gave six lectures on the unfinished general theory of relativity at this University. In classical field theories - Newtonian gravity, electromagnetism, hydrodynamics, etc. - energy is locally conserved, and the same was true in the special theory of relativity. The principle of local conservation of energy only seemed to fail in the general theory of relativity, and understanding why this problem - which Hilbert described as the failure of the energy theorem- held many of the most reputable mathematicians of the time in check.

Emmy Noether showed that the so-called glitch is not a glitch but is in fact a characteristic feature of the general theory. She quantified it and explained why it occurs: because of the nature of the group of symmetries involved. Albert Einstein used these contributions for the formulation of some aspects of general relativity.

She wrote around 45 research papers and inspired other big names in maths as Max Deuring, Hans Fitting, Chiungtze Tsen or Olga Taussky Todd, among others.

In 1935, she died four days after an operation to remove a tumour that had been detected.

Retrieved from: https://mujeresconciencia.com/2014/06/02/emmy-noether-la-madre-del-algebra-abstracta/ Author: Capi Corrales Rodrigáñez (01/02/2022).

Biography of Emmy Noether:  https://www.buscabiografias.com/biografia/verDetalle/8589/Emmy%20Noether Authors: Víctor Moreno, María E. Ramírez, Cristian de la Oliva, Estrella Moreno and others (24/03/2022).

Obres

Bibliografia

- Corrales Rodrigánez, Capi, “Emmy Noether, madre del álgebra abstracta” in Mujeres con ciencia, (01/02/2022) <https://mujeresconciencia.com/2014/06/02/emmy-noether-la-madre-del-algebra-abstracta/>

- O’Connor, J. J. y Robertson, E. F., “Emmy Amalie Noether” in MacTutor, (14/02/2022), <https://mathshistory.standrews.ac.uk/Biographies/Noether_Emmy/>

- Rodríguez Sánchez, Blanca, “Emmy Noether. Los anillos noetherianos” in Matemáticas en femenino, (01/02/2022), <https://matematicasenfemeninoplural.wordpress.com/2019/03/01/emmy-noether/ >

- Víctor Moreno, María E. Ramírez, Cristian de la Oliva, Estrella Moreno y  otros,“Biografía de Emmy Noether” en Busca Biografías (24/03/2022) <https://www.buscabiografias.com/biografia/verDetalle/8589/Emmy%20Noether> 

Enfocament Didàctic

Emmy worked abstractly, trying to generalize concepts by finding very general results which then had consequences in other disciplines such as physics. It can be used in algebra subjects, as well as in physics and chemistry when applying conservation laws, as they are all based on Noether's theorem.

It is important to note that Emmy started out studying languages and history, but finally opted for mathematics, to show that decisions are not irrevocable in general. The environment in which she grew up probably influenced her decision and vocation. It is very important to have references to study science. Moreover, the fact that she was not paid is very remarkable, because if Emmy had not come from a wealthy family she would not have worked for free and we would have missed out on all her contributions. The social and economic context related to this is important.

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