Emmy Noether revolutionized abstract algebra, filled in gaps in relativity, and was responsible for a critical theorem about conserved quantities in physics.
The theory of general relativity seemed to violate the law of conservation of energy, however Emmy Noether created Noether’s theorem that solved the dilemma not only for relativity but for any system with symmetries, she also made important contributions to algebra with the theory of rings and field theory, Einstein, Aleksandrov and Dieudonné described her as the most important woman in the field of mathematics.
On 16 July 1918, before a scientific organization in Göttingen, Felix Klein read a paper written by Emmy Noether, because she was not allowed to present the paper herself. In particular, in what is referred to in physics as Noether’s theorem, this paper identified the conditions under which the Poincaré group of transformations (now called a gauge group) for general relativity defines conservation laws. Noether’s papers made the requirements for the conservation laws precise. Among mathematicians, Noether is best known for her fundamental contributions to abstract algebra, where the adjective noetherian is nowadays commonly used on many sorts of objects.
With J. E. Littlewood, Mary Lucy Cartwright was one of the first mathematicians to study what would later become known as chaos theory.
The physicist Freeman Dyson heard Cartwright lecture when he was a student at Cambridge in 1942. He comments Cartwright & Littlewood’s work:
The whole development of radar in World War Two depended on high power amplifiers, and it was a matter of life and death to have amplifiers that did what they were supposed to do. The soldiers were plagued with amplifiers that misbehaved, and blamed the manufacturers for their erratic behaviour. Cartwright and Littlewood discovered that the manufacturers were not to blame. The equation itself was to blame.
Freeman Dyson
In other words, odd things happened when some sorts of values were fed into the standard equation they were using to predict the amplifiers’ performance. Cartwright and Littlewood were able to show that as the wavelength of radio waves shortens, their performance ceases to be regular and periodic, and becomes unstable and unpredictable. This work helped explain some perplexing phenomena engineers were encountering.
The results unexpectedly obtained from the equations predicting the oscillations of radio waves are part of the foundation for the modern theory that accounts for the unpredictable behaviour of all manner of physical phenomena, from swinging pendulums and fluid flow, to the stock market.
The recognition that chaotic behaviour is a vital part of many physical systems in the world around us came in 1961, when Edward Lorenz was running a weather simulation through an early computer. When he tested a particular configuration a second time he found that the outcome differed dramatically from his earlier run. Eventually he tracked the difference down to a small alteration he had inadvertently made in transferring the initial data, by altering the number of decimal places.
Lorenz immortalised this discovery in a lecture entitled “Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?”.
Source: “A Point of View: Mary, queen of maths” by Lisa Jardine, 2013
Grete Hermann (1901 – 1998)
Grete Hermann
Grete Hermann published in 1926 the foundational paper for computerized algebra. It was her doctoral thesis, titled “The Question of Finitely Many Steps in Polynomial Ideal Theory”, and published in Mathematische Annalen.
She made a pioneering philosophical work on the foundations of quantum mechanics.
Maryam Mirzakhani’s work on theoretical mathematics has implications in fields ranging from cryptography to “the theoretical physics of how the universe came to exist”, according to Stanford University.
On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics.
Source: “Maryam Mirzakhani, first woman to win mathematics’ Fields medal, dies at 40”, The Guardian, 2017
