Emmy Noether Quotes (1882-1935)

“Noether's theorem demonstrates that wherever there is symmetry in nature, there is also a conservation law, and vice versa. In other words, the symmetries of space and time are not only linked with conservation of energy, momentum, and angular momentum, but each implies the other. Conservation laws are necessary consequences of symmetries, and symmetries necessarily entail conservation laws. The simplicity, power, and depth of Noether's theorem only slowly became apparent. Today, it is an indispensable part of the groundwork of modern physics... [with] over a dozen important conservation laws and their associated symmetries...”

“In the judgement 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 generation of younger mathematicians.”

“A keen mind and infectious enthusiasm for mathematical research made Emmy Noether an effective teacher. Her classroom technique, like her thinking, was strongly conceptual. Rather than simply lecturing, she conducted discussion sessions in which she would explore a topic with her students. ...Outstanding mathematicians often make their greatest contributions early in their careers. Emmy Noether was an exception: she began to produce her most powerful and creative work around the age of 40. ...She never attained the top rank of full professor, although she contributed so much to making Göttingen the premier mathematical center in Europe—many would say in the world. When the Nazis seized power in 1932, one of their first acts was to deprive non-Aryan[s]... of their positions. ...For a time Emmy Noether continued to meet informally with students and colleagues, inviting groups to her apartment... In the meantime, efforts were being made on her behalf... and she secured a temporary position at Bryn Mawr College, a new college for women near Philadelphia.”

“Conservation laws were old acquaintances from classical physics. ...Noether's theorem asserts that any continuous symmetry leads to a conservation law. It is rather intuitive... After all, symmetry reflects invariance under a transformation, and therefore there must exist a quantity that remains invariant or, in other words, that is conserved. For instance, a circle is invariant under rotations about its centre. ...Hence, the symmetry of a circle is associated with the conservation of distance ...The power of Noether's theorem was to show that this intuitive concept is valid for any continuous symmetry ...from Noether's theorem we discover that the conservation of electric charge is the consequence of the special rotational symmetry of QED... [acting upon] an abstract space defined by the quantum fields.”

“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.”

“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.”

“The first "modern" text in algebra, van der Waerden's Modern Algebra, which appeared in 1931, was heavily influenced by Emmy Noether. It is an enlightening exercise to compare this work with algebra books of just a few decades earlier to see the profound influence that she had on our present conception of algebra. Nevertheless, even Noether realized that one needs to be familiar with a wide variety of concrete examples from all parts of mathematics before one can understand the value of the generalizations she was able to make.”

“Her thesis ends with a table of the complete system of covariant forms for a given ternary quartic consisting of not less than 331 forms in symbolic representation. It is an awe-inspiring piece of work; but today I am afraid we should be inclined to rank it among those achievements with regard to which Gordan himself once said when asked about the use of the theory of invariants: "Oh, it is very useful indeed; one can write many theses about it."”

“The computation of algebraic invariants did not end with Hilbert's work. Emmy Noether... did a doctoral thesis in 1907 "On Complete Systems of Invariants for Ternary Biquadratic Forms." She also gave a complete system of covariant forms for a ternary quartic, 331 in all. In 1910 she extended Gordan's result to n variables. The subsequent history of algebraic invariant theory belongs to modern abstract algebra. ...From 1911 to 1919 Emmy Noether produced many papers on finite bases for various cases using Hilbert's technique and her own. In the subsequent twentieth-century development the abstract algebraic viewpoint dominated. As Eduard Study complained in his text on invariant theory, there was lack of concern for specific problems and only abstract methods were pursued.”

“Group theory is the mathematical language of symmetry, and it... seems to play a fundamental role in the very structure of nature. ...In the midst of the fomenting of the new twentieth century physics was the... life of the greatest female mathematician who ever lived, Emmy Noether. ...At Göttingen, Noether achieved fame for her research into the fundamental structure of mathematics. However, she stepped briefly into the realm of theoretical physics... Noether's theorem is a profound statement, perhaps running as deeply into the fabric of our psyche as the famous theorem of Pythagoras. Noether's theorem directly connects symmetry to physics, and vice versa. It frames our modern concepts about nature and rules modern scientific methodology. ...For scientists it is the guiding light to unraveling nature's mysteries, as they delve into the innermost fabric of matter ...To this task scientists apply ...the great particle accelerators ...Emmy Noether's work interweaves our understanding of nature—through physics and mathematics—with the beauty and harmony that surrounds us... Noether's theorem provides a natural centerpiece for any discussion that unifies physics and mathematics, such as in the teaching of these... in a way that enlivens them both.”

“She started by examining continuous symmetries. These are symmetries under transformations that can be varied continuously, such as rotations (where the angle can be changed continuously). The result... was stunning. She showed that to every continuous symmetry of the laws of physics there corresponds a conservative law and vice versa. In particular, the familiar symmetry of the laws under translations corresponds to conservation of momentum, the symmetry with respect to the passage of time (the fact that the laws do not change with time) gives us conservation of energy, and the symmetry under rotations produces conservation of angular momentum. ...Noether's theorem fused together symmetries and conservation laws—these two giant pillars of physics are actually nothing but different facets of the same fundamental property.”

“[A]bstract algebra, as a conscious discipline, starts with Noether's 1921 paper "Ideal Theory in Rings."”

“In crediting Emmy Noether with her share in this transformation of mathematics, most biographers have followed Hermann Weyl's analysis... noting that it falls in three periods, of which the first, lasting until about 1919, was one of "relative dependence," whereas the other two were characterized by the algebraic work for which she is remembered. ...[D]ifficulties arise in drawing a sharp distinction between... "relatively dependent" and the rest, however. One can find examples of originality in her early work, and many instances of dependence in her later period... the exclusion of "dependent" work from consideration makes it impossible to study any process of conceptual change. ...The work that was most influential was done when she was in her forties; The "Noether school" of those who collaborated with her in attempting to make algebra the tool and foundation of all mathematics consists of individuals who knew her only in the last decades of her life. In short, her historic influence in effecting conceptual change is based on the events in the last decade of her life. Her stature as a creative mathematician is better understood if we examine her mathematical career in its entirety, however. Only then can we appreciate to what extent Emmy Noether's work fits Poincare's famous description of mathematical creativity...”

“In clarifying conservation law issues for the coupled matter-field systems of relativistic gravitation, Emmy Noether helped David Hilbert, Felix Klein, and Albert Einstein put the finishing touches on the general theory of relativity in 1915. ...Because of the central role of conservation laws, one could argue that Noether's Theorem offers a strategic unifying principle for most if not all of physics.”

“Emmy Noether's creative power was directed quite generally towards the clarification of mathematical structures and concepts through abstraction, which means leaving all unnecessary entities and properties aside and concentrating on the essentials. Her basic work in this direction can be subsumed under algebra, but her methods eventually penetrated all mathematical fields, including number theory and topology.”

“One of the major problems of algebra as it is practiced in today's schools is the lack of mathematical, pedagogical, and psychological connection between these two kinds of algebra—between the pre- and post-Noether views of the subject.”

“It is queer that a formalist like Gordan was the mathematician from whom her mathematical orbit set out; a greater contrast is hardly imaginable than between her first paper, the dissertation, and her works of maturity; for the former is an extreme example of formal computations and the latter constitute an extreme and grandiose example of conceptual axiomatic thinking in mathematics that abhorred all calculation and operated in a much thinner air of abstraction than Hilbert, the young lion, ever dared.”