When Minsky kept the audience waiting while an overhead projector was wheeled into place and adjusted, he drily quipped: “I just work with computers; I don’t like them.” A forever endearing comment.

]]>**The Turing Test DEVO Test** From ordered foundations in rationality, self-construct/self-deconstruct self-realizing general intelligences. Because we’ll know, for sure, that strong AI has arrived, when its avatars start wearing Energy Domes. 🙂

For details, interested *Shtetl Optimized* readers are referred to Chapter 2 “How I Acquired Charisma” of Michael Harris *Mathematics Without Apologies* (2015).

Its notable (even surprising) that Harris’ book refers nowhere to his own Clay Research Award; Harris’ narrative rather is mainly concerned with (what Harris calls) “the relaxed field” that remains when peripheral considerations of personal honors, national interests, state secrets, and intellectual property are *removed* from centrality to mathematical practice.

Needless to say, not everyone agrees on the merits of Harris’ view of mathematics as a practice that (ideally) is “not subject to the pressures of material gain and productivity.”

Thank you, Attila Smith, for helping to inspire these corrections, reflections and citations.

]]>Noether’s mathematical work has been divided into three “epochs”.

In the first epoch (1908–19,

Noether age 26 to 37), she made contributions to the theories of algebraic invariants and number fields. Her work on differential invariants in the calculus of variations, Noether’s theorem, has been called “one of the most important mathematical theorems ever proved in guiding the development of modern physics”.In the second epoch (1920–26,

Noether age 38 to 44), she began work that “changed the face of [abstract] algebra”. In her classic paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921) Noether developed the theory of ideals in commutative rings into a tool with wide-ranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor.In the third epoch (1927–35,

Noether age 45 to 53), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals.In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.

How unfortunate it is, that Noether’s tragically early death (at age 53) deprived humanity of a fourth “Emmy Epoch”. As Hermann Weyl said at her funeral “Her heart knew no malice; she did not believe in evil.” … oy … 🙁

Jean Dieudonné’s survey “The Historical Development of Algebraic Geometry” (1972, see comment #19) provides further details, and an extended mathematical context, regarding the transformational impact(s) of Emma Noether’s work (and that of her mathematician-father Max Noether too).

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