FOM: "home truths"
mattes at math.ucdavis.edu
Sun Nov 2 21:17:10 EST 1997
I am not sure I completely understand your proposal.
Would you call the following foundational?
1.) Chow's theorem that any complex projective manifold is algebraic.
[You might say that this says something striking and basic about (an
important type of) shapes, and their relations to functions.]
2.) Goedel's result that it is possible to have closed time-like curves in
the theory of relativity. [view towards unity of human knowledge]
3.) The introduction of generalized functions (Dirac).
4.) The concept of symmetry. Groups.
5.) The concept of a limit.
6.) The existence of exotic R^4. [surely striking, and flat space is
the most basic shape I can think of (except for points)].
7.) Anything in applied mathematics or statistics, besides algorithms
(e.g. the concept of proability).
8.) The recent reconnection of mathematics and physics (path integral,
string theory, Seiberg-Witten, quantum cohomology, etc. etc.).
9.) Noncommutative geometry. [says striking things about the relation
between shapes and functions]
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