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gurfle

Math became my first (and at the time only) study subject of devotion when, in sixth grade, I was singled out by a math teacher as the only one in class who had aced a test (no one else knew that the answer to $2^3$ was 8). This affected me greatly, as until that point I was generally one of the worst performers in all classes.

About a year later, I became fascinated with how to build the beautiful results of simple Euclidean Geometry by logical deduction from its basic axioms. Without realizing it at the time, I was beginning right then to do "real" Math even though I was just having fun with homework.

Geometry has remained my favorite Math topic, along with Topology and Combinatorics, which I studied further as a graduate student under the late Victor Klee in the early 1980's. More recently I have completed an MS in Physics, but am finding myself gravitating back to my original interest (and better talent) in the more abstract world of Math.

A year ago I completed a full, blow by blow reading of Tristan Needham's "Visual Complex Analysis", including the completion of virtually all its exercises (certainly all needed to complete any proofs in the main text). Apart from Spivak's "Calculus on Manifolds", this is the only Math book I finished cover-to-cover in this way. I was probably able to do this because of the inimitable beauty of Needham's book's visual style, most notably its diagrams.

Presently I am working my way similarly through Penrose and Rindler's "Spinors and space-time", having reached about the half way mark in Volume 1. Its development of a coordinate-free and commutative abstract tensor algebra that so elegantly captures all possible uses in Physics (where presumably they will never be needed on anything besides paracompact, Hausdorf Manifolds) comes across to me as second to none. Now, if only this could become the standard everyone uses for tensor manipulations!

These two extremely enjoyable recent reading projects are reminding me of why Geometry was such a favorite of mine as far back as my early teens.

Generally, I would describe the sum of my Mathematical achievements up to this year of 2018 as extremely modest, limited to little more than a few things like the creation a very simple set of algebraic permutation rules for solving Rubik's cube. Of course that descriptive simplicity does not translate to anywhere near a minimal number of operations, but all I was interested in was an uncomplicated enough solution I could remember. A slightly less modest example is here. The strange experience of attempting to publish this work reaffirmed my decision to abandon any formal (academic) career in Math. It was in fact so remarkably distasteful, that when the paper was in the end quite unexpectedly accepted for publication (in the long ago shuttered Journal of Algorithms), I decided to seal its (and my own) fate by pulling the submission!

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