Thursday, July 13, 2006

Annals of Lost Things: The Calculus on Manifolds Notebook

Category theory starts with the observation that many properties of mathematical systems can be unified and simplified by a presentation with diagrams of arrows.

[. . .]

The fundamental idea of representing a function by an arrow first appeared in topology about 1940, probably in papers or lectures by W. Hurewicz on relative homotopy groups.

His initiative immediately attracted the attention of R. H. Fox and N. E. Steenrod, whose [1941] paper used arrows and (implicitly) functors . . . It expressed well a central interest of topology. Thus a notation (the arrow) led to a concept (category).

Categories for the Working Mathematician (1971), Saunders Mac Lane

I live an untidy mostly confused life. Indolence marches in lock step with ignorance. At some point in my life I quit thinking of the situation as a moral failure. Now, I consider it something in my genes: a most convenient fiction.

When life becomes too chaotic because of my nature, I turn to mathematics as a way to escape. Mathematics works as a sedative for me. I will not chronicle all the mathematics books I have seriously tried to master when the going got rough. One example suffices. I have been on a lifetime crusade to solve or prove all the problems presented in Spivak’s Calculus on Manifolds. After thirty years, the work is almost done. I cannot find the notebook in which I wrote the results. I should cry if it is indeed truly lost. However, I don’t feel up to the emotional investment required for tears.

I have wondered what people might think of me if they peruse my mathematics notebooks after I am gone. Most likely they will say, he lived a most untidy and indolent life.

2 Comments:

At 7:30 PM, Blogger janus said...

One example suffices. I have been on a lifetime crusade to solve or prove all the problems presented in Spivak’s Calculus on Manifolds.

a good choice!

 
At 1:12 AM, Blogger Lynn said...

janus-

Thanks. I never expected a comment on this post.

 

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