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Topic: Matheology § 218
Replies: 2   Last Post: Feb 13, 2013 10:46 AM

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Posts: 18,076
Registered: 1/29/05
Matheology § 218
Posted: Feb 12, 2013 3:36 AM
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Matheology § 218

What is Mathematics? Most mathematicians don't know and don't care.
Mathematics is what mathematicians do. [...] In fifty years (at most)
human mathematicians will be like lamp-lighters and ice-delivery men.
All serious math will be done by computers. Let's hope that human
philosophy will still survive, but we need to adjust naturalism to the
practice of math in the future and to the way it will be done by
machines. Of course, we don't know exactly how, so let's put this
project of Naturalist mathematical philosophy on hold and wait to see
how things turn out in fifty years.

Tim Gowers said that we are all formalists, but most of us don't know
it (and if we knew, we wouldn't care). I kind of agree, but this is
only a corollary of a more profound truth: Everything is
Combinatorics. Classify Lie Algebras? It is just root systems and
Dynkin Diagrams. Finite Groups? The Monster is a Combinatorial Design.
Even when it is not obviously combinatorics, it could be made so. If
it is too hard for us, then we need a computer! But computer science
is all Discrete Math, alias combinatorics. In a way Logic is too. But
Logic is so low-level, like machine language. It is much more fun and
gratifying to work in Maple, and do higher-level combinatorics.

I am also a trivialist. [...] We humans, and even our computers, can
only prove trivial results. Since all knowable math is ipso facto
trivial, why bother? So only do fun problems, that you really enjoy
doing. It would be a shame to waste our short lives doing "important"
math, since whatever you can do, would be done, very soon (if not
already) faster and better (and more elegantly!) by computers. So we
may just as well enjoy our humble trivial work.

[Doron Zeilberger: "Opinion 69: Roll Over Platonism, Logicisim,
Formalism, Intuitionism, Constructivism, Naturalism and Humanism! Here
Comes Combinatorialism and Trivialism." (2005)]

Regards, WM

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