

On proof and progress in mathematics - mreid
http://arxiv.org/abs/math/9404236

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gchpaco
"But to people not already familiar with what’s going on the same patterns are
not very illuminating; they are often even misleading. The language is not
alive except to those who use it." struck me as significant, and "The standard
of correctness and completeness necessary to get a computer program to work at
all is a couple of orders of magnitude higher than the mathematical
community’s standard of valid proofs." is the closest I've ever seen to
someone stating the one of the most important differences there.

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jrp
I would like to see more accessible exposition of modern mathematics to the
interested public. There seem to be two opposing forces - assuming more
prerequisites lets you talk more easily and go into more depth, but cuts your
target market very quickly. Is this an inevitable dilemma?

~~~
gchpaco
The problem is the devil is invariably in the details. It is almost impossible
to say something useful about category theory starting from even a modern
undergraduate mathematics education in less than about a week, because you
need to talk about definitions and utility lemmas before that (and category
theory is so abstract it's hard to develop an intuition for it). A lot of
stuff like topology is more approachable but it's a lot like popularizing the
climate research, although less politically loaded; the real theory is much
more _nuanced_ than any simple description could be.

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cma
If you are interested in this topic and you haven't already done so, check out
"The Mathematical Experience"

[http://www.amazon.com/Mathematical-Experience-Phillip-J-
Davi...](http://www.amazon.com/Mathematical-Experience-Phillip-J-
Davis/dp/0395929687)

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jrp
By the way, the author is William Thurston, a renowned mathematician and
Fields medalist.

