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bananas

(27,509 posts)
Wed May 29, 2013, 08:21 PM May 2013

One of the most abstract fields in math finds application in the 'real' world

http://www.sciencenews.org/view/generic/id/350567/description/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world

One of the most abstract fields in math finds application in the 'real' world

By Julie Rehmeyer
Web edition: May 20, 2013

Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research is an art form like, say, Olympic gymnastics (with a much smaller audience); or a stammered response that so much of pure math has ended up finding application that maybe, perhaps, someday, it will turn out to be useful.

That last possibility is now proving itself to be dramatically true in the case of category theory, perhaps the most abstract area in all of mathematics. Where math is an abstraction of the real world, category theory is an abstraction of mathematics: It describes the architectural structure of any mathematical field, independent of the specific kind of mathematical object being considered. Yet somehow, what is in a sense the purest of all pure math is now being used to describe areas throughout the sciences and beyond, in computer science, quantum physics, biology, music, linguistics and philosophy.

<snip>

David Spivak of MIT has perhaps the boldest vision for category theory’s potential. In a paper posted February 27 on arXiv.org, he argues that all scientific thought can be expressed in a structured way using category theory. Both ideas and the data supporting them can be encoded in the universal language of category theory, allowing scientists to present a database with their full work. Spivak even imagines a Facebook-like interface with people’s full thoughts and experiences presented in a category theoretic database that would connect people whose databases overlap.

<snip>


Via http://golem.ph.utexas.edu/category/2013/05/in_the_news.html

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One of the most abstract fields in math finds application in the 'real' world (Original Post) bananas May 2013 OP
I have FAR too much experience with category theory. Lucky Luciano May 2013 #1

Lucky Luciano

(11,242 posts)
1. I have FAR too much experience with category theory.
Wed May 29, 2013, 10:46 PM
May 2013

Too many commuting diagrams! Though, that is really the beauty of it. It is like meta-math. Then people go too far and talk about the category of categories with the functoes being the morphisms between categories.

I promptly sold out to the highest bidder and learned to program and do applied math. A pure math person needs to take an oath of poverty.

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