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Topic: The Taxonomy of Mathematics
Replies: 7   Last Post: Sep 7, 1999 10:53 PM

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Peter Percival

Posts: 95
Registered: 12/8/04
Re: The Taxonomy of Mathematics
Posted: Sep 5, 1999 7:45 PM
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Paul M. Johnson wrote:

> <snip>

> But however this may work as a classification, it isn't the structure
> that I'm looking for. Foundations (math. logic, set theory, etc.)
> couldn't possibly be a branch at the same level as these others. And a
> branch couldn't be a conjunction for another thing. And, in general,
> there is no saying from this just why this division should be
> exhaustive.
> <snip>

> This is really an old-fashioned project. I had assumed that there must
> have been some systematizers who had worked on this, even if one had to
> go back a bit in time to find them.


Yes, I wouldn't be surprised if the ancients did classify maths in the way
you seek. But there is a danger that an old classification will not take
into account recent work. The idea that "math. logic, set theory, etc." to
quote you, provides a foundation for all of mathematics is as recent as the
late nineteenth/early twentieth century. More recently still category
theory has been proposed as a foundation for (or an encompassing of) "all"
mathematics. If you do find or produce the classification you are looking
for do let us know.

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