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[Foundational areas of MathMap]

Foundational Branches of Mathematics

[Return to start of tour] [Up to The Divisions of Mathematics]

These areas consider the framework in which mathematics itself is carried out. To the extent that these consider particular mathematical topics, they border on other areas of the Mathematics Subject Classification; to the extent that these consider the nature of proof and of mathematical reality, they border on philosophy!

(Also shown in the map is a section 04 (Set Theory) which has been folded into section 03 with the 2000 version of the MSC.)

Considerations in logic of complexity and provability lead to topics in theoretical computer science; questions of decidability arise in a natural way in number theory and group theory. The apparent paradoxes of set theory (particularly from use of the Axiom of Choice) lead to foundational issues in topology and measure theory. An emphasis on axioms leads to the development of abstract algebra and (synthetic) geometry.

You might want to continue the tour with a trip through algebra.


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Last modified 2000/01/24 by Dave Rusin. Mail: