abstractmath.org 2.0
help with abstract math

Produced by Charles Wells     Revised 2017-04-13

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In mathematics you don’t understand things, you just get used to them. –John von Neumann

This page is intended to raise your consciousness about the many ways there are to understand “understand” in math. A link to each chapter about understanding math is given here with some comments about the ideas expressed in it.


Math objects

Math Structures

A mathematical structure is a special kind of math object defined as a set with some associated objects called structure.  Equivalence relations, partitions, groups and topological spaces are examples of mathematical structures.

Representations and models

“Representation” and “model” have several related meanings.

Images and metaphors

As these examples illustrate, we think about math objects in terms of images and metaphors that we have developed out of our experience with them.  These are valuable insights but they generally cannot be used to prove theorems about them.

There is a way of thinking about any math object that helps when you are trying to prove something: the rigorous view of math objects, also discussed in this chapter.

Conceptual and Computational

When mathematicians consider a math object they are typically interested in two different aspects of the object:

Proofs can have a conceptual side and a computational side too.

Other aspects of understanding math

This catch-all chapter talks about several special phenomena that are involved in understanding math.

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