Can maths be mapped?

Question

I always thought that we can imagine mathematics as a structure that was based on an unique principle and that we can see algebra, geometry, ... emerging when we're adding axioms to the first one.

In this way, all the mathematics could be represented in a large map. Someone could say how a theory and its axioms are distant from the first principle and how it relies to other theories.

Is my conception of maths wrong ? If not, what would be the founding principles ?

I would give anything to see such a diagram.

Sure. http://stacks.math.columbia.edu does some of this. Example dependency graph. — Patrick Stevens, Sep 02 '17 at 10:04
It seems that they "only" graph a few chapters. Is there anything similar graphing the maths from the beginning ? The first principles' question remains. — tripth, Sep 02 '17 at 10:21
I think that all mathematicians would agree that it is vain to think that mathematics proceed from a unique principle. — Jean Marie, Sep 02 '17 at 10:35
That's an awful answer ... How mathematics relate to each other if we can't think about them as a tree structure ? — tripth, Sep 02 '17 at 11:02

score 1 · Answer 1 · answered Sep 02 '17 at 11:17

1

The Metamath project seems like it might be part of what you're looking for; you might also be interested in a map of mathematics developed by Redditors in response to another such map which they found lacking.

answered Sep 02 '17 at 11:17

Alexis

371

The metamath project is an interesting one. I will read some books on the subject, dig the link you sent and come back with new questions. – tripth Sep 02 '17 at 16:45

Can maths be mapped?

1 Answers1