The natural structure of mathematics

[DavidLaPierre]

As I understand it, mathematics is a study that is founded on the principles of logic and set theory and branches out into specialized fields. I was just wondering about what that structure would look like. It seems like there might be significantly different ways to do this since there is often more that one way to prove something. How do you see this?
Here's a rough idea of what I mean. This isn't meant to be complete, and definitely isn't totally accurate. But, it's 5 am here and I need to get some sleep
Thanks for the input everyone.


I. Fundamentals
a. Logic
b. Set Theory
II. Arithmetic
a. Addition
b. Subtraction
c. Multiplication
d. Division
e. Exponentiation
III. Numbers
a. Integers & Number Theory
b. Rational Numbers
c. Irrational Numbers
d. Transcendent Numbers
e. Imaginary Numbers
f. Complex Numbers
IV. Geometry & Trigonometry
a. Two Dimension
i. Flat Space
ii. Curved Space
b. Higher Dimensions
V. Calculus
a. Differentiation
b. Integration

[DavidLaPierre]

I wish I could edit that list, it doesn't show the structure well. Anyone know how I could do that? Even if I can't fix this post, it would be good for the future.
Roman numerals are primary sections
Letters are 2nd level sections
i tally's are 3rd level sections

[The Chaz]

I wish I could edit that list, it doesn't show the structure well. Anyone know how I could do that? Even if I can't fix this post, it would be good for the future.
Roman numerals are primary sections
Letters are 2nd level sections
i tally's are 3rd level sections

You earn the option to edit after a certain number of posts. In the meantime, just create a post that is exactly what you want, and message a moderator to delete all the other posts!

[CRGreathouse]

I think that the natural structure would be a DAG, not a list.