# Mathematics Isa Big Messy Graph

Thinking of LifeIsaBigMessyGraph and EveryLanguageFixesSomething, it seems also Mathematics is too. If one were to draw links representing dependencies between definitions/axioms theorems and subsequent theorems for various BranchesOfMathematics?, would there be a common pattern/structure? I don't think they would be Lattices as there would not be a sup and inf but it is interesting to imagine. I was going to make a VisualTour of some of the interlinked mathematical definitions on Wiki as an example but it is not working so here is a more concrete one:

For instance take a few SetTheory definitions:

def1:A intersect B = {x:x elem A and x elem B}

def2:A union B = {x:x elem A or x elem B}

def3:A subset B -> (x elem A -> x elem B)

def4:A = B <-> A subset B and B subset A

thm1:A intersect (B union C) = (A intersect C) union (A intersect C)

thm2:(A intersect B) subset A subset (A union B)

thm3:(A subset B) <-> (A intersect B) = A

The proofs of these example theorems have the dependencies (as a DirectedGraph):

{(def1,thm1),(def2,thm1),(def1,thm2),(def2,thm2),(def3,thm2),(def1,thm4),(def2,thm4),(thm3,thm4),(def4,thm4)}

Perhaps the graph could be made less messy by only showing links from the previous level, ie if

a -> b -> c and also a ->c don't show a -> c. Perhaps this would aid memorization for TheoremProving and reduce the perception that MathIsHard.

Buddy, if you think the above has any chance of reducing the perception that MathIsHard, you need to get out and socialize more!

You mean like so: ? (BrokenImage)

For some of us here, I suppose that is as close as we come to "socialize" :-)
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