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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