Pure Math Skills Have Proven Useful in My Applied Work

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Lots of pure math skills (pinning down definitions & theorems, looking for counterexamples, etc.) have proven extremely useful in my applied work.

For instance, many knowledge graph validations come down to pinning down the formal definition of some desirable mathematical property and checking for counterexamples.

One validation that I implemented tonight involved defining the following property:

“For every edge (a,b) where a is a parent topic and b is a child topic, for every course B containing b, there must exist a course A containing a such that A = B or A is an ancestor of B.”

And this is not just rigor for the sake of rigor (though I’ll admit the rule does look pretty cool when expressed purely symbolically, “∀(a,b)∈E, ∀B∋b, ∃A∋a: A≤B” where E is the set of edges) –

this validation was inspired by a bug that someone reported today, whose root cause was a single piece of invalid connectivity (one edge out of about 20,000), that was breaking the rule above. The validation caught one other invalid edge like that.

(Note: the rule is a bit simplified – in practice it’s actually a bit more complicated in that we are really only interested in violations where, additionally, some course containing the parent topic is a progeny of some course containing the child topic, i.e., there is a case of a topic edge and a course edge being strictly anti-parallel and not just skew.)

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