Again motivated by a Blog of E. Derman . Frogs like digging in the details, birds flying high have the overview. What does this mean to mathematical disciplines? Birds are interesting but wrong? Frogs are correct, but the details do not make a "picture"?
When I was educated, descriptive geometry was an important topic for technical disciplines. It is about the representations of 3D objects in two dimensions (you trace rays, follow beams, ... ).
Starting at the mid 80ies we have reasonable Geometric Modelers (GM) on computers. They allow us to create and manipulate 3D objects and visualize them in great aesthetics. The software uses the lates results of geometric disciplines, including descriptive geometry, made by the geometry frogs.
Even if you just naively use a GM you can get new insights and sharpen your imagination of the most complex geometric configurations, .... All provided the algorithms are accurate and robust and do not create artefacts misleading your imaginations. And they must be fast enough to create enough variations. For the eyes of the birds.
Some say, Black-Scholes-continuous-hedging birds have a beautiful scheme, but it isn't quite right. I do not totally disagree, but what else? Those models can be extended and refined (the detail frogs find and implement). And the finance birds apply those models in all type of imaginable and real market scenarios to get insight, imaginations as decision support. But again, the foundations must be accurate, robust and fast.
This is where we, at UnRisk, are good at. And, we frogs, continuously talk to the birds.