I think the greatest link is aesthetic, the instinct for power and simplicity. Mathematics and programming are both the creation of weightless structures that

I think the greatest link is aesthetic, the instinct for power and simplicity. Mathematics and programming are both the creation of weightless structures that are limited only by their tractability by human intellect. Of course that perspective ignores two important things: physical constraints on performance, and the relationship of data to facts in the real world. From these constraints programming also takes on the characteristics of natural science and engineering. These considerations come into play as well, but so often the limiting resource is human time and intellectual bandwidth, requiring a simpler, easier solution. In mathematics, the scale can be much grander than anything yet produced in computing. Calculus is just breathtaking -- the signature accomplishment of the greatest mathematicians of their time, refined over hundreds of years into a tool that can be wielded by ordinary teenagers. It might seem shallow to compare such a sweeping achievement to mundane programming tasks such as writing enterprise business logic. Yet, if you ignore scale and universality, the intellectual task is the same: to take something that requires careful thought and close familiarity with the product requirements today, and boil it down to something that can be understand at a glance six months from now by someone who was not involved in the initial development. To distill patterns of thought internalized via close familiarity with the motivating problems into easily defined and digested concepts.