On Math
The greatest difficulty in addressing a new problem is figuring out the right questions to ask. Mathematics is useful because it reduces complicated phenomena to their fundamental components, or what we call abstraction. For me, mathematics and abstraction are the language and the tools with which we ask meaningful, empowering questions.
On Computers
Adults check carefully before crossing the street because we have all at some point interacted with a belligerent driver. We remind children to look both ways before stepping into traffic not because they are stupid, but because they lack our experiences. Real world phenomena are rife with easy to make assumptions not borne out in practice. Facing a poorly understand phenomenon alone, we use our best judgement in much the same way a child wanders blindly into a busy street. Computers bridge a computational, rather than intellectual, gap. Properly leveraged, modern computing power empowers us to play out scenarios via simulations, visualize complex data structures such that salient features are immediately clear, and automate mundance processes to focus human brains on what truly matters.
On Understanding
Somwhere between the purely concrete and abstract is where I strive to work. Specificity and examples provide motivation and guide reseach and discovery. Whereas pure abstraction can be fun and beautiful on its own, a moderate level of abstraction generalizes beyond what has been observed to what may be observed, allowing us to make confident, testable predictions about the as yet unobserved.