MATHEMATICAL DESIGN

Mathematics provides an interesting reflection on some of our favorite themes; knowledge, learning, abstraction, etc. Mathematics’ principal function is to problem solve. We use math if we need to know the area of a circle, or if we want to know if we have enough money to buy a desired trinket.

The basic model of mathematics is Perception, then Abstraction, then Perception. That is to say, mathematicians start with a real world problem that can be sensorily perceived, then they apply abstract mathematical principals and formulas. At the end they are back in the real perceptual and sensorial world with new information and a new solution.

The steps of our problem solving are nearly identical to mathematics. We also start with a real world problem, then we apply the abstraction of drawing. At the end is something hopefully very real world; either an enclosure or an object.

The stereotypical way of thinking about this is that the mathematician uses tried and true formulas, whereas designers do not.

But what happens when creativity is required in mathematics? What happens when the solution cannot be derived by rote? What happens when a synthesis is required to solve the problem? Then, I submit, the creative efforts of the mathematician is very similar to that of the designer. Both of us has to think in the abstract. Yet at the same time we have to think toward solving the problem. Both of us need to maintain a perceptual base as we think. To be effective problem solvers, we both employ formal processes so as to do productive work.

We’ve been blaming a lot of things on the Greeks, and this is another one. It was the Greeks who eliminated direct visual perceptions from mathematical problem solving. They instead advocated a complete reliance on axioms and the connection of logical propositions. There was a complete separation from visual perception. And low and behold, this is the way that we still teach and therefore are taught to think.

I was heartened to see the similarities of thinking like a mathematician and thinking like a designer. It turns out we both problem solve. Who would have thought that the exalted mathematician and the lowly designer follow the same process.