23rd April 2008, 2 min read

Rigor or relevance: choose one

Back when I was a Mathematics undergraduate student at the University of Toronto, I was told by some of my peers that I was not a Mathematician but a problem solver. This was meant as a derogatory remark, but I thought it was a correct assessment. In short, I cared only about a given theorem if it allowed me to solve some interesting problems. I was not interested in Mathematics for its own sake. Rigor was not enough, I wanted relevance.

A given scientific or mathematical results has two properties: rigor and relevance. You usually can have one, or the other, but not both.

Engineers and technologists are good at determining relevance. They will discard quickly results that they do not need. The average software engineer is unable to prove that his program is correct. Even when rigor is important, such as when designing medical gear, the engineer is often not interested in proving the optimality of the techniques being used. By sacrificing some rigor, the engineer is able to innovate: if he had to prove every detail, he could never get work done. Scientists make a business out of correctness. To ensure rigor and depth simultaneously, scientists stay close to the shore. Most scientists specialize in a narrow niche and take months to study what might be considered to be a minor point. This same minor point will get revisited by others. Their work tend to be very incremental. However, scientists are bad at being critical of the revelance of their own work. Indeed, if they did question their work too often, they may need to change topic too often which would reduce considerably their productivity. This explains why we end up with fields such as String theory or classical AI. Notice that you cannot measure relevance by the number citations from people in your field. In fact, the relevance of one’s research is usually never formally measured.

You would think that being critical would be a good thing in science, no? Alas, no. As an experiment, try to go to the next conference in your field and ask your peers whether what you are doing is relevant. It is a good recipe to become unpopular.

References:

Aubrey D.N.J. de Grey, Curiosity Is Addictive, and This Is Not an Entirely Good Thing, Rejuvenation Research. February 1, 2008, 11(1): 1-3. Dijkstra’s second rule for successful scientific research: “We all like our work to be socially relevant and scientifically sound. If we can find a topic satisfying both desires, we are lucky; if the two targets are in conflict with each other, let the requirement of scientific soundness prevail.”