Tuesday, April 09, 2013

Battle of the Eds

One of the scientists I most admire, Edward O. Wilson, recently wrote an article in the WSJarguing that you don't need much math to be a scientist - even a great scientist. He doesn't admit knowing much himself, but he did learn some calculus as a tenured Professor.

Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.

Everyone sometimes daydreams like a scientist. Ramped up and disciplined, fantasies are the fountainhead of all creative thinking. Newton dreamed, Darwin dreamed, you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.

Pioneers in science only rarely make discoveries by extracting ideas from pure mathematics. Most of the stereotypical photographs of scientists studying rows of equations on a blackboard are instructors explaining discoveries already made. Real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone. Eureka moments require hard work. And focus.

Mathematician Edward Frenkel disagrees. He thinks that Wilson is a relic of a bygone age, whose ideas are no longer relevant. Paul Krugman takes a somewhat middle ground, arguing that you need some math, probably arithmetic and calculus, but is a bit suspicious of the need for more. I've been an applied physicist and engineer for a while, and I like math for it's own sake, but I can't remember many non-academic applications where I've needed anything beyond differential equations. Every once in a while I think some differential geometry might help, but it hardly ever does (help me, that is).

I have to think, though, that someday biologists are going to find abstract algebra pretty useful.