Wednesday, June 20, 2018
News Roundup

Why math is your friend

BERKELEY, Calif. — E.O. Wilson is an eminent Harvard biologist and best-selling author. I salute him for his accomplishments. But he could not be more wrong in his recent piece in the Wall Street Journal (adapted from his new book Letters to a Young Scientist), in which he tells aspiring scientists that they don't need mathematics to thrive. He starts out by saying: "Many of the most successful scientists in the world today are mathematically no more than semiliterate . . . I speak as an authority on this subject because I myself am an extreme case." This would have been fine if he had followed with: "But you, young scientists, don't have to be like me, so let's see if I can help you overcome your fear of math."

Alas, the octogenarian authority on social insects takes the opposite tack. Turns out he actually believes not only that the fear is justified, but that most scientists don't need math. "I got by, and so can you" is his attitude. Sadly, it's clear from the article that the reason Wilson makes these errors is that, based on his own limited experience, he does not understand what mathematics is and how it is used in science.

If mathematics were fine art, then Wilson's view of it would be that it's all about painting a fence in your backyard. Why learn how to do it yourself when you can hire someone to do it for you? But fine art isn't a painted fence, it's the paintings of the great masters. And likewise, mathematics is not about "number-crunching," as Wilson's article suggests. It's about concepts and ideas that empower us to describe reality and figure out how the world really works. Galileo famously said, "The laws of Nature are written in the language of mathematics." Mathematics represents objective knowledge, which allows us to break free of dogmas and prejudices. It is through math that we learned Earth isn't flat and that it revolves around the sun, that our universe is curved, expanding, full of dark energy, and quite possibly has more than three spatial dimensions. But since we can't really imagine curved spaces of dimension greater than two, how can we even begin a conversation about the universe without using the language of math?

Charles Darwin rightfully spoke of math endowing us "with something like a new sense." History teaches that mathematical ideas that looked abstract and esoteric yesterday led to spectacular scientific advances of today. Scientific progress would be diminished if young scientists were to heed Wilson's advice.

It is interesting to note that Wilson's recent article in Nature and his book claiming to show support for so-called group selection have been sharply criticized, by Richard Dawkins and many others. Some of the critics pointed out that one source of error was in Wilson's math. Since I'm not an expert in evolutionary theory, I can't offer an opinion, but I find this controversy interesting given Wilson's thesis that "great scientists don't need math."

One thing should be clear: While our perception of the physical world can always be distorted, our perception of the mathematical truths can't be. They are objective, persistent, necessary truths. A mathematical formula means the same thing to anyone anywhere - no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand year from now. And that's why mathematics is going to play an increasingly important role in science and technology.

One of the key functions of mathematics is the ordering of information. With the advent of 3-D printing and other new technology, the reality we are used to is undergoing a radical transformation: Everything will migrate from the layer of physical reality to the layer of information and data. We will soon be able to convert information into matter on demand by using 3-D printers just as easily as we now convert a PDF file into a book or an MP3 file into a piece of music. In this brave new world, math will be king: It will be used to organize and order information and facilitate the conversion of information into matter.

It might still be possible to be "bad in math" (though I believe that anyone can be good at math if it is explained in the right way) and be a good scientist - in some areas and probably not for too long. But this is a handicap and nothing to be proud of. Granted, some areas of science currently use less math than others. But then practitioners in those fields stand to benefit even more from learning mathematics.

It would be fine if Wilson restricted the article to his personal experience, a career path that is obsolete for a modern student of biology. We could then discuss the real question, which is how to improve our math education and to eradicate the fear of mathematics that he is talking about. Instead, trading on that fear, Wilson gives a misinformed advice to the next generation, and in particular to future scientists, to eschew mathematics. This is not just misguided and counterproductive; coming from a leading scientist like him, it is a disgrace. Don't follow this advice - it's a self-extinguishing strategy.

Edward Frenkel is professor of mathematics at the University of California at Berkeley. His book "Love and Math: The Heart of All Things" will be published in October.

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