Opinion
Two Views: How Much Everyone sometimes daydreams like a scientist. Ramped
up and disciplined, fantasies are the fountainhead of all
creative thinking. Newton dreamed, Darwin dreamed, you
Math Do Scientists dream. The images evoked are at first vague. They may
shift in form and fade in and out. They grow a bit firmer
Need? 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
On April 5, 2013, The Wall Street Journal published an essay
extracting ideas from pure mathematics. Most of the
by the Harvard biologist E. O. Wilson, “Great Scientist ≠
stereotypical photographs of scientists studying rows
Good at Math”. Berkeley mathematician Edward Frenkel
of equations on a blackboard are instructors explaining
responded to it in Slate on April 9, 2013. We reprint the
discoveries already made. Real progress comes in the
two essays below, with permission from The Wall Street
field writing notes, at the office amid a litter of doodled
Journal and Slate. paper, in the hallway struggling to explain something to
a friend, or eating lunch alone. Eureka moments require
Great Scientist ≠ Good at Math hard work. And focus.
Ideas in science emerge most readily when some part
E. O. Wilson Shares a Secret: Discoveries Emerge
of the world is studied for its own sake. They follow from
from Ideas, Not Number-Crunching
thorough, well-organized knowledge of all that is known or
For many young people who aspire to be scientists, the can be imagined of real entities and processes within that
great bugbear is mathematics. Without advanced math, fragment of existence. When something new is encoun-
how can you do serious work in the sciences? Well, I have tered, the follow-up steps usually require mathematical
a professional secret to share: Many of the most successful and statistical methods to move the analysis forward. If
scientists in the world today are mathematically no more that step proves too technically difficult for the person
than semiliterate. who made the discovery, a mathematician or statistician
During my decades of teaching biology at Harvard, I can be added as a collaborator.
watched sadly as bright undergraduates turned away from In the late 1970s, I sat down with the mathematical
the possibility of a scientific career, fearing that, without theorist George Oster to work out the principles of caste
strong math skills, they would fail. This mistaken assump- and the division of labor in the social insects. I supplied
the details of what had been discovered in nature and the
tion has deprived science of an immeasurable amount of
lab, and he used theorems and hypotheses from his tool
sorely needed talent. It has created a hemorrhage of brain
kit to capture these phenomena. Without such informa-
power we need to stanch.
tion, Mr. Oster might have developed a general theory, but
I speak as an authority on this subject because I myself
he would not have had any way to deduce which of the
am an extreme case. Having spent my precollege years in
possible permutations actually exist on earth.
relatively poor Southern schools, I didn’t take algebra until Over the years, I have co-written many papers with
my freshman year at the University of Alabama. I finally mathematicians and statisticians, so I can offer the fol-
got around to calculus as a thirty-two-year-old tenured lowing principle with confidence. Call it Wilson’s Principle
professor at Harvard, where I sat uncomfortably in classes No. 1: It is far easier for scientists to acquire needed col-
with undergraduate students only a bit more than half laboration from mathematicians and statisticians than it
my age. A couple of them were students in a course on is for mathematicians and statisticians to find scientists
evolutionary biology I was teaching. I swallowed my pride able to make use of their equations.
and learned calculus. This imbalance is especially the case in biology, where
I was never more than a C student while catching up, factors in a real-life phenomenon are often misunderstood
but I was reassured by the discovery that superior math- or never noticed in the first place. The annals of theoretical
ematical ability is similar to fluency in foreign languages. biology are clogged with mathematical models that either
I might have become fluent with more effort and sessions can be safely ignored or, when tested, fail. Possibly no
talking with the natives, but being swept up with field and more than 10 percent have any lasting value. Only those
laboratory research, I advanced only by a small amount. linked solidly to knowledge of real living systems have
Fortunately, exceptional mathematical fluency is re- much chance of being used.
quired in only a few disciplines, such as particle physics, If your level of mathematical competence is low, plan to
astrophysics and information theory. Far more important raise it, but meanwhile, know that you can do outstanding
throughout the rest of science is the ability to form con- scientific work with what you have. Think twice, though,
cepts, during which the researcher conjures images and about specializing in fields that require a close alternation
processes by intuition. of experiment and quantitative analysis. These include
most of physics and chemistry, as well as a few specialties
in molecular biology.
DOI: http://dx.doi.org/10.1090/noti1032
August 2013 Notices of the AMS 837
Opinion
Newton invented calculus in order to give substance begin a conversation about the universe without using the
to his imagination. Darwin had little or no mathemati- language of math?
cal ability, but with the masses of information he had Charles Darwin rightfully spoke of math endowing us
accumulated, he was able to conceive a process to which “with something like a new sense.” History teaches that
mathematics was later applied. mathematical ideas that looked abstract and esoteric
For aspiring scientists, a key first step is to find a sub- yesterday led to spectacular scientific advances of today.
ject that interests them deeply and focus on it. In doing Scientific progress would be diminished if young scientists
so, they should keep in mind Wilson’s Principle No. 2: For were to heed Wilson’s advice.
every scientist, there exists a discipline for which his or It is interesting to note that Wilson’s recent article in
her level of mathematical competence is enough to achieve Nature and his book claiming to show support for so-
excellence. called group selection have been sharply criticized, by
—E. O. Wilson Richard Dawkins and many others. Some of the critics
Harvard University, Emeritus pointed out that one source of error was in Wilson’s math.
ewilson@oeb.harvard.edu Since I’m not an expert in evolutionary theory, I can’t offer
an opinion, but I find this controversy interesting given
(Reprinted with permission from The Wall Street Journal) 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
Don’t Listen to E. O. Wilson of the mathematical truths can’t be. They are objective,
persistent, necessary truths. A mathematical formula
Math Can Help You in Almost Any Career. There’s means the same thing to anyone anywhere—no matter
No Reason to Fear It what gender, religion, or skin color; it will mean the same
thing to anyone a thousand years from now. And that’s
E. O. Wilson is an eminent Harvard biologist and best-
why mathematics is going to play an increasingly impor-
selling author. I salute him for his accomplishments.
tant role in science and technology.
But he couldn’t be more wrong in his recent piece in The
One of the key functions of mathematics is the ordering
Wall Street Journal (adapted from his new book Letters of information. With the advent of the 3-D printing and
to a Young Scientist), in which he tells aspiring scientists other new technology, the reality we are used to is under-
that they don’t need mathematics to thrive. He starts going a radical transformation: Everything will migrate
out by saying: “Many of the most successful scientists in from the layer of physical reality to the layer of informa-
the world today are mathematically no more than semi- tion and data. We will soon be able to convert information
literate … I speak as an authority on this subject because into matter on demand by using 3-D printers just as easily
I myself am an extreme case.” This would have been fine as we now convert a PDF file into a book or an MP3 file
if he had followed with: “But you, young scientists, don’t into a piece of music. In this brave new world, math will
have to be like me, so let’s see if I can help you overcome be king: It will be used to organize and order information
your fear of math.” Alas, the octogenarian authority on and facilitate the conversion of information into matter.
social insects takes the opposite tack. Turns out he actu- It might still be possible to be “bad in math” (though I
ally believes not only that the fear is justified, but that believe that anyone can be good at math if it is explained
most scientists don’t need math. “I got by, and so can in the right way) and be a good scientist—in some areas
you” is his attitude. Sadly, it’s clear from the article that and probably not for too long. But this is a handicap and
the reason Wilson makes these errors is that, based on nothing to be proud of. Granted, some areas of science
his own limited experience, he does not understand what currently use less math than others. But then practitioners
mathematics is and how it is used in science. in those fields stand to benefit even more from learning
If mathematics were fine art, then Wilson’s view of mathematics.
it would be that it’s all about painting a fence in your It would be fine if Wilson restricted the article to his
backyard. Why learn how to do it yourself when you can personal experience, a career path that is obsolete for a
hire someone to do it for you? But fine art isn’t a painted modern student of biology. We could then discuss the
fence, it’s the paintings of the great masters. And likewise, real question, which is how to improve our math educa-
mathematics is not about “number-crunching”, as Wilson’s tion and to eradicate the fear of mathematics that he is
article suggests. It’s about concepts and ideas that em- talking about. Instead, trading on that fear, Wilson gives
power us to describe reality and figure out how the world a misinformed advice to the next generation, and in par-
really works. Galileo famously said, “The laws of Nature ticular to future scientists, to eschew mathematics. This is
are written in the language of mathematics.” Mathematics not just misguided and counterproductive; coming from
represents objective knowledge, which allows us to break a leading scientist like him, it is a disgrace. Don’t follow
free of dogmas and prejudices. It is through math that this advice—it’s a self-extinguishing strategy.
we learned Earth isn’t flat and that it revolves around the —Edward Frenkel
sun, that our universe is curved, expanding, full of dark University of California at Berkeley
energy, and quite possibly has more than three spatial frenkel@math.berkeley.edu
dimensions. But since we can’t really imagine curved
spaces of dimension greater than two, how can we even (Reprinted with permission from Slate)
838 Notices of the AMS Volume 60, Number 7
