Mathematics has a unique capacity to infuriate people, so when a world-leading scientist announced his belief that advanced math is unnecessary for the modern scientist, the response from the nerdosphere was blistering.
In the last week or so, since an excerpt of Edward O. Wilson’s new book, Letters To A Young Scientist, ran in the Wall Street Journal, the evolutionary biologist and ant expert has been criticized as “insulting,” “misinformed,” “sad,” “misguided,” “counterproductive,” “frustrating,” “flat-out wrong,” and “a disgrace.” He is “trading on fear” of math, and “uncritically accepting the idea that math is something inherently unpleasant.”
“Don’t listen to E.O. Wilson,” one mathematician wrote of the Harvard professor emeritus. “He does not understand what mathematics is.”
In the book, the two time Pulitzer Prize-winning Prof. Wilson shares what he calls a secret: that many top scientists today are mathematically merely “semiliterate,” and this is not so bad, because they can work with mathematicians as needed.
The problem — he calls it, quaintly, a “bugbear” — is that math is hard, and it scares good conceptual thinkers away from science. The over-mathematization of science squeezes out the more imaginative minds who happen to lack computational chops, causing what he calls a “hemorrhage of brain power we need to stanch.”
“During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail,” he writes in the book. “This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent.”
“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.”
Paul Krugman, the Nobel Laureate Princeton economist and New York Times columnist agreed, and in a reply to Prof. Wilson, described a major paper he wrote in which he “picked up the little [math] I needed after I had already figured out the papers.”
He coyly added that, for economists, the right amount of math to know is precisely the amount each one happens to know: “Anyone who knows less just doesn’t have the tools, anyone who knows more is excessively teched up.”
Others were less jovial.
“Without a firm foundation in mathematics, chaos can ensue,” wrote Gary Marcus and Ernest Davis, professors of psychology and computer science at New York University, in response to Prof. Wilson. “If a scientist does not understand how statistics works and instead relies on a software package, they run the risk of doing completely irrelevant computations and arriving at meaningless results.”
Science and math have always been uneasy allies, neither fighting quite the same war. Science looks for answers in the world. Math looks for them on paper or, increasingly, on a computer. Science requires evidence. Math requires proof. As Richard Feynman, one of the 20th century’s greatest physicists, put it, “Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment.”
Charles Darwin, famously, had no math and found it “repugnant,” but he lived in an age when that view was open to a scientist. That age has passed. Today, Galileo’s notion that the laws of nature are written in the language of mathematics has entranced even the social sciences, which now seek to burnish their credibility with dense equations.
“The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail.” writes Prof. Wilson, a theoretical biologist.
To address this problem, he offers his “young scientist” what he calls Wilson’s Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.”
This is a version of Thomas Edison’s line that “I can hire a mathematician but a mathematician cannot hire me,” which seems to unfairly shove mathematicians to the sidelines of scientific insight, as if they were hired hands.
This tension is not new. Logic was mathematized to great effect in the 19th century, laying the basis for computer science. Economics followed, leading to the fiscal revolutions of the 20th century.
Physics has always been more or less number heavy, even as theory surpassed powers of observation, such that today we have concepts, like string theory, that emerge from math with no hope of a real life confirmation.
‘The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail’
But by the time psychology was mathematized, in the mid 20th century, the worst problems started showing themselves, as researchers starting using computers to dredge data for any grain of significance, however illusory.
In the social sciences especially, mathematical crimes litter the record over the last few years, from faked data to conclusions not borne out by the data on which they were supposedly based, such as Diederik Stapel, a leading Dutch social psychologist who fabricated data for dozens of peer-reviewed articles, and was exposed in 2011.
“There is now enough evidence to say what many have long thought: that any claim coming from an observational study is most likely to be wrong in the sense that it will not replicate if tested rigorously,” wrote S. Stanley Young and Alan Karr of the U.S. National Institute of Statistical Sciences in a recent critique of the trend.
Now, even philosophy wants in on the numerical action, as evidenced by the sexy (for philosophy) new field of experimental philosophy, or X-Phi, in which data is sought from participants in thought experiments.
Marc Hauser, a Harvard primate psychologist who lost his job in 2011 after he fabricated data and manipulated results, also ran the Moral Sense Test, an online survey in the philosophical field of “trolleyology,” an ethical thought experiment about a runaway trolley and the various ways you could sacrifice one life for others, which would be right, and which would be wrong.
Right and wrong have traditionally been set apart by appealing to universal principles, or utilitarian benefit, or religious doctrine, or even to
evolutionary theory. But to do it based on survey results is something new and strange.
The problem for science is that the numbers are not the things, and an undue focus on mathematical structure can leave you arguing about the ideal, having lost touch with the real. Like strength and bravery, or language and love, science and math are complementary, but they have different goals.
Prof. Wilson’s title – the book is out in Canada May 8 – is a play on Letters To A Young Poet, a collection of letters by the great German lyrical poet Rainer Maria Rilke to an actual young poet, a cadet at the military academy Rilke once attended. The young scientist, on the other hand, is in Prof. Wilson’s imagination as an ideal reader, a composite student, for whom he weaves together personal anecdotes and sweeping observations about science as a human project.
The effect is not the same.
Rilke bared his soul, and shared the secrets of his craft, telling young Franz Xaver Kappus: “There is only one single way. Go into yourself.”
Though similarly revealing personally, Prof. Wilson’s advice to his young scientist is precisely the opposite, recalling his days collecting bugs with a sweep net in Alabama or Mozambique, or pulling back the bark on a log to reveal a strange society of insects.
He says to look out into the world with clear eyes, whether you fit his scientific archetypes of an explorer in virgin territory, or a questing knight in search of a Holy Grail insight, or a warrior for good against evil. This outward view is the way to divine the structure of the world, he advises, no matter how you feel about math.
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