Communicating Mathematics to the Public

Michael Schrage

MIT Media Lab/Sloan School; Columnist, Los Angeles Times

Three statisticians go rabbit hunting. They spot a rabbit. The first statistician shoots—and misses the rabbit's head by 12 inches. So the second statistician takes aim and fires—and misses the rabbit's tail by a foot. The third statistician immediately cries out, "We got 'em!"

Here's another. How about that Sydney Harris cartoon of two besmocked scientists—mathematicians?—looking at a blackboard smeared with a notational riot of Greek letters and equations. In one frame, the two look deathly somber; in the next, they're having a terrific laugh.

These two bits of "math humor" neatly define the pop culture stereotype of mathematics and mathematicians. On the one hand, mathematicians are idiosyncratically precise—but not, alas, inherently connected to the realities of everyday life. On the other, they're breathtakingly obscure and complex—so obscure and complex that only real insiders can get the joke.

Unfair? Unfunny? Humor, relevance, and elegance are all in the mind of the beholder, of course. In the mass marketplace of ideas, however, mathematicians have very little to do with how people perceive the humor, the relevance, or the elegance of mathematics. The public context of mathematics—particularly sophisticated mathematics—is awkward and ill defined. Even worse, much of the public holds what might charitably be described as a "passive-aggressive" attitude toward mathematics. People—especially those liberal arts grads who managed to escape from university without taking a single math class—warily respect what they don't understand even as they quietly resent the impenetrability of the numbers. Mathematics as mathematicians see it is not seen as part of America's culture—pop or otherwise.

This is not a healthy situation. This is a bad situation. In short order, it could become a crisis situation. Already, the culture of mathematics has devolved into subcultures of mathematicians. Within a generation, the mathematics community could splinter into a collection of cults—arrogant, brilliant, self-righteous, and effectively divorced from mainstream issues, empathy, and support. At a time when a major research university declares its desire to jettison its graduate mathematics department, at a time when a math professor cum math popularizer writes a New York Times op-ed piece asserting that the roots of the suspected Unabomber's madness might be found in the fact that he was a mathematician, there should be no question that even the mathematics community is now asking itself how it should be perceived by America's mainstream media and institutions.

This essay—and this is more an impressionistic essay than hard analysis—is an effort to identify key public perception issues facing the mathematical sciences community and to offer some tentative approaches to dealing with them. This is written from the perspective of someone (emphatically not a mathematician!) who is intimately familiar with how both the mass media and the elite media cover science and technology. Some of the generalizations may seem more rhetorical than empirical, but their purpose here is to evoke—and provoke—useful discussion on how mathematics is perceived by its relevant publics. The accent should be on the word useful. The goal is to identify how the mathematics community can influence both its public policy and public perception agendas.



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Communicating Mathematics to the Public Michael Schrage MIT Media Lab/Sloan School; Columnist, Los Angeles Times Three statisticians go rabbit hunting. They spot a rabbit. The first statistician shoots—and misses the rabbit's head by 12 inches. So the second statistician takes aim and fires—and misses the rabbit's tail by a foot. The third statistician immediately cries out, "We got 'em!" Here's another. How about that Sydney Harris cartoon of two besmocked scientists—mathematicians?—looking at a blackboard smeared with a notational riot of Greek letters and equations. In one frame, the two look deathly somber; in the next, they're having a terrific laugh. These two bits of "math humor" neatly define the pop culture stereotype of mathematics and mathematicians. On the one hand, mathematicians are idiosyncratically precise—but not, alas, inherently connected to the realities of everyday life. On the other, they're breathtakingly obscure and complex—so obscure and complex that only real insiders can get the joke. Unfair? Unfunny? Humor, relevance, and elegance are all in the mind of the beholder, of course. In the mass marketplace of ideas, however, mathematicians have very little to do with how people perceive the humor, the relevance, or the elegance of mathematics. The public context of mathematics—particularly sophisticated mathematics—is awkward and ill defined. Even worse, much of the public holds what might charitably be described as a "passive-aggressive" attitude toward mathematics. People—especially those liberal arts grads who managed to escape from university without taking a single math class—warily respect what they don't understand even as they quietly resent the impenetrability of the numbers. Mathematics as mathematicians see it is not seen as part of America's culture—pop or otherwise. This is not a healthy situation. This is a bad situation. In short order, it could become a crisis situation. Already, the culture of mathematics has devolved into subcultures of mathematicians. Within a generation, the mathematics community could splinter into a collection of cults—arrogant, brilliant, self-righteous, and effectively divorced from mainstream issues, empathy, and support. At a time when a major research university declares its desire to jettison its graduate mathematics department, at a time when a math professor cum math popularizer writes a New York Times op-ed piece asserting that the roots of the suspected Unabomber's madness might be found in the fact that he was a mathematician, there should be no question that even the mathematics community is now asking itself how it should be perceived by America's mainstream media and institutions. This essay—and this is more an impressionistic essay than hard analysis—is an effort to identify key public perception issues facing the mathematical sciences community and to offer some tentative approaches to dealing with them. This is written from the perspective of someone (emphatically not a mathematician!) who is intimately familiar with how both the mass media and the elite media cover science and technology. Some of the generalizations may seem more rhetorical than empirical, but their purpose here is to evoke—and provoke—useful discussion on how mathematics is perceived by its relevant publics. The accent should be on the word useful. The goal is to identify how the mathematics community can influence both its public policy and public perception agendas.

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While it is undeniably true that many of the math community's problems are self-inflicted, it is equally true that much of the difficulty lies in the nature of mathematics. Mathematics is hard. People are intimidated by the complexities, thought processes, rigor, and unforgiving precision that mathematics demands. For the overwhelming majority, math is not a subject that lets you be an autodidact. To make matters even worse, mathematics remains one of the most poorly taught subjects in both K-12 and university education. Indeed, the nature of mathematics is such that one can have superb teachers for five or six consecutive years—but that one poor teaching experience can effectively undermine both the interest and the ability to further pursue the subject. Efforts to reform the math curricula have invariably led to disappointment. The practice in many schools of singling out the mathematically gifted and putting them in accelerated classes or special programs further underscores that math is the province of a quantitative elite rather than a discipline that should be relevant and accessible to the mainstream. Even those who perform well in mathematics do not necessarily like the subject; and people who perform at average or below-average levels tend to dislike and avoid it. Indeed, it is shocking how few public high schools and universities have instituted anything beyond minimal competency requirements in mathematics for their nonscience students to graduate. While virtually everyone in the educational establishment acknowledges the ''importance" of mathematics, there remains absolutely no agreement about how that importance should be mapped onto a curriculum. Even if there were consensus, do the schools even have the teachers who could effectively communicate that? That said, the ideal of a "mathematically literate" public becomes completely ridiculous. The pursuit of a mathematically literate population is doomed to be a dead end and a waste of time. Yes, there is no consensus as to what constitutes mathematics literacy. But, more importantly, even if some sort of realistic criteria for math literacy were defined and the resources were magically there, just how long would it take to achieve it? Just how much would today's math-indifferent population care about their degree of math literacy? Indeed, even if the population were not indifferent, just how long would it take to acquire the skills and knowledge to become literate? The harsh reality is that the educational foundation for mathematical literacy is just not there. So the challenge becomes what to do when appropriate literacy is neither possible nor practical. To further complicate the challenge, the mathematics community has grievously wounded itself by alienating the very communities that should be its natural allies. One Stanford engineering professor recalls, with incredulity and annoyance, taking a grad math class at the California Institute of Technology because his math friends said that the professor was tops in the field. The engineer did poorly in the class because his proofs weren't deemed "elegant" enough by the math professor. To this day, he speaks of the episode with a mix of bitterness and annoyance. Indeed, many science and technology students who reside two full standard deviations above the popular norm in math skills and knowledge speak resentfully of their math education in university. They feel as if they are treated as stupid general contractors and handymen by the mathematics architects—as people who are competent enough to build, but not gifted enough to appreciate, the "true" value of mathematics. Consequently, even people who inherently appreciate the importance of mathematics as a discipline are less than enamored of the mathematics community as its guardian—they learned in

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spite of, rather than because of, the math department. Indeed, the past 20 years have seen engineering departments and computer science departments gradually take over the quantitative training of their graduates with only minimal participation by mathematicians. Thus, math departments are being dis-intermediated by the very constituencies that should be looking to them for guidance and insight into the future of computation and analysis. The essential point is that mathematics may be an extraordinarily powerful and important intellectual discipline, tool, and adventure, but the mathematical community is not seen as particularly powerful or important in helping others acquire or appreciate math as a discipline, tool, and adventure. G.H. Hardy's A Mathematician's Apology is a sobering reminder of a key paradox—too often, mathematicians with enormous influence outside their field choose to dismiss their influence in favor of a focus on their own work. They treat "relevance" more as a disease than a virtue. All this is written to create the context for what follows: mathematics doesn't just have a public relations and/or communications problem—it has real problems. Those real problems are faithfully reflected in its poor public relations and dysfunctional communications. Any meaningful discussion about how to improve the quality of communications and dialogue between the mathematics community and the rest of the world must begin there. With the exception of stories like the four-color problem or Fermat's last theorem, mathematics generally receives practically no useful coverage in either the scientific or the popular press. Of course, stories like Fermat's last theorem are more about the artifact of the problem and the unique tale underlying it than any intrinsic appreciation of the mathematics. Similarly, the four-color problem is sufficiently easy to explain (who hasn't seen a map?) and controversial (should computers be allowed as part of rigorous proofs?) that crafting an accessible story poses a worthy challenge rather than an arduous task. Let's take as a given that the community of journalists is woefully ignorant in mathematics. Intriguingly, that really shouldn't be a barrier in media coverage. The media are filled with people who are writing about topics they know very little about. Content knowledge rarely determines who gets to cover what. This is something that many specialists simply do not understand about the media culture. On the contrary, they point to media ignorance as the very reason why the media (and, indeed, the public at large) should be held in such contempt. At this point, I'm compelled to remember something that Ben Bradlee, my editor at the Washington Post, once said: "We don't print the truth; we print what people say." The reality of media coverage is that most journalists—whether brilliantly experienced or breathtakingly naive essentially write (or tape) what people say. They count on their sources to generate the story and identify what's important. The best stories in the popular and elite press are almost always shaped, determined, and influenced by the quality of their sources. The quality of the sources—their ability to quickly respond to media inquiries; to frame responses in ways that make the story easier to produce; to encourage the journalist to expand or narrow the story in a way that reinforces what the journalist is really trying to do, and that respects the limitations of the medium and the journalist rather than treating them as excuses for dismissal—is the single most important criterion for determining the quality of media coverage. Sources shape stories more than stories shape sources. Period. Much of the inherent problem with mathematics coverage is that, more often than not, it's difficult to pick the right metaphor that enables a math story to be both accessible and compelling. Physics, chemistry, biology, and technology all lend themselves better to metaphor

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and analogy than does mathematics. Mathematics does not intrinsically lend itself to narrative. Mathematicians do not "construct" stories or narratives in the ways that, say, sociobiologists, molecular biologists, or computer scientists do. To see what happens when media culture collides with math culture, consider the very words mathematicians use when describing their discipline. Mathematicians often refer to mathematics as a kind of a language with its own subjects, verbs, adjectives, and nouns. Indeed, mathematics is both literally and figuratively a dazzling array of many languages, dialects, and creoles. Now, ask yourself: How often are languages covered in the popular and elite press? How often are new French phrases quoted or Japanese kanji cited or Chinese ideograms explained in, say, a month's worth of Wall Street Journals or Fortune magazines? When are translations of Russian graffiti and New Right German neologisms a part of videos done by CNN or ABC? The answer, of course, is almost never. Yes, the media cover France, Japan, Germany, and China as countries and cultures but rarely do they focus on the languages. Mathematics is covered not as a community or as a culture but as a language and, as a result, it falls into the journalistic mindset of something that is seldom written about by the mainstream press. (However, a notable exception to this is how jargon seeps into everyday language—it's easy to pitch a story about how technical slang from computers enters colloquial speech, or how medical terminology from a hit show like "ER" becomes a linguistic meme. If certain math terms began to seep into the pop vocabulary, you can be sure there would be a New York Times story and a tongue-in-cheek CNN feature within 6 months.) Similarly, another term that mathematicians use to describe their favorite work is "elegant." They describe the intrinsic "beauty" of their math; they describe a genuine, heartfelt aesthetic. So what's the metaphor here? It is the metaphor of "high art"—an art so rarefied and obscure that only the most refined aesthetic palates might appreciate it. Now, how often do the mainstream press and the elite media cover the avant-garde canvases and sculptures of little-known European artists? Yes, art exhibits in the mainstream museums and galleries are covered regularly by the mainstream media (although not by publications like USA Today or any of the major television networks). But truly "breakthrough" art in the smallish galleries and museums remains the province of—surprise—obscure journals and "fanzines.'' Indeed, these publications have circulations comparable to peer-reviewed math journals. In reality, mass media coverage of the sophisticated arts occurs about as frequently as coverage of sophisticated mathematics. The mainstream media avoid obscurantist art (but not, necessarily, obscurantist artists) as rigorously as they avoid obscurantist mathematics (but not, necessarily, obscurantist mathematicians). Mainstream media (even elite media) prefer to cover mainstream—and accessible—art, just as they would prefer to cover mainstream mathematics. What, in the 1990s, qualifies as mainstream mathematics? Stories about statistics and probability; encryption; new algorithms that make computers calculate faster or compress imagery better—that is to say, mathematics that can in some way prove relevant to the mainstream. The point of these examples is very simple: the very metaphors that mathematicians use to describe their field are metaphors that the media typically ghettoize in their coverage. They are metaphors that limit rather than metaphors that expand. (To be fair about this, it would be difficult for most newspapers to cover math well even if a gifted journalist wanted to get a provocative equation on the front page: at the Washington Post, New York Times, Wall Street

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Journal, and Los Angeles Times, a reporter would have to call either the art department or the computer typesetting people to make sure the fight symbols were laid out in the right order on the page. Getting math notation into a newspaper is not as straightforward as writing a sentence with italics or boldface. There are genuine technical barriers to serious math coverage in the mainstream media.) Consequently, if the mathematics community wants to dramatically improve its media image, it has to be prepared to invest its intellectual resources in coming up with metaphors that the media can easily grasp. Note that metaphors are not the same as sound bites. Obviously, it's easier to come up with metaphors for statistics and probability than, perhaps, for real analysis. Then again, the role mathematicians are playing in importing topological analysis to protein folding and molecular biology offers a magnificent example of how once-"pure" math can offer rich insights into the fundamental processes of nature. Is the real story here how mathematics illuminates nature or how nature gives insight into mathematics? The knee-jerk and gratuitous suggestion is that the math community will find it far easier to peddle stories about the growing "relevance" of mathematics to core disciplines that people care about, i.e., medicine, nature, ecology, computers, software, encryption/privacy, gambling, economics, finance, and so on. To be sure, the mathematics community has done a miserable job of doing even that. However, a more challenging context for mathematicians to explore would be to market not "relevance," but "perspective." What kind of useful and valuable perspectives does the mathematical mindset offer? What is the relationship between the culture of mathematics and mathematicians and the kinds of perspectives they bring to bear on problems in other disciplines? How do other disciplines—medicine, economics, meteorology, and so on—beg, borrow, and steal from innovations in mathematical thought? Similarly, the math community should take the risk of being covered as both culture and community. In the same way that the "cold fusion" controversy illustrated many useful and intriguing insights into the rivalries between physicists and chemists, perhaps it might also be useful to let people see the schisms between, say, "pure" mathematicians and industrial mathematicians, and mathematicians and statisticians. In other words, let the media use the culture of math as a lens to look at math as a discipline. Indeed, the role that mathematicians played a while back in blocking Samuel Huntington's elevation to the NAS was, in retrospect, an opportunity missed in helping establish in the public mind what values mathematicians hold as scientists. With these points in mind, here are specific suggestions on options the mathematics community might consider to help influence both perceptions and policy in the media: Give up the notion of mathematical literacy in favor of mathematical awareness. What trends and ideas in mathematics should taxpayers and mainstream Americans be aware of over the next 2 years? Stress the value of the perspective mathematics brings to various disciplines rather than the substance of math itself. Identify no more than 20 media outlets, that is, highly targeted sections of broader media outlets—the Science section of the New York Times; the Finance section of Business Week; "Science & Technology Week" on CNN; etc.—that reach what the community deems to be a desirable audience. Analyze which stories produced over the last 6 months could have been

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improved by a quote, contribution, or guidance from a mathematician. The point is to leverage existing coverage rather than try to create a new genre or set of stories about mathematics itself. Develop a working group of 10 to 12 people who are familiar with trends in math itself and who will try to express these innovations in metaphors and analogies that are communicable to nonmathematicians. Every gathering of mathematicians should have a working session where participants are funded to come up with a presentation or concept that is designed for a lay audience. Make sure that people can articulate the history and the story behind the idea. It is often easier to explain an idea in the context of its origins than to explain the idea itself. History is inherently narrative. Create one-day workshops for members of the media (and relevant federal and state staff) that invite the best mathematicians around to give accessible tutorials on major math themes. The goal should be not to produce faux literacy but rather to promote a conceptual appreciation of why that particular aspect of math warrants further study. The analogy is Leonard Bernstein teaching people how to listen to Beethoven. People don't have to be able to read music to better listen to it. Parasitize other public relations initiatives by the science and technology community. When engineers or physicists are putting on a press briefing or a conference that attracts media coverage, make sure that mathematicians are there to put their spin on how mathematics is influencing advances in those fields. Make a concerted effort to infiltrate the business press. Between Wall Street quants, economists' simulations, and computation, the quantitative content of the business world is rapidly increasing. Mathematicians should be commenting on how the future of math will shape the future of value creation. In other words, how can math—like microprocessors—be seen as a "mission-critical" part of the information economy? Identify the rivalries and cultural conflicts in the math community and "market" them to the media as signs of an institution undergoing introspection and renewal. Science magazine "News and Comment" stories like this invariably get picked up by the mainstream media. The challenge: How can these conflicts be portrayed in ways that give the mainstream greater insights into how mathematicians define their field? There is no doubt that mathematics remains a vibrant and evocative discipline whose intellectual influence is expanding in spite of the limitations of the community that defines it. It is time that the mathematics community recognized—and acted upon the recognition—that it has a moral obligation to make it easier for people to appreciate what mathematics can be. Knowledge and understanding are too much to ask; appreciation and awareness are not.