Mathematical Exhibitions: Reactions and Concerns

December 1, 2005

A Möbius strip, from the exhibit Mathematica—A World of Numbers. © 2005, Eames Office LLC (

By Philip J. Davis

Over the years, I have visited a number of science museums or exhibitions, both in the USA and abroad. While traveling in Europe during the past year, I visited the Museum of Science and Technology in London (Exhibition Road) and the Einstein Centenary Exhibit in the Kronprinzessinen-Palais in Berlin. To some extent, I except the special-purpose Einstein exhibit from the discussion that follows; it was a lavishly laid out and sharply focused celebration (almost an apotheosis) not only of Einstein's great contributions to science but also of his personal, social, and political life.

I didn't take notes on what I saw in London, but a few impressions of the mathematical displays remain with me. Located adjacent to the computer section, in which Babbage's Difference Engine and the early electronic behemoths can be found, I saw polyhedra and crystals, twisted surfaces, knots galore, a magnificent collection of old, beautifully wrought mechanical linkages designed to draw a variety of curves. What I didn't see was any substantial number of viewers--either adults or children. Like seeds in a maraca, a few other adults and I rattled around among the glass cases. Where were the children? You will guess that they were all in the museum's IMax theater watching a show about robots.

More recently, Gail Corbett (editor of SIAM News) and I visited the New York Hall of Science in Flushing Meadows, Queens, New York City. We were greeted warmly at the entrance by Alan Friedman, director of NYHS, who knew that we would be visiting. I told Dr. Friedman that I frequently suffer from the well-known "museum fatigue" syndrome and therefore wanted to limit our viewing to the section on mathematics. He assented but jovially pointed out that all the exhibits have an underlay of mathematics. True enough, but how to make the public aware of this is a largely unsolved problem.

A museum of science has an informational function, an educational function, an inspirational function, an amusement function, a research function. It may house a collection of famous pieces of equipment (Archimedes' lever, if only a curator could get hold of it!); it may have an archival function: collecting the letters, notebooks, plans, lectures, of the great. A museum of science must be aimed at a wide clientele. It should attract kids, older students, and adults. It must be hands-on, it must dramatize and update its material. Its presentations cannot be too static or too technical. The visual must dominate the conceptual.

What a visitor finds in a science museum, of which I'm sure there are over a hundred in the world, results from the close collaboration of scientists, technologists, historians, artists, craftspeople, layout people whose divergent ideas have somehow been reconciled. A science museum is part of the world of communication; it is one of the media and must compete with all other media in getting its message across. The director and the planning staff must take into account and satisfy these and many, many other considerations as best they can given the inevitable restraints of time, money, and space.

Mathematically, current visitors to NYHS have two options: One is an up-to-date presentation on the theme of networks; the other, titled Mathematica--A Worldof Numbers, is an exhibition laid out forty years ago by Charles and Ray Eames, de-signers (think of the famous Eames chair) and mathophiles. It opened in March 1961, in a new science wing of the California Museum of Science and Industry in Los Angeles. I believe that Raymond Redheffer, late professor of mathematics at UCLA, was one of the consultants to this exhibition. After moving around a bit over the years, Mathematica has come to rest at the NYHS, under the stricture set by the Eames family that not a jot or tittle of the original is to be changed. Strictures be damned; time marches on, and Dr. Friedman, together with a committee of professional mathematicians, is currently planning an update.

Among the individual exhibits are: (1) An 8 x 8 x 8 cube of light bulbs that display the results of keyed-in multiplications; if, for example, you key in 5 and 7, 35 bulbs light up in some pattern. (2) Thousands of balls falling in a Galton board of 200 steel pegs and approximating a normal distribution. (3) A huge Möbius strip with a "choo-choo" running along its one sided surface. A number of displays exhibit visual projections: minimal surfaces generated on wire frames dipped into a solution and a bunch of ball bearings running round a conoidal surface and ultimately dropping off into a "black hole." The latter is said to illustrate celestial dynamics.

My recent visits to all three of the science museums mentioned took place on days when hundreds of school children, their teachers, and their parents swarmed through the halls and raised the decibel level to "painful." Kids of all ages would come into an exhibit area, push and pull mindlessly (and not always gently) on the interactive knobs, after which something would happen visually. Then they would go on to the next knob. What do kids learn from such a push-me/pull-you experience? To add some structure to their experience, the NYHS hires college students as "interpreters"; these student interpreters are trained to answer questions and give demos. They are also a source of feedback as to the effectiveness of the exhibits. Twice a year, an outside organization also conducts random surveys of museum visitors; if the effectiveness of an individual exhibition piece is deemed low, the piece is junked ASAP.

There is also much static material of the type that one sees pictured in "math can be fun" popularizations: e.g., patterns, pre-Mandelbrot fractals, people, biographical and historical quotations. (Gail, who is a weaver, especially liked this wall.) The famous Mathematical Time Line (covering the period from about 1100 to 1950), distributed by IBM years ago and overloaded with information, is here in its pristine glory. Copies of the Time Line are still to be seen in the hallways of many math departments.

Let me now express a few more reactions to what I've observed in the math sections of the science museums I've visited. No doubt the museum staffs have already given thought to most of them.

In our age of frenetic motion and haste, the static material, particularly the material posted on the walls and elsewhere, though well thought through, is "dead." I wonder how many children have the patience to stand still and read. I include in the notion of the "static" the old pieces of equipment, displayed in cases and just sitting there. In London, when I saw the beautiful linkages in the glass cases, I wished for a docent who could lift them out of their cages and show me how they worked. The world is not yet all digital, and there is still aesthetic pleasure in seeing a well-oiled mechanism at work. The material displayed is either elementary or much too sophisticated--so much so that I cannot imagine "normal" people understanding it.

Science museums face substantial competition from imaginative, interactive mathematical Web sites, of which there are now many. Why bother to schlepp all the way to a museum when good stuff is available online? I really wonder whether the math museum of the future will be online. Of course, a trip to Flushing Meadows does get the kids out of the house, the classroom, or the street. And, of course, there is much more to absorb than just the math.

I come now to the one string I often harp on. It relates to the way the media of whatever shape, size, or form present mathematics. I limit my remarks here to museums. There is no gainsaying that soap films, archimedean polyhedra, pictures of magic squares, labyrinths, pictures of Euler and Hilbert are all part of the world of mathematics. But where's the beef? By the beef, I mean the mathematics that today impacts the lives of every one of us. Where are the displays of the mathematics that advances--and even defines--our civilization and influences our lives in many different ways? Some examples follow.

Just think what a different (perhaps better) life we would lead if IQ and SAT scores were not around to tell us who is "intelligent" and who is not. How would we live if there were no blood pressure or cholesterol numbers to advise us? If there were no pre-election polls on every conceivable issue? If the trajectory of a missile or a rocket were computed by guesswork? If, when we went to the supermarket, the checkout clerk took a pencil from behind his ear, marked down the prices of our 18 items, and toted them up, rather than swiping our purchases past a bar code reader?

Does the public know how the U.S. House of Representatives is apportioned among the states after a census? The mathematical procedure, called the "method of equal proportions," is now part of statutory law (Title 2, U.S. Code) and has been judged constitutional by the U.S. Supreme Court.

How many people, looking at a weather map, with its isobars and isotherms, or at the conjectured path of a hurricane, know that mathematical algorithms underlie the production of these pictures? Are users of search engines aware that it is a mathematical strategy that brings up the citations?

More and more people receive computerized medical diagnoses. And the advice governing their investment portfolios is often shaped by an application of stochastic calculus. With much of the world at war, could a demonstration of the role of mathematics in warfare fail to find interested viewers?

All of these experiences, and hundreds more, are based on an underlay of mathematical ideas and methods, some trivial, some deep, but rarely called to the attention of the general public as something worthy of its attention. We are living in a mathematized civilization, but most of the mathematics is buried in chips and hidden from view. I pose as a challenge to the developers of mathematical exhibitions (whether in buildings or on the Web) to expose the applied mathematics in our current lives. This is not an easy job and will require more than a bit of ingenuity.

Despite these criticisms, I have yet to go into the math section of a science museum without finding something that I didn't know. In the NYHS exhibit, I saw a three-dimensional construction that converted rotary motion into linear motion. Not reported in any history of math book that I know, this mechanism scooped the publicized Peaucellier–Lipkin linkage of the 1860s by a number of years.

I wish the NYHS well as it proceeds with its update of the Eames exhibit. It will surely display immersive virtual reality--not available online--as one of its features. I hope it also shows how math stats are now affecting the strategies of major league base-ball. And who knows but that twenty-five or so years from now some professional mathematician will assert that, for him or her, lift-off into the clouds of mathematical creativity occurred after a visit to the NYHS.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at

The reviewer at work: Philip Davis pauses in his inspection of the Charles and Ray Eames Mathematica exhibit, which opened originally in 1961 and has found a permanent home at the New York Hall of Science. Visible in the background is the well-known Mathematical Time Line (1100–1950), which, along with the rest of the exhibit, is scheduled for an update.

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