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Opening the Doors to the Life of Pi. By Edward Rothstein. The New York Times, December 13, 2012

For those of us who have been intoxicated by the powers and possibilities of mathematics, the mystery isn’t why that fascination developed but why it isn’t universal. How can students not be entranced? So profound are the effects of math for those who have felt them, that you never really become a former mathematician (or ex-mathematics student) but one who has “lapsed,” as if it were an apostasy.

So why, until now, has there apparently been no major museum of mathematics in the United States? Why, when so many identities and advocacies have representation in the museological pantheon, has math been so neglected? Here and there, perhaps, a hobbyist has displayed puzzles, and our gargantuan science centers occasionally deem it worth their while to descend into algebraic abstraction. But a museum devoted to math? You have to immerse yourself in the history of science museums in Europe — where math sits at the foundation of things — to get an inkling of what it might mean.

Or, for an entirely different experience, you can go to Madison Square Park in Manhattan to see the new Museum of Mathematics, which opens on Saturday. It refers to itself as MoMath (and since it is near MoSex — the Museum of Sex — that means we now have a museum district explicitly evoking the mind-body problem).

MoMath is not what you might expect. At first you might not even guess its subject. There are a few giveaways, particularly if you recognize the symbol for pi on the door or discover the pentagonal sinks in the bathrooms. But what is that cylinder constructed of plastic tubes stretching toward the ceiling with a seat inside (“Hyper Hyperboloid”)? Or that transparent wagon that slips along multicolored acorns in a trough (“Coaster Rollers”)? Or a tricycle with three square wheels, each of a different size, rolling along a bumpy circular track (“Square-Wheeled Trike”)?

And what is that screen on which you paint electronic designs with a brush (“Polypaint”)? The two adjustable sloping paths on which you race objects (“Tracks of Galileo”)? The pixelated illuminated floor that responds to your movements (“Math Square”)?

This is not a museum, you might think, it is a high-tech playground, some 19,000 square feet with 30 attractions on two floors. I stand in front of a screen, and I see myself as a tree sprouting branches of mini-me’s (“Human Tree”). I cover a wall with interlocking monkeys (“Tesselation Station”). I dip a paint roller into water and map footprints on a blackboard (“Water Frieze”). Child’s play or something else?

And that is part of the point. The museum’s founder is Glen Whitney, who parlayed his training as a mathematical logician into a lucrative position as quantitative analyst for a hedge fund; he then decided to create a museum that would celebrate math. His collaborator was Cindy Lawrence, an accountant and educator who is associate director. And the design chief is Tim Nissen, who worked for Ralph Appelbaum Associates and developed the original exhibits. The museum cost $15 million;$22 million was raised.

The goal, each principal emphasized in conversations this week, was to show that math was fun, engaging, exciting. MoMath is a proselytizing museum. And despite its flaws, it is exhilarating to see math so exuberantly celebrated. And while fourth through eighth are said to be the intended grade levels, it is hard to imagine a younger child or mature adult not drawn in by some exhibits here. In many ways the sensations of the displays are more compelling than the explanations of their content.

That is also one of the flaws. The reason that there haven’t been many math museums is that the enthusiasm the subject inspires is not easily communicated and not readily discovered. In the United States, where student math performance is far from stellar, it is easy to see why a compensatory straining at “fun” is more evident than a drive toward illumination.

To attract the uninitiated, a display must be sensuous, readily grasped and memorable. Yet the concepts invoked are often abstract, requiring reflection and explanation. How are these opposing needs to be reconciled? With widely varying results. When I visited the museum twice this week not every display was completed, but the exhibits covered a broad spectrum of achievement. Many on the higher end of that range should be celebrated; much on the lower should be scrutinized and brought up to grade level.

So first, celebrate: in many of these exhibits the physical sensation of being immersed in a world shaped by a mathematical idea will have lasting resonance. If you sit on a chair at the center of “Hyper Hyperboloid,” for example, you are surrounded by colored cables arranged in two surrounding circles. As you rotate the chair, they begin to angle in opposing directions, until the column of cables is pulled together in the center above your head. You are literally on the central axis of a graceful and surprising shape, its surfaces and contours outlined by series of stretched lines.

Or ride that square-wheeled trike or the “coaster” rolling on acorns. In each case your instincts tell you to expect jerky disruptions, since only circles or spheres can be counted on to maintain smoothness in motion. But the acorns are shaped to have constant width, just as spheres do, so there is no sense of rise and fall as the wagon slides.

And the “trike’s” square wheels rotate just fine on a surface designed to accommodate them. The surprising thing is that this surface is a curve called a catenary, which is also the shape of a drooping chain. It allows the axis of the odd wheels to remain level as the contraption rolls along. (You can even give the wheels other improbable shapes.)

In both cases there is a startling aspect to the experience that must be explained, and that leads us into thinking about shapes and curves in a different way. This is the kind of thing that happens repeatedly in the museum’s best exhibits: You see yourself as a tree sprouting identical images of yourself and learn about fractals; or watch laser lights slice through transparent solids and revise your sense of space.

The problem is that we don’t get enough guidance to be led deeper. The exhibits offer touch screens that can display three different explanations, the appropriate level sensed from a coded card provided each visitor. But these explanations are the museum’s weakest part. The most basic are often stilted or overly elaborate; the most advanced, not sufficiently suggestive.

A “basic” comment in the hyperboloid display, for example, needlessly refers to “two-dimensional objects which can be thought of as the graphs of second degree equations in three variables, typically x, y, z.” I doubt that anybody less than virtuosic at the Rubik’s Cube and group theory will readily follow the guide to its solution offered in another exhibit space, the “Enigma Café.”

On the other hand, information can be missing. In the trike and coaster displays there are things we might want to know about objects of constant width or catenary curves, but there is little detail. There are connections to be made between some of these displays — even the “Tracks of Galileo” with its allusion to “cycloids” and the rectangular-wheeled trike — that might have also been subtly explored.

Occasionally a display is less enlightening than its promise. A two-story paraboloid — a shape created by a cuplike parabola rotating in space — is used as a calculator to multiply numbers from 1 to 10 by having illuminated strings crisscross its central axis. That is difficult to imagine, but it is not made simpler by seeing a two-story model of the project. It is not readily generalized into other kinds of insights and it reverses the mathematical ambition of making complicated things simple.

And I wish that “Harmony of the Spheres,” designed with the Princeton music theorist Dmitri Tymoczko, had been more clearly explained, and provided with levels of “experiments” to perform by touching its colored spheres to produce three-note chords. It is the kind of exhibit that would have once led me into deeper explorations.

But with luck that will happen for many visitors interacting with the exhibits here already. The problems with text and explanation can readily be fixed. Over time the Enigma Café will be filled with varieties of puzzles. The “Math Square” will light with diverse programmable possibilities. And perhaps, eventually, the proselytizing of MoMath will turn theory into practice.