From THE BOSTON SUNDAY GLOBE, CLOSER LOOK, Page NH18, 11/7/99

Show brings attention to US math problem

Art and math meet at exhibit to spotlight a national problem

By Gail Kelley

It works. Whenever political or religious leaders, businesses, or any groups with a point of view want to reach the masses, they turn to the arts for help.

Now it's mathematicians. Mathematics - necessary to all the sciences, economics, architecture, most of the trades, and many areas of the arts - is in trouble.

According to a National Science Foundation report released last year, the United States has been able to hold on to its position as a world leader in mathematical sciences because of "a large influx of foreign mathematicians" in recent years, mostly from the former Soviet Union. Given present trends, the report warns, "it is unlikely the US will maintain its world leadership in mathematics" and that "without re-medial action by universities and the NSF, there will not be enough excellent, US-trained mathematicians, nor will it be practicable to import enough experts from elsewhere, to meet the nation's needs."

What is undermining mathematical sciences in this country? In a phrase, poor math education.

Studies by the US Department of Education and the National Science Foundation have found:

1 The eighth-grade math curriculum in too many of the nation's schools is equivalent to seventh-grade instruction in western European and Pacific Rim countries.

2. Fewer than half of the eighth-grade math teachers in this country have ever taken a course in teaching math at this level.

3. Nearly a third of the math majors in American high schools did not major or minor in math in college.

4. The number of college math majors and math graduate students has steadily declined over the past several years.

The department of mathematics at Dartmouth College took a look at this sorry state of affairs and decided to do something about it Led by math professor Dorothy Wallace and aided by a five-year grant from the National Science Foundation, Dartmouth initiated its Math across the Curriculum Project in 1995.

To raise awareness of the role of mathematics in other fields, the project has developed interdisciplinary courses in concepts of time, math in music, and math in science fiction.

The project also funded a joint effort of a mathematician, a geologist and a fabric artist that resulted in the creation of a shibori mural replicating enhanced images of satellite data of the earth's surface. The mural is on public display at the Cold Regions Research and Experimentation Laboratory in Hanover.

Now, in the last year of the National Science Foundation grant, the project and Dartmouth's Hood Museum of Art have assembled an exhibition, "Visual Proof: The Experience of Mathematics in Art."

The show consists of works chosen from the museum's collection by mathematics professors and a few teachers in fields outside of math. These people then wrote essays explaining the mathematical principles behind their selections. The essays constitute the catalog for the show.

It is an eclectic assortment of artwork, ranging from Renaissance drawings to op art and abstract sculpture. Since these pieces represent concepts of varying complexity, from basic (symmetry and patterns, perspective, proportion) to higher math (group theory, calculus), the exhibition can appeal to a broad spectrum of ages and levels of mathematical sophistication.

A Navajo blanket, A Pima hand-woven basket, and a Yoruba fabric with hand-painted designs illustrate types of symmetry.

A 16th-century engraving by Giorgio Ghisi of Raphael's fresco "School of Athens," depicting a crowd of toga-clad men in a hall of archways and colonnaded walls, contains mathematical references both through its images of the great Greek mathematicians Plato, Pythagoras, Euclid and Ptolemy and through the use of perspective and systems of architectural proportions in its composition.

George Tooker's painting "Farewell," a sequence of nested boxes that creates the illusion of a receding tunnel in which a small female figure stands in front of the vanishing point, is a commemorative of the death of the artist's mother. It is also an artistic representation of the mathematical equation describing infinity.

M.C. Escher offers another representation of the same concept using tessellation and perspective in a black and white woodcut of interlocking angels and devils, titled "Circle Limit IV."

The exhibition is interactive, with puzzles and lists of other suggested activities accompanying several of the works. All of these devices and materials were designed and constructed by the Hood Museum staff.

A set of black and white, rubber, lizzard-shaped pieces is provided for visitors who would like to create their own tessellation.

A sculpture of an incomplete cube by Sol LeWitt in the center of the exhibition space is one of the artist's solutions to a mathematical problem he posed for himself. How many ways are there for creating a three-dimensional sculpture that suggests a cube without using all of its edges? For those who would like to get a sense of how LeWitt derived the answer, there are rectangular blocks that snap together like Legos to form incomplete cubes.

Visitors may also piece together a scaled-down replica puzzle of Richard Anuszkiewicz's op art painting of a diamond inside a square. Anuszkiewicz made the canvas look like an enormous piece of graph paper and painted each square red, blue or green.

For the borders of the diamond and the square, he divided each of the "graph paper" squares into four or 16 smaller squares, creating the illusion of a definite demarcation line around the diamond. This makes the puzzle devilishly difficult to assemble - for adults, that is; Wallace says children are able to do it in a snap.

The work in this show that provides the keenest insight into the field of mathematics, however, contains no mathematical references. It is a page of sketches Jackson Pollock made of a portion of the Orozco mural in Dartmouth's Baker Library when he saw it in 1936.

Dartmouth mathematics professor Dan Rockmore chose this work because it "reminds" him of an aspect of math. "Actually," he said in a public lecture last week, "almost anything reminds me of math. It's one of the hazards - or joys - of my job."

Rockmore has done extensive reading about Pollock and seen exhibitions of his notebooks and his paintings. He knows Pollock had no gift for drawing. Yet, the artist filled notebook after notebook with copies of magazine illustrations, imitations of the work of other artists, and exercises in shading and geometric drawings. These notebooks were his homework, his problem sets. This was how he trained himself in the mechanics of image-making so that eventually his ability to manipulate a line would become automatic and he could concentrate on other matters in his work.

Similarly, says Rockmore, few mathematicians are born with a gift for numbers. They acquire their skills through years of homework, doing algebraic equations, geometric problems, integrals, matrix operations and differential equations. When mathematicians reach the point where mechanics become routine, then, like artists, they are free to wrestle with other ideas and follow inspiration where it leads them.

This exhibition has a wider reach than anything else the Math across the Curriculum Project has done. Wallace has conducted a daylong workshop for teachers on ways to use the exhibit in their math classes. Several school groups from surrounding communities have visited the exhibition. This past week 50 teachers from the Nashua area attended a mini-workshop at the Hood Museum on how to replicate the exhibition in their classrooms through slides and activities developed by the museum staff and project professors.

Making the show easily exportable was one of the criteria in putting it together, says Katherine Hart, the Hood's curator for academic programming.

In the next decade, says the US Department of Education, 250,000 more teachers will be needed in math and science. What contributions the efforts at Dartmouth will make in filling that need may never be known.

The exhibition, says Rockmore, "is just a small step in an area with a population of only about 10,000." But all it takes is watching the adults and children who visit the exhibition - witnessing the time they spend looking at each piece, the conversations they have, and seeing how quickly they are drawn into the puzzles and how determined they are to stick with them - to know this is a highly effective step.


"Visual Proof" remains on view until Dec. 12. Teaching packets, with slides of works in the show, background information and suggested classroom activities, may be purchased from the Hood Museum of Art for a nominal charge. Call 646-2808.

matc