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How Math Makes Art Possible

May 26, 2008
A popular stereotype holds that some students are "math people" and some students, "humanities people." "Humanities people" excel in such subjects as English, visual art, history, drama, and social studies, because of their high creativity or "right-brainedness," while "math and logic people" struggle with creative subjects but excel at logic-driven disciplines. This idea is disputed by brain researchers, who point out that people cannot be sorted so easily. But it also fails to hold up under the scrutiny of anyone who knows the history of art.

Math and the arts are so closely allied that, during the middle ages, music was thought of as a branch of mathematics. Some of that synergy survives today, in the work, for example, of literary maestro David Foster Wallace, who followed up his massive and erudite 1995 cult classic Infinite Jest with a 2004 book of nonfiction, Everything And More, on the life of set theorist Georg Cantor.

But in the life of Leonardo Da Vinci, the fruitful cross-pollination of math and art perhaps reached its peak in Western history. Born near Florence, Italy, in 1452, da Vinci excelled as a mathematician and scientist as well as dominating Western painting and sculpture (his Last Supper is probably the most widely-known and parodied painting in the world; the other serious contender, the Mona Lisa (or La Gioconda), is also a da Vinci).

He conceived and, in some cases, drew up plans for helicopters, tanks, solar-power concentration, and calculators "these plans remained pipe dreams, not always because of any problem with da Vinci's designs but because the metallurgy and engineering needed to make them did not yet exist" but he also made contributions, during his lifetime, to the fields of civil engineering, hydrodynamics, anatomy and optics.

One of da Vinci's major contributions was his experimental, practical approach to science - he derived his ideas from close observation of phenomena, rather than referring to theories written by Aristotle or others on the subject (which was a common approach during the Middle Ages). But that close observation of reality, of course, was important to his development as a painter, and it's here that his knowledge of math also aided him.

During Leonardo's period, artists and architects such as Brunelleschi and Alberti had written treatises on the science of perspective - the ability to paint or draw so that objects appear as they do to the eye, so that faraway objects, for example, become smaller, and close-up objects larger. (Perspective was something of a lost art for the painters of the Middle Ages, the period which directly preceded and laid the groundwork for the Renaissance.)

Perspective requires math; Leonardo, like Giotto, Brunelleschi and Alberti before him, used complicated geometry and algebra to determine how distant lines should be placed, but Leonardo's version of perspective, because of his emphasis on direct observation, was the first to acknowledge the way that air affects light over distances, so that an object's color changes slightly over a long distance. His mastery of perspective depended directly on his grasp of the mathematics underlying it.

Why was he able to be successful in so many diverse fields? To start with, of course, we should look at the time period. The educational philosophy of the Renaissance stressed the idea of developing every possible skill; educational disciplines were not as neatly separated then as now (the word "philosophy" could apply equally well to essays in science, math, and to the kind of free-floating enquiry that we would now call philosophical); no one saw any conflict between being a great scientist and a great artist.

The point of education was to develop all of a person's capacities, rather than, as is frequently the case today, helping a student to figure out which subjects he or she excels in, and encouraging him or her to "major" in those.

Why, then, do so many students experience math as a chore? In a classroom of thirty pupils and one teacher, the instruction has to move at a certain plodding pace, which leaves some students bored and others, who are slower to grasp a concept, frustrated. "Those who are not ready to make the necessary conceptual leap when they meet one of these [new] ideas will feel insecure about all the mathematics that builds on it," mathematician Timothy Gowers has written. "Gradually they will get used to only half understanding what their mathematics teachers say, and after a few more missed leaps they will find that even half is an overestimate.

Meanwhile, they will see others in their class who are keeping up with no difficulty at all. It is no wonder that mathematics lessons become, for many people, something of an ordeal."

But Gowers sees hope for such frustrated students in math tutoring: "I am convinced that any child who is given one-to-one tuition in mathematics from an early age by a good and enthusiastic teacher will grow up liking it."
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