Duchamp is perhaps best known for his so-called readymades--a bicycle wheel mounted on a kitchen stool, a wooden hat rack, an Underwood typewriter cover, a snow shovel, a wood and metal coatrack, a steel comb, an advertisement for Sapolin enamel paints, a bottle-drying rack, his infamous urinal, and a number of others.

At first glance, the underlying idea seems to be that an artist can transform everyday, mass-produced objects into works of art simply by selecting them. Such items eventually move into art galleries and museums, completing their transformation into respectable art objects.

Duchamp himself stated that it didn't matter who had originally manufactured his readymades. The point was that he, Duchamp, had chosen them. Those words echo Poincaré's notion that mathematical discovery means selection--discerning patterns and laws hidden within apparent randomness.

In his 1908 essay "Science and Method," Poincaré described an instance when he was unable to sleep because of an excess of black coffee. Wide awake, he found his mind jammed with ideas. "I sensed them clashing until a pair would hook together...to form a stable combination," he wrote. By the next morning, Poincaré had the solution to a mathematical problem that had plagued him for weeks.

"Discovery is discernment, selection," Poincaré argued. "The real work of the discoverer consists in choosing between...combinations with a view to eliminating those that are useless."

However, he went on to say that this unconscious work doesn't supply a result "ready-made." What it produces are merely points of departure for deliberate effort.