Excerpt from "The Man Who Loved Only Numbers" - The difference between physicists and mathematicians

"The Man Who Loved Only Numbers" by Paul Hoffman is a biography about the memorable personality that is Paul Erdős, the prolific mathematician, who published with over 500 collaborators. Erdős, who is well-known for his contributions to number theory, set theory, probability theory, graph theory, and more, as well as the invention of the Erdős Number, a measure of one's proximity to having collaborated with him, is of course a subject himself. That said, in Hoffman's biography of him, there is a bit about the behavior of mathematicians and a lone physicist that does well to embody the spiritual and cognitive differences between the two groups, both of which share a passion for mathematical thinking but nevertheless are separable beasts. 

The excerpt of interest tells of a mathematics conference in which a group of mathematicians return to the coffee table after a talk only to find a puzzle.

The rest filed out and raced toward a folding table that supported two large brown plastic tanks, one labeled WITH CAFFEINE, the other WITHOUT CAFFEINE. The mathematicians had already tanked up once, before the graph theo- rist's talk, and now the labels on the tanks were curiously switched. The mathematicians were in a tizzy and stared, puzzled, at the tanks. Their collective brainpower, fine for discerning the latest wrinkles in infinite graph theory, was stalling out on the case of the true Joe.

Finally a lightbulb went off in the head of a jovial, beer-bellied fellow in a JOY OF SETS T-shirt. He stepped forward and filled his Styrofoam cup, half from one tank and half from the other. 

"I see," laughed one of his compatriots, "the game-theoretic solution!"

"I have another solution," said a thin man whose hands trembled slightly, apparently from a caffeine high. He filled his cup a quarter full from one of the tanks. "This is the asymptotic solution," he announced. "I'm already so wired I only want a little bit more; whatever is in the cup, I win."

A bystander who was a physicist rather than a mathematician didn't understand the need for all this sophisticated thinking. He pointed out that one tank was bigger than the other, and that the bigger tank presumably held caffeinated coffee since more people drink it than drink decaf.  The mathematicians were taken aback by the simplicity of the solution. "Our different approaches," said the physicist, "remind me of an old joke. A physicist and a mathematician are flying cross-country together. Each is keeping a diary of the trip. They fly over a white horse in Iowa. The physicist writes, 'There is a white horse in Iowa.' The mathematician writes, 'There exists, somewhere in the Midwest, a horse, white on top.'"

For all that has been written about the difference between physicists and mathematicians, especially with the goal of illuminating their inner minds, this passage provides both a reasonable illustration and a good laugh.

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