18 September 2005

Should math be beautiful, or practical?

The readers of Physics World recently voted on the greatest equation of all time. The result was a tie. One of the top vote-getters was Maxwell's equations, which describe electromagnetism. One physics professor I know said that understanding these equations was a big hurdle for students; once mastered, Einstein's work was a doddle. (He may have exaggerated a bit, but only a bit.) The usefulness of these equations is hard to overstate.

The other winner was Euler's formula, which can be written as:
e + 1 = 0
When mathematicians first see this, they find it incredible. This formula includes two basic transcendental numbers, e and π, the multiplicative identity (1), the additive identity (0), and the basis for the imaginary numbers (i) with nothing extraneous. At first blush, it's hard to believe that an imaginary exponent of a real number should wind up as a real. But seeing that it does is a wondrous experience.

I would guess that if you interviewed the voters, you would find that those who voted for Maxwell's equations were scientists and engineers, who value usefulness. But those who voted for Euler's formula would be mostly mathematicians, who value beauty.

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