One of the perplexing problems confronting early mathematicians involved the imaginary number i, which represents the square root of -1. Mathematicians had been able to conceive of real numbers as points on a line. Addition, subtraction, multiplication, and division could then be interpreted as movements along that line. But complex numbers of the form a + bi could not be located along the line and thus had no geometric interpretation. A possible solution to this problem had been suggested in a remarkable paper by the Danish surveyor and mathematician Caspar Wessel (1745-1818) in 1798. Wessel proposed that a complex number be represented by a pair of lines at an angle to each other, one representing the real part of the number (a) and the other representing the imaginary part (bi). A third line joining these two could then represent the complex number. Unfortunately, Wessel's paper was published in an obscure...