# Fuzzy Math? Imaginary numbers are just as real as any other digits; they just got some bad PR, and the term stuck, Assistant Professor Joan Lind argues.

Lind, a faculty member in the Department of Mathematics, explains that imaginary numbers stand for values we can’t ordinarily express with digits, namely the square root of a negative number (or the inverse: a number that, when squared, yields a negative number). Mathematicians can plug these variables into equations to map out shapes and patterns in two dimensions, as well as how these shapes can change over time.

“An equation would look like x + iy, where i is the imaginary number. You think of x and y being any of our normal numbers, like 2 or the square root of 5 or ?, and there are all sorts of things you can build in this form,” she says.

Lind, who received her PhD from the University of Washington, specializes in complex analysis and probability. At UT, she teaches classes on differential equations and other areas of math.

Complex analysis—a branch of mathematics that studies the use of complex numbers, both real and imaginary—can be used by physicists to study magnetic models and temperature changes, or it can be used to study polymer chains or crystal growth. Lind also works specifically with the Loewner differential equation, which is one method of modeling changing two-dimensional sets.

“The simplest way to think of it is that you’re growing a curve. It starts at some point, and as time evolves the curve keeps growing in two dimensions. The way it grows can be modeled by Loewner equations,” she explains.