"Wave equations help describe waves of light, sound and water as they occur in physics. Also known as partial differential equations, or PDEs, they have valuable potential for predicting weather or earthquakes, or certain types of natural disasters. For example, during the late stages of a tsunami, they could help forecasters calculate when it will hit land. "PDEs are a big reason why math is useful," says Terence Tao.

Tao, a professor of mathematics at UCLA, is interested in the theoretical side of these equations, seeking to discover with computer algorithms whether they can behave in a way that typically is the opposite of what occurs in the real world. He wants to see whether they can "exhibit blowup," or, essentially, explode."

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