Why fuss over pure math?

When British mathematician Sir Andrew J. Wiles was awarded the Abel Prize Laureate in math on 15 March for cracking a centuries-old hypothesis, a friend asked me, "Why did he get the prize, and will this solve any real-world problem?" Quoting from the statement that the Norwegian Academy of Science and Letters gave to the press, I told him that 63-year-old Wiles had been given the annual award "for his stunning proof of (French mathematician Pierre de) Fermat's last theorem by way of the modularity conjecture for semi-stable elliptic curves, opening a new era in number theory". So let me try to simplify it a bit. Number theory--also sometimes referred to as the "queen of mathematics" or "higher arithmetic"--is a branch of pure math, devoted primarily to the study of the properties of whole numbers. Fermat--a prominent mathematician of the 17th century--contributed significantly to number theory, probability theory, analytic geometry and the early development of infinitesimal calculus. Fermat's last theorem states that no three positive integers a, b, and c satisfy the equation an bn cn for any integer value of n that is greater than two.