Christopher Hacon, a mathematician at the University of Utah, and James McKernan, a physicist at the University of California at San Diego, won this year's Breakthrough Prize in Mathematics for proving a long-standing conjecture about how many types of solutions a polynomial equation can have. Polynomial equations are mainstays of high-school algebra — expressions like `x^2+5x+6 = 1` — in which variables are raised to the whole number exponents and added, subtracted and multiplied. The mathematicians showed that even very complicated polynomials have just a finite number of solutions.

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