In 1967, Robert P. Langlands set out a road map to prove a “grand unified theory” that would tie together disparate areas of mathematics.

The conjectures of Dr. Langlands, now 81 and an emeritus professor at the Institute for Advanced Study in Princeton, N.J., have proven fertile ground for mathematical advances in the past half-century. And although his suppositions remain far from fully proven, the Norwegian Academy of Science and Letters announced on Tuesday that Dr. Langlands was this year’s winner of the Abel Prize, which many view as a Nobel Prize of mathematics.

“He’s a visionary,” said Sun-Yung Alice Chang, a mathematician at Princeton University who served on the five-member prize committee. The panel reviewed more than 100 candidates before selecting Dr. Langlands, Dr. Chang said.

There is no Nobel Prize in mathematics. (Contrary to myth, that is not because of an affair between a mathematician and Alfred Nobel’s wife. For one, Nobel never married.)