Louis Nirenberg, a mathematician who explored the complexities of equations commonly used by physicists and engineers, and who shared the 2015 Abel Prize, a top math award modeled after the Nobels, died on Sunday in Manhattan. He was 94.

His death, at NewYork-Presbyterian Hospital/Columbia University Medical Center, was announced by New York University, where Dr. Nirenberg spent his entire academic career.

“It’s really hard to overstate how important” Dr. Nirenberg was, Walter A. Strauss, an emeritus professor of mathematics and applied mathematics at Brown University, said in a phone interview. “He was one of the great mathematicians of the 20th century.”

Dr. Nirenberg’s work focused on partial differential equations, which describe the vibrating of strings and drums, the flow of heat, the movement of water and many other phenomena.