Simons is known for his studies on pattern recognition. He also developed (with Shiing-Shen Chern) the Chern–Simons form, and contributed to the development of string theory by providing a theoretical framework to combine geometry and topology with quantum field theory. From 1968 to 1978, Simons was a mathematics professor and chairman of the mathematics department at Stony Brook University.
In 1994, Simons founded the Simons Foundation with his wife to support research in mathematics and fundamental sciences. He is one of the biggest donors to the University of California, Berkeley's Mathematical Sciences Research Institute where he also serves as a member of Board of Trustees, and established the Simons Institute for the Theory of Computing at Berkeley in 2012. In 2016, asteroid 6618 Jim Simons, discovered by Clyde Tombaugh in 1936, was named after Simons by the International Astronomical Union in honor of his contributions to mathematics and philanthropy
In 2008, he was inducted into Institutional Investors Alpha's Hedge Fund Manager Hall of Fame along with Alfred Jones, Bruce Kovner, David Swensen, George Soros, Jack Nash, Julian Roberston, Kenneth Griffin, Leon Levy, Louis Bacon, Michael Steinhardt, Paul Tudor Jones, Seth Klarman and Steven A. Cohen. A book about Simons and his investing methods, The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman (Penguin Group; 382pp), was released November 5, 2019. In 2018, Trinity College Dublin awarded him with an honorary doctorate.