Simons' mathematical work has primarily focused on the geometry and topology of manifolds. His 1962 Berkeley PhD thesis, written under the direction of Bertram Kostant, gave a new proof of Berger's classification of the holonomy groups of Riemannian manifolds. He subsequently began to work with Shing-Shen Chern on the theory of characteristic classes, eventually discovering the Chern–Simons secondary characteristic classes of 3-manifolds. Later, a mathematical physicist Albert Schwarz discovered early topological quantum field theory which is an application of the Chern–Simons form. It is also related to the Yang-Mills functional on 4-manifolds, and has had an effect on modern physics. These and other contributions to geometry and topology led to Simons becoming the 1976 recipient of the AMS Oswald Veblen Prize in Geometry. In 2014, he was elected to the National Academy of Sciences of the USA.

On July 22, 2014, Simons was subject to bipartisan condemnation by the U.S. Senate Permanent Subcommittee on Investigations for the use of complex basket options to shield day-to-day trading (usually subject to higher ordinary income tax rates) as long-term capital gains. "Renaissance Technologies was able to avoid paying more than $6 billion in taxes by disguising its day-to-day stock trades as long term investments," said Sen. John McCain (R., Ariz.), the committee's ranking Republican, in his opening statement.

In 2014, Simons reportedly earned US$1.2 billion including a share of his firm's management and performance fees, cash compensation and stock and option awards. According to Forbes magazine Simons had a net worth of $18 billion in 2017, making him #24 on the Forbes 400 richest people list. In 2018, he was ranked 23rd by Forbes, and in October 2019, his net worth was estimated to be $21.6 billion. In March 2019, he was named one of the highest-earning hedge fund managers and traders by Forbes.