Shiing-Shen Chern

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Lore & Background

Shiing-Shen Chern worked with James Harris Simons on the theory of characteristic classes, eventually discovering the Chern–Simons secondary characteristic classes of 3-manifolds. This work contributed to the development of string theory by providing a theoretical framework to combine geometry and topology with quantum field theory. Later, mathematical physicist Albert Schwarz discovered early topological quantum field theory, 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. Chern's collaboration with Simons represents a key moment in the intersection of mathematics and theoretical physics.

Reader's Guide

Chern's significance in mathematics is highlighted by his collaboration with James Harris Simons on the Chern–Simons form. This work, which grew out of their work on the theory of characteristic classes, has had lasting impact on both mathematics and physics. The Chern–Simons form is used in topological quantum field theory and is related to the Yang-Mills functional on 4-manifolds. Chern's contributions to geometry and topology were recognized by the American Mathematical Society, which awarded the Oswald Veblen Prize in Geometry to Simons in 1976. Chern himself was elected to the U.S. National Academy of Sciences in 2014. His work continues to influence research in geometry, topology, and theoretical physics.

Did You Know?

• Chern developed the Chern–Simons form with James Harris Simons, which contributed to the development of string theory.
• The Chern–Simons form is related to the Yang-Mills functional on 4-manifolds and has had an effect on modern physics.
• Mathematical physicist Albert Schwarz discovered early topological quantum field theory, an application of the Chern–Simons form.
• Simons received the 1976 American Mathematical Society Oswald Veblen Prize in Geometry for contributions including the Chern–Simons work.
• Chern was elected to the U.S. National Academy of Sciences in 2014.

Mathematical Genius and the Chern–Simons Legacy

Simons' academic work centered on the geometry and topology of manifolds, a field where his contributions would ripple far beyond pure mathematics. His 1961 doctoral thesis at the University of California, Berkeley, supervised by Bertram Kostant, offered a fresh proof of Berger's classification of holonomy groups for Riemannian manifolds. Building on that foundation, he turned his attention to characteristic classes in collaboration with the renowned geometer Shiing-Shen Chern. Together they uncovered the Chern–Simons secondary characteristic classes of three-dimensional manifolds, a discovery that would later prove pivotal in physics. Mathematical physicist Albert Schwarz subsequently identified an early form of topological quantum field theory built directly on the Chern–Simons form, and the construction also connects to the Yang–Mills functional on four-manifolds. These contributions helped Simons earn the American Mathematical Society's Oswald Veblen Prize in Geometry in 1976, and in 2014 he was elected to the U.S. National Academy of Sciences. His theoretical framework for weaving geometry, topology, and quantum field theory together also left a lasting mark on the development of string theory.

Renaissance Technologies and the Quantitative Revolution

Simons' foray into finance began when he founded a hedge fund management firm initially called Monemetrics, which he later renamed Renaissance Technologies, headquartered in East Setauket, New York. His core insight was that the market data he was collecting could be modeled mathematically, so he assembled a team of mathematicians—including Leonard E. Baum and James Ax—to build those models. In 1988 the firm launched the Medallion Fund, a vehicle closed to outside investors that has since generated more than $100 billion in trading profits, translating to a 66.1 percent average gross annual return and a 39.1 percent net return over the 1988-to-2018 window. Renaissance also manages three open funds—RIEF, RIDA, and a global equity fund—that held roughly $55 billion in combined assets by April 2019. The extraordinary track record earned Simons the epithets "greatest investor on Wall Street" and "most successful hedge fund manager of all time." Even Edward Witten, the Princeton theoretical physicist, remarked on the astonishment of watching a top-tier mathematician dominate an entirely different arena. Simons was named Financial Engineer of the Year in 2006 and stepped back as active manager in January 2010, remaining as nonexecutive chairman.

Philanthropy and the Simons Foundation

In 1994, Simons and his wife Marilyn established the Simons Foundation, a philanthropic organization dedicated to advancing research in mathematics and the fundamental sciences. The foundation became the single largest benefactor of Stony Brook University, Marilyn's alma mater, and also made major contributions to MIT and the University of California, Berkeley, both of which were Simons' own academic homes. His board memberships spanned the Stony Brook Foundation, the MIT Corporation, and the Simons Laufer Mathematical Sciences Institute in Berkeley, while he personally chaired the boards of Math for America, the Simons Foundation, and Renaissance Technologies. In 2004 he founded Math for America, a nonprofit aimed at improving mathematics education in American public schools by recruiting better-qualified teachers. The foundation's most staggering gift came in 2023, when it donated $500 million to Stony Brook University—the second-largest single donation to a public university in U.S. history. In 2016 the International Astronomical Union honored him by naming asteroid 6618, originally spotted by Clyde Tombaugh in 1936, "Jimsimons" in recognition of his dual legacy in mathematics and giving.

Early Life, Education, and Pivotal Choices

James Harris Simons was born on April 25, 1938, the only child of Marcia Kantor and Matthew Simons, an American Jewish family in Brookline, Massachusetts. He earned a bachelor's degree in mathematics from MIT in 1958, completing the program in just three years, and followed it with a doctorate from UC Berkeley in 1961 at the age of twenty-three, working under Bertram Kostant. After leaving MIT he famously rode a motor scooter from Boston all the way to Bogotá, Colombia. His early career took him into national-security work: in 1964 he collaborated with the National Security Agency on code-breaking, and from 1964 to 1968 he served on the research staff of the Institute for Defense Analysis' Communications Research Division while teaching at MIT and Harvard. A brief attempt to launch a trading company called iStar with colleague Richard Leibler collapsed when management intervened. Simons was ultimately forced out of IDA because of his public opposition to the Vietnam War, after which he joined Stony Brook University, where he chaired the mathematics department from 1968 to 1978. In 1973, IBM recruited him to attack the Lucifer block cipher, a direct precursor to the Data Encryption Standard. He passed away on May 10, 2024, with an estimated net worth of $31.4 billion.