The power and charm of mathematics and mathematicians: born out of “nothing”

James Harris Simons (April 25, 1938 — May 10, 2024) was an American hedge fund manager, mathematician, and philanthropist. He is the founder of Renaissance Technologies, a quantitative hedge fund headquartered in East Setauket, New York.

As we all know, he and his fund are quantitative investors, using mathematical models and algorithms to derive investment returns from inefficient markets. Due to the long-term total return on investment from Renaissance and its Medallion Fund, Simmons has been described as “Wall Street's greatest investor” and more specifically “the most successful hedge fund manager of all time.”

Simmons' net worth at the time of his death was estimated at $31.4 billion, making him the 51st richest person in the world.

Simmons is famous for his research on pattern recognition. He developed the Chen Shengshen-Simmons form (with Chen Shengshen) and contributed to the development of string theory by providing a theoretical framework combining geometry, topology, and quantum field theory.

Chan-Simmons theory is a Schwarz-style three-dimensional topological quantum field theory proposed by Edward Witten (Edward Witten). It was first discovered by mathematical physicist Albert Schwartz. It is named after mathematicians Shiing-Shen Chern (Shiing-Shen Chern) and James Harris Simons (James Harris Simons), who proposed the Chen Shengshen-Simmons 3 formula. In Chern-Simons theory, action is proportional to the integral of the Chern-Simons 3-form.

In condensed matter physics, the Chan-Simmons theory describes the topological order of fractional quantum Hall effect states. In mathematics, it has been used to calculate junction invariants and tri-manifold invariants, such as the Jones polynomial.

In particular, the Chan-Simmons theory is specified by selecting a simple Li group G (called the theoretical norm group) and a number called the theoretical energy level, which is a constant multiplied by the action. This effect is related to the specification, but the allocation function of quantum theory is clearly defined when the energy level is an integer and the strength of the specification field disappears at all boundaries of 3-dimensional space and time.

It is also a core mathematical object in the theoretical model of topological quantum computers (TQC). Specifically, SU (2) Chern-Simons theory describes TQC's simplest non-Abelian arbitrary submodel, the Yang-Lee-Fibonacci model.

The dynamics of Chan-Simmons theory on the two-dimensional boundary of 3-manifolds is closely related to the fusion rules and conformal blocks in conformal field theory, particularly WZW theory.

Chan-Simmons theory is a normative theory, which means that the classical configuration of M's canonical group G in Chan-Simmons theory is described by the main G complex on M. The connection of this complex is characterized by connecting a form A, which is assigned a value in the Lie algebra g of Lee group g. Generally speaking, connection A is defined only on each coordinate block, and A values on different blocks are associated through a mapping called a canonical transformation. They are characterized by the fact that the covariant derivative (the sum of the outer derivative operator d and connection A) is transformed in the accompanying representation of the specification group G. The covariant derivative and its own square can be interpreted as a g value 2-form F, called the curvature form or field strength. It is also transformed in the accompanying representation.

To quantify the Chan-Simmons theory prescriptively, we defined a state on each two-dimensional surface sigma in M. As with any quantum field theory, these states correspond to rays in Hilbert space. There is no preferred concept of time in Schwarz-type topology field theory, so it is possible to require σ to be a Cauchy surface; in fact, a state can be defined on any surface.

The cosdimension of sigma is 1, so M can be cut along sigma. After such a cut, M will be a bounded manifold; in particular, classically, the dynamics of Sigma will be described by the WZW model. Witten showed that this correspondence is even true in quantum mechanics. More accurately, he proved that Hilbert's state space is always finite dimensional and can be canonically equivalent to the conformal block space of k-level G WZW models.

For example, when Sigma is a 2-sphere, this Hilbert space is one-dimensional, and therefore has only one state. When sigma is a 2-ring surface, the state corresponds to an integrable representation of the affine Lie algebra corresponding to k grade g. For Witten's Chan-Simmons theoretical solution, there is no need to characterize conformal blocks of a higher genus.

In 1994, Simmons and his wife Marilyn founded the Simmons Foundation to support research in mathematics and basic science. The foundation is the top donor to Marilyn's alma mater, Stony Brook University, and a major donor to her alma mater, MIT and the University of California, Berkeley. Simmons is a board member of the Stony Brook Foundation, the Massachusetts Institute of Technology, and the Simmons Lauffer Institute for Mathematical Sciences in Berkeley, and the chairman of the board of directors of American Mathematics, Simmons Foundation, and Renaissance Technology. In 2023, the Simmons Foundation donated $500 million to Stony Brook University, the second-largest donation to a public university in US history.

In 2016, the International Astronomical Union named asteroid 6618 “Jim Simmons,” discovered by Clyde Tombaugh in 1936 and named after Simmons in recognition of his contributions to mathematics and philanthropy.

Chern-Simons theory (English: Chern-Simons theory), named after Chen Shengshen and James Harris Simmons, describes three-dimensional topological quantum field theory, and has many applications in physics. This theory uses the Chen-Simmons form.

Simmons is famous for his research on pattern recognition. He developed the Chen Shengshen-Simmons form (with Chen Shengshen) and contributed to the development of string theory by providing a theoretical framework combining geometry, topology, and quantum field theory. Simmons' mathematical work focused mainly on the geometry and topology of manifolds. His 1962 Berkeley doctoral dissertation, written under the direction of Bertram Kostant, provided new evidence for Berger's classification of complete groups of Riemann manifolds. Afterwards, he began to study the characteristic class theory with Chen Shengshen, and finally discovered the 3-form Chen Shengshen-Simmons secondary characteristic class. Later, mathematical physicist Albert Schwartz discovered the early topological quantum field theory, an application of the Chan-Simmons form. It is also related to the Young Mills function on the 4-manifold and has had an impact on modern physics. These and other contributions to geometry and topology made Simmons the recipient of the 1976 American Mathematical Society (AMS) Oswald Wiblen Geometry Prize. In 2014, he was elected a member of the US National Academy of Sciences.

In 1964, Simmons collaborated with the National Security Agency to decipher the code. From 1964 to 1968, he worked as a researcher at the Defense Analytical Research Institute (IDA's CRD) Communications Research Division and taught mathematics at MIT and Harvard University. Forced to leave IDA due to his public opposition to the Vietnam War, he later joined Stony Brook University to teach. From 1968 to 1978, he was the head of the Department of Mathematics at Stony Brook University. In 1973, IBM asked Simons to attack the packet password Lucifer, an early but direct pioneer of the Data Encryption Standard (DES). Simmons founded the non-profit organization Math for America in January 2004 with a mission to improve math education in American public schools by recruiting more highly qualified teachers.

For more than 20 years, the hedge funds of Renaissance Technology, a subsidiary of Simmons, have been trading in markets around the world, using mathematical models to analyze and execute transactions, many of which are automated. Renaissance uses computer-based models to predict price changes in financial instruments. These models are based on analyzing as much data as possible and then looking for non-random motion to make predictions.

Medallion is a major fund that is not open to outside investors and has earned over $100 billion in trading profits since its inception in 1988. This means that the average annual total return between 1988 and 2018 was 66.1%, and the average annual net return was 39.1%. Renaissance Technologies also manages three other funds — the Renaissance Institutional Equity Fund (RIEF), Renaissance Institutional Diversification Alpha (RIDA), and the Renaissance Institutional Diversification Global Equity Fund — which had combined assets of approximately $55 billion as of April 2019 and are open to outside investors.

Renaissance employs experts with non-financial backgrounds, including mathematicians, physicists, signal processing experts, and statisticians. The company's newest fund is the Renaissance Agency Equity Fund (RIEF). RIEF has historically lagged behind the company's more well-known Medallion Fund, which is a separate fund containing only the personal funds of the company's executives.

Edward Witten (Edward Witten), a physics professor at the Princeton Institute of Advanced Studies in New Jersey, said, “It's amazing to see such a very successful mathematician succeed in another field.” He is considered by many of his peers to be the most accomplished theoretical physicist today.

In 2006, Simmons was named Financial Engineer of the Year by the International Association of Financial Engineers. In 2020, his personal income was estimated at $2.6 billion, 2007 was $2.8 billion, 2006 was $1.7 billion, 2005 was $1.5 billion (the highest paid hedge fund manager in that year), and $670 million in 2004. On October 10, 2009, Simmons announced that he would retire on January 1, 2010, but will remain with Renaissance as a non-executive chairman.

According to reports, Simmons' revenue in 2014 was $1.2 billion, which included a portion of the company's management and performance fees, cash compensation, and stock and options incentives. According to Forbes magazine, Simmons' net worth reached $30 billion in 2023, ranking 25th on the Forbes list of the 400 richest people. In 2018, he was ranked 23rd on the Forbes list, and in October 2019, his net worth was estimated at $21.6 billion. In March 2019, he was named by Forbes as one of the highest paid hedge fund managers and traders.

Simmons avoids the spotlight and is rarely interviewed, citing Benjamin the Donkey from “Animal Farm” as explaining: “'God gave me a tail to drive away flies. But I'd rather have no tails and no flies. ' That's how I feel about the promotion.”

In 1996, his 34-year-old son Paul was hit and killed by a car while cycling on Long Island. In 2003, his 24-year-old son Nicholas drowned while traveling to Bali, Indonesia. His son Nat Simons (Nat Simons) is an investor and philanthropist, and his daughter Liz Simons (Liz Simons) is an educator and philanthropist.

Simmons owns a motor yacht called Archimedes. It was built by Dutch yacht manufacturer Royal Van Lent and delivered to Simmons in 2008. But Simmons wasn't wearing socks.

Simmons is a major contributor to the Democratic Political Action Committee. According to OpenSecrets, Simmons was ranked fifth in the 2016 election cycle as a federal candidate donor, behind Renaissance Technologies' co-CEO Robert Mercer (Robert Mercer), who ranked first and usually donates to the Republican Party. Simmons donated $7 million to Hillary Clinton's “America First Action,” $2.6 million to the House and Senate Majority Political Action Committee, and $500,000 to Emily's List. He also donated $25,000 to Republican Senator Lindsey Graham's Super Political Action Committee. Since 2006, Simmons has donated approximately $30.6 million to the federal election campaign. Renaissance Technologies has contributed $59,081,152 to the federal campaign since 1990, and spent $3,730,000 lobbying since 2001 until 2016.

In August 2020, Simmons donated $1.5 million to the Senate Majority Political Action Committee (the Democratic Party's Super Political Action Committee).

According to the Wall Street Journal in May 2009, Simmons was questioned by investors due to the huge performance gap in Renaissance Technology's portfolio. The Medallion Fund is exclusively open to current and former employees and their families. Despite its high costs, the 2008 fund rose 80%; the Renaissance Institutional Equity Fund (RIEF), which is held by outsiders, lost money in 2008 and 2009; and the RIEF fell 16% in 2008.

On July 22, 2014, Simmons was criticized by both parties by the US Senate Standing Investigation Subcommittee for using complex basket options to protect everyday transactions (which usually require higher ordinary income tax rates) as long-term capital. “By disguising its everyday stock transactions as long-term investments, Renaissance Technologies can avoid paying more than $6 billion in taxes,” the committee's Republican Senator John McCain (John McCain) said in his speech. Opening remarks.

According to an article published in the New York Times in 2015, Simmons was involved in one of the biggest tax wars of the year, and Renaissance Technology “is undergoing review by the US Internal Revenue Service (IRS) due to a loophole that saved their funds about $6.8 billion in taxes in 2015.” About ten years.” In September 2021, Simmons and his colleagues announced they would pay billions of dollars in taxes, interest, and fines to resolve the dispute, one of the biggest disputes in IRS history.

In total, Simmons has donated more than $4 billion to charity. Simmons and his wife Marilyn Hawrys Simons (Marilyn Hawrys Simons) co-founded the Simmons Foundation in 1994, a charitable organization that supports education and health-related projects in addition to scientific research. The Simons Foundation established the Simons Foundation Autism Research Program (SFARI) in 2003 as a scientific program in a series of Simmons Foundation programs. SFARI's mission is to improve understanding, diagnosis, and treatment of autism spectrum disorders.

Simmons founded Math for America in 2004, and the Simmons Foundation initially promised $25 million; he later doubled that commitment in 2006. The foundation continues to fund its operations, donating nearly $22 million in 2018.

Simmons was one of the biggest contributors to his undergraduate alma mater, MIT. The couple and their foundation funded the renovation of the math department building, named after them in 2016, and funded the Simmons Social Brain Center. Simmons is a lifelong honorary member of the Massachusetts Institute of Technology.

Simmons was a major donor to his alma mater, Berkeley. On July 1, 2012, the Simmons Foundation promised to provide Berkeley with 60 million US dollars to establish the Simmons Institute for Computational Theory, the world's leading cooperative research institution for theoretical computer science. In 2020, the foundation allocated a total of more than $46 million in individual grants to Berkeley to increase the Institute's donations and support its operations. In October 2023, the university announced that the Simmons Foundation would provide an additional $25 million to the college as a supporting commitment. Simmons and his wife also provided significant funding to Berkeley affiliates, particularly the Simons Slover Institute of Mathematical Sciences and the Berkeley Laboratory.

The Simons Foundation established the Flatiron Institute in 2016 to host 5 groups of computational scientists (60 or more doctoral researchers each). The Institute consists of four cores or departments: CCB (Center for Computational Biology), CCA (Center for Computational Astrophysics), CCQ (Center for Computational Quantum Mechanics), CCM (Center for Computational Mathematics), and CCN (Center for Computational Neuroscience). Located in Manhattan, the new research institute represents a major investment in basic computational science.

In honor of Paul (Paul), his son born to his first wife Barbara Simons (Barbara Simons), he founded Avalon Nature Preserve (Avalon Nature Preserve) in Stony Creek, a 130-acre (0.53 square kilometer) nature reserve. The Avalon Preserve was expanded to 216 acres in 2024.

Another son, Nick Simons (Nick Simons), drowned while traveling to Bali, Indonesia in 2003 and died at the age of 24. Nick used to work in Nepal. The Simmons family is a major donor of health care in Nepal through the Nick Simmons Institute.

In 2006, Simmons and his wife Marilyn donated $25 million to Stony Brook University through the Stony Brook Foundation, the largest donation in the history of the State University of New York at the time. On February 27, 2008, then-Governor Elliot Spitzer announced the Simmons Foundation's donation of 60 million US dollars to establish the Simmons Center for Geometry and Physics in Stony Brook, the largest donation to a public university in New York State history. In 2011, the couple broke that record again, donating $150 million to Stony Brook for medical science research, building a life science building, establishing a neuroscience research institute and bioimaging center, cancer and infectious disease research, 35 new professorships, and 40 graduate scholarships. To receive this donation, Stony Brook was allowed to raise annual tuition fees, in violation of traditional New York State policy. In 2023, the university announced that it had received a $500 million donation gift from the Simmons Foundation, the second-largest donation ever received by a public university.

Simmons died on May 10, 2024 in New York at the age of 86. He remained actively committed to the work of the Foundation until the end of his life. Simmons left behind a wife, three children, five grandchildren, and a great-grandchild.

In 2008, he was inducted into the Institutional Investors Alpha Hall of Fame for Hedge Fund Managers.

In 2006, he was named the “World's Smartest Billionaire” by the Financial Times.

He was elected a member of the American Philosophical Society in 2007. In 2011, he was selected as one of the 50 Most Influential People by Bloomberg Market Magazine.

Gregory Zuckerman (Gregory Zuckerman)'s book “The Market Solver: How Jim Simmons Launched a Quantitative Revolution” was published on November 5, 2019. He was awarded honorary doctorates from York University and York University in 2016, and Trinity College Dublin in 2018.