Sylvain Edward Cappell (born 1946), is a

Belgian American Belgian Americans are Americans who can trace their ancestry to people from Belgium who immigrated to the United States. While the first natives of the then-Southern Netherlands arrived in America in the 17th century, the majority of Belgian immi ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and former student of William Browder at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

, is a

topologist In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing h ...

who has spent most of his career at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

at NYU, where he is now the Silver Professor of Mathematics. He was born in

Brussels Brussels (french: Bruxelles or ; nl, Brussel ), officially the Brussels-Capital Region (All text and all but one graphic show the English name as Brussels-Capital Region.) (french: link=no, Région de Bruxelles-Capitale; nl, link=no, Bruss ...

, Belgium and immigrated with his parents to

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the U ...

in 1950 and grew up largely in this city. In 1963, as a senior at the

Bronx High School of Science The Bronx High School of Science, commonly called Bronx Science, is a public specialized high school in The Bronx in New York City. It is operated by the New York City Department of Education. Admission to Bronx Science involves passing the Sp ...

, he won first place in the

Westinghouse Science Talent Search Westinghouse may refer to: Businesses Current companies *Westinghouse Electric Corporation, the company that manages the Westinghouse brand, with licensees: **Westinghouse Electric Company, providing nuclear power-related services ** Westingho ...

for his work on "The Theory of Semi-cyclical Groups with Special Reference to Non-Aristotelian Logic." He then graduated from

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...

in 1966, winning the Van Amringe Mathematical Prize. He is best known for his "codimension one splitting theorem", which is a standard tool in high-dimensional

geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originat ...

, and a number of important results proven with his collaborator

Julius Shaneson Julius L. Shaneson (born July 24, 1944, Richmond, Virginia) is an American mathematician. He works at the University of Pennsylvania, where he was department chair from 2002 to 2006 and is currently the Class of 1939 Professor of Mathematics.

(now at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universit ...

). Their work includes many results in

knot theory In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

(and broad generalizations of that subject) and aspects of

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot the ...

. They gave the first nontrivial examples of topological conjugacy of linear transformations, which led to a flowering of research on the topological study of spaces with singularities. More recently, they combined their understanding of singularities, first to lattice point counting in polytopes, then to Euler-Maclaurin type summation formulae, and most recently to counting lattice points in the circle. This last problem is a classical one, initiated by

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

, and the paper is still being vetted by experts. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

. Cappell was elected and served as a vice president of the AMS for the term of February 2010 through January 2013. In 2018 he was elected to be a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...

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* * {{DEFAULTSORT:Cappell, Sylvain 1946 births Living people Belgian emigrants to the United States 20th-century American mathematicians 21st-century American mathematicians Topologists Columbia College (New York) alumni Princeton University alumni Courant Institute of Mathematical Sciences faculty Fellows of the American Mathematical Society Institute for Advanced Study visiting scholars Scientists from Brussels Sloan Research Fellows