James Waddell Alexander II (September 19, 1888 September 23, 1971) was a

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, structure, space, models, and change. History O ...

and

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 ...

of the pre-World War II era and part of an influential Princeton topology elite, which included

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was long ...

Solomon Lefschetz Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ...

, and others. He was one of the first members of the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

(1933–1951), and also a professor 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 nin ...

(1920–1951).

Early life, family, and personal life

James was born on September 19, 1888, in

Sea Bright, New Jersey Sea Bright is a borough in Monmouth County, New Jersey, United States. As of the 2010 United States Census, the borough's population was reflecting a decline of 406 (−22.3%) from the 1,818 counted in the 2000 Census, which had in turn increa ...

.Staff
''A COMMUNITY OF SCHOLARS: The Institute for Advanced Study Faculty and Members 1930–1980''
p. 43.

, 1980. Accessed November 20, 2015. "Alexander, James Waddell M, Topology Born 1888 Seabright, NJ." Alexander came from an old, distinguished Princeton family. He was the only child of the American portrait painter John White Alexander and Elizabeth Alexander. His maternal grandfather, James Waddell Alexander, was the president of the Equitable Life Assurance Society. Alexander's affluence and upbringing allowed him to interact with high society in America and elsewhere. He married Natalia Levitzkaja on January 11, 1918, a

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eight ...

n woman. Together, they had two children. They would frequently spend time, until 1937, in the

Chamonix Chamonix-Mont-Blanc ( frp, Chamôni), more commonly known as Chamonix, is a commune in the Haute-Savoie department in the Auvergne-Rhône-Alpes region of southeastern France. It was the site of the first Winter Olympics in 1924. In 2019, it had ...

area of France, where he would also climb mountains and hills. Alexander was also a noted

mountaineer Mountaineering or alpinism, is a set of outdoor activities that involves ascending tall mountains. Mountaineering-related activities include traditional outdoor climbing, skiing, and traversing via ferratas. Indoor climbing, sport climbing, an ...

, having succeeded in many major ascents, e.g. in the

Swiss Alps The Alpine region of Switzerland, conventionally referred to as the Swiss Alps (german: Schweizer Alpen, french: Alpes suisses, it, Alpi svizzere, rm, Alps svizras), represents a major natural feature of the country and is, along with the Swis ...

and Colorado

Rockies The Rocky Mountains, also known as the Rockies, are a major mountain range and the largest mountain system in North America. The Rocky Mountains stretch in straight-line distance from the northernmost part of western Canada, to New Mexico ...

. When in Princeton, he liked to climb the university buildings, and always left his office window on the top floor of

Fine Hall Fine may refer to: Characters * Sylvia Fine (''The Nanny''), Fran's mother on ''The Nanny'' * Officer Fine, a character in ''Tales from the Crypt'', played by Vincent Spano Legal terms * Fine (penalty), money to be paid as punishment for an off ...

open so that he could enter by climbing the building.

Education

He graduated from

with a Bachelor of Science degree in 1910. He received his Masters of Arts degree in 1911 and his doctoral degree in 1915.

Military career

During World War I, Alexander served with tech staff in the Ordnance Department of the United States Army overseas. He retired as a Captain.

Academic career

He was a pioneer in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...

, setting the foundations for

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

's ideas on

homology theory In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topolo ...

and furthering it by founding cohomology theory, which developed gradually in the decade after he gave a definition of

cochain In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of ...

. For this, in 1928 he was awarded the Bôcher Memorial Prize. He also contributed to the beginnings of

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 ...

by inventing the Alexander invariant of a knot, which in modern terms is a

graded module In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups R_i such that R_i R_j \subseteq R_. The index set is usually the set of nonnegative integers or the ...

obtained from the homology of a "cyclic covering" of the

knot complement In mathematics, the knot complement of a tame knot ''K'' is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is the 3-sphere minus the space near the knot. To make this precise, suppose that ''K'' is a ...

. From this invariant, he defined the first of the

polynomial knot invariant In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. History The first knot polynomial, the Alexander polynomial, was intro ...

s. With Garland Briggs, he also gave a combinatorial description of knot invariance based on certain moves, now (against the history) called the

Reidemeister move Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Götti ...

s; and also a means of computing homological invariants from the

knot diagram 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 ...

. Towards the end of his life, Alexander became a recluse. He was known as a socialist and his prominence brought him to the attention of McCarthyists. The atmosphere of the McCarthy era pushed him into a greater seclusion. He was not seen in public after 1954, when he appeared to sign a letter supporting

J. Robert Oppenheimer J. Robert Oppenheimer (; April 22, 1904 – February 18, 1967) was an American theoretical physicist. A professor of physics at the University of California, Berkeley, Oppenheimer was the wartime head of the Los Alamos Laboratory and is often ...

Death and legacy

He died on September 23, 1971. The Alexander's Chimney, in the

Rocky Mountain National Park Rocky Mountain National Park is an American national park located approximately northwest of Denver in north-central Colorado, within the Front Range of the Rocky Mountains. The park is situated between the towns of Estes Park to the east and ...

, is named after him.

References

Sources

* James, I. M., Portrait of Alexander (1888–1971), Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 2, 123–129. * Cohen, Leon W.
James Waddell Alexander (1888–1971)
Bull. Amer. Math. Soc. 79 (1973), no. 5, 900—903.

External links

*
Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructu ...

{{DEFAULTSORT:Alexander, James Waddell Alexander, Ii 1888 births 1971 deaths 20th-century American mathematicians Topologists Institute for Advanced Study faculty Princeton University faculty People from Sea Bright, New Jersey Princeton University alumni Mathematicians from New Jersey