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, mathematical structure, structure, space, Mathematica ...

and topologist 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 lo ...

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

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

(1933–1951), and also a professor at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

(1920–1951).

Early life, family, and personal life

James was born on September 19, 1888, in Sea Bright, New Jersey. 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 country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

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

Chamonix Chamonix-Mont-Blanc (; ; (no longer in use)), more commonly known simply as Chamonix (), is a communes of France, commune in the departments of France, department in the regions of France, region in Southeastern France. It was the site of the f ...

area of

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

, where he would also climb mountains and hills. Alexander was also a noted mountaineer, having succeeded in many major ascents, e.g. in the

Swiss Alps The Alps, Alpine region of Switzerland, conventionally referred to as the Swiss Alps, represents a major natural feature of the country and is, along with the Swiss Plateau and the Swiss portion of the Jura Mountains, one of its three main Physica ...

and Colorado Rockies. When in Princeton, he liked to climb the university buildings, and always left his office window on the top floor of Fine Hall 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 invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

, setting the foundations for

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

's ideas on

homology theory In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the term is to take the ''homology of a chain complex'', resulting in a sequence of abelian grou ...

and furthering it by founding cohomology theory, which developed gradually in the decade after he gave a definition of cochain. For this, in 1928 he was awarded the

Bôcher Memorial Prize The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five yea ...

. He also contributed to the beginnings of

knot theory In topology, knot theory is the study of knot (mathematics), 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 be und ...

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

graded module Grade most commonly refers to: * Grading in education, a measurement of a student's performance by educational assessment (e.g. A, pass, etc.) * A designation for students, classes and curricula indicating the number of the year a student has reac ...

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 invariants. With Garland Briggs, he also gave a combinatorial description of knot invariance based on certain moves, now (against the history) called the Reidemeister moves; and also a means of computing homological invariants from the knot diagram. Alexander was an elected member of both the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

and the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) 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, and other ...

. 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.

Death and legacy

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

Rocky Mountain National Park Rocky Mountain National Park is a List of national parks of the United States, national park of the United States located approximately northwest of Denver in north-central Colorado, within the Front Range of the Rocky Mountains. The park is s ...

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