Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American

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 On ...

, was one of the founders of

symbolic Symbolic may refer to: * Symbol, something that represents an idea, a process, or a physical entity Mathematics, logic, and computing * Symbolic computation, a scientific area concerned with computing with mathematical formulas * Symbolic dynamic ...

and

topological dynamics In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology. Scope The central object of study in topol ...

Biography

Hedlund was born May 7, 1904, in

Somerville, Massachusetts Somerville ( ) is a city located directly to the northwest of Boston, and north of Cambridge, Massachusetts, Cambridge, in Middlesex County, Massachusetts, United States. As of the 2020 United States Census, the city had a total population of 81, ...

. He did his undergraduate studies at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, earned a master's degree 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 Manhatt ...

, and returned to Harvard for his doctoral studies. He was a student of

Marston Morse Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the ''calculus of variations in the large'', a subject where he introduced the technique of differential topology now known a ...

, under whose supervision he received a Ph.D. in 1930 with thesis entitled "I. Geodesics on a Two-Dimensional Riemannian Manifold with Periodic Coefficients II. Poincare's Rotation Number and Morse's Type Number"..G. A. Hedlund Papers, 1941-1945, 2008
Dolph Briscoe Center for American History, The University of Texas at Austin, retrieved 2011-09-10.. While still studying at Columbia, Hedlund taught at

Hunter College Hunter College is a public university in New York City. It is one of the constituent colleges of the City University of New York and offers studies in more than one hundred undergraduate and postgraduate fields across five schools. It also admi ...

, and after receiving his doctorate he took a position at

Bryn Mawr College Bryn Mawr College ( ; Welsh: ) is a women's liberal arts college in Bryn Mawr, Pennsylvania. Founded as a Quaker institution in 1885, Bryn Mawr is one of the Seven Sister colleges, a group of elite, historically women's colleges in the United St ...

, where he remained for nine years. From 1939 to 1948 he taught at the

University of Virginia The University of Virginia (UVA) is a Public university#United States, public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United S ...

, after which he moved to

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

. At Yale, he became the Philip Schuyler Beebe Professor of Mathematics, and chaired the mathematics department for ten years. He was also a member 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 ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

, which he visited in 1933, 1938, and 1953. He was the Director of IDA's Communications Research Division in Princeton 1962-1963. He retired from Yale in 1972, but afterwards held a visiting professorship at

Wesleyan University Wesleyan University ( ) is a Private university, private liberal arts college, liberal arts university in Middletown, Connecticut. Founded in 1831 as a Men's colleges in the United States, men's college under the auspices of the Methodist Epis ...

. Hedlund died in 1993. He has over 200 academic descendants, many of them through two of his students at Virginia,

Walter Gottschalk Walter Helbig Gottschalk (November 3, 1918 – February 15, 2004) was an American mathematician, one of the founders of topological dynamics. Biography Gottschalk was born in Lynchburg, Virginia, on November 3, 1918, and moved to Salem, Virginia a ...

and W. Roy Utz, Jr.

Research

One of Hedlund's early results was an important theorem about the

ergodicity In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies th ...

geodesic flow In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection ...

s. He also made significant contributions to

symbolic dynamics In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (e ...

, whose origins as a field of modern mathematics can be traced to a 1944 paper of Hedlund, and to

. The

Curtis–Hedlund–Lyndon theorem The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlun ...

, a topological characterization of

cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

, is named after Hedlund. Hedlund first published this theorem in 1969, crediting

Morton L. Curtis Morton Landers Curtis (November 11, 1921 – February 4, 1989) was an American mathematician, an expert on group theory and the William Lewis Moody, Jr., W. L. Moody, Jr. Professor of Mathematics at Rice University.

and

Roger Lyndon Roger Conant Lyndon (December 18, 1917 – June 8, 1988) was an American mathematician, for many years a professor at the University of Michigan.. He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation a ...

as co-discoverers. Hedlund was the co-author of the book ''Topological Dynamics'' (with

, American Mathematical Society, 1955).

Awards and honors

Hedlund was elected to

Sigma Xi Sigma Xi, The Scientific Research Honor Society () is a highly prestigious, non-profit honor society for scientists and engineers. Sigma Xi was founded at Cornell University by a junior faculty member and a small group of graduate students in 1886 ...

in 1943. In 1972, a conference on topological dynamics was held to honor Hedlund on the occasion of his retirement from Yale. The editor of the

festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the h ...

from the conference,

Anatole Beck Anatole Beck (19 March 1930 – 21 December 2014) was an American mathematician. Beck graduated from Stuyvesant High School in 1947, studied at Brooklyn College (Bachelor's degree 1951) and in 1956 received his PhD from Yale University under Shi ...

, wrote that it was "our token of respect to the man who did so much to foster and build this field"..

References

* {{DEFAULTSORT:Hedlund, Gustav Arnold 1904 births 1993 deaths 20th-century American mathematicians Harvard University alumni Columbia University alumni Hunter College faculty Bryn Mawr College faculty University of Virginia faculty Wesleyan University faculty Yale University faculty Symbolic dynamics Topological dynamics Cellular automatists 20th-century Swedish mathematicians American people of Swedish descent People from Somerville, Massachusetts Mathematicians from Massachusetts