Leonard Gillman
Encyclopedia
Leonard E. "Len" Gillman (January 8, 1917 – April 7, 2009) was an American mathematician
, emeritus
professor at the University of Texas at Austin
. He was also an accomplished classical pianist
.
in 1917. His family moved to Pittsburgh, Pennsylvania
in 1922. It was there that he started taking piano
lessons at age six. They moved to New York City
in 1926, and he began intensive training as a pianist. Upon graduation from high school
in 1933, Gillman won a fellow
ship to the Juilliard Graduate School of Music
.
After one semester at Juilliard, he enrolled in evening classes in French
and mathematics
at Columbia University
. He received a diploma in piano from Juilliard in 1938, then continued his studies at Columbia, graduating with a B.S. in mathematics in 1941. He stayed on as a graduate student, and completed the coursework
for a mathematics Ph.D.
by 1943.
In 1943 Gillman accepted a position at Tufts College, working on a special project for the Navy Department. While there he wrote a thesis
based on their work on pursuit curves, and he received his master's degree
from Columbia in 1945. He moved to Washington, D.C.
where he continued doing Navy work for the Operations Evaluation Group (OEG), affiliated with the Massachusetts Institute of Technology
. After five years he took a one-year sabbatical at MIT to write a doctoral thesis. Originally he intended to it to be on game theory
, but he happened to read a book by Wacław Sierpiński and became suddenly interested in set theory
. With no specialists to advise him, Gillman wrote and published a paper that became his thesis: "On Intervals of Ordered Sets". He also sent the paper to Alfred Tarski
, beginning a correspondence that led Tarski to claim Gillman as "my Ph.D. by mail". In 1952 Gillman accepted an instructorship at Purdue University
, and in 1953 he finally received his Ph.D. in mathematics from Columbia.
At Purdue he began to do research in topology
, in collaboration with Melvin Henriksen, Meyer Jerison
, and others. This work concentrated on the ring
of all real
-valued continuous function
s whose domain
is a given topological space
. They explored the relationships between topological properties of the space and algebraic properties of the ring. Gillman & Henriksen defined and characterized the classes of P-spaces and F-spaces, and Gillman & Jerison published an entire textbook on the subject: Rings of Continuous Functions, ISBN 0387901981.
In 1958 Gillman was awarded a Guggenheim Fellowship
, and he spent the next two years as a visiting member at the Institute for Advanced Study
. He and former OEG colleague Nathan Fine
defined remote points and showed that if the continuum hypothesis
holds, then the real line
(or any separable Tychonoff space
that is not pseudocompact
) has remote points.
In 1960 he became chairman of the department of mathematics at the University of Rochester
. He was active in recruiting top mathematicians to the department, including Arthur Harold Stone
and his wife Dorothy Maharam
. At Rochester, Gillman also became involved in activities of the Mathematical Association of America
(MAA). In 1969 he was appointed a regional Associate Secretary of the American Mathematical Society
, but he had to give it up after moving to the University of Texas that same year. He chaired the UT mathematics department until 1973, when he was elected Treasurer
of the MAA. He held this office for 13 years. Gillman retired from UT in 1987 and served as President of the MAA for the term 1987–1988.
Gillman was involved in local classical music
everywhere he worked, and performed four times at the Joint Mathematics Meeting
, twice with William Browder
. Gillman died on April 7, 2009 in Austin, Texas
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, emeritus
Emeritus
Emeritus is a post-positive adjective that is used to designate a retired professor, bishop, or other professional or as a title. The female equivalent emerita is also sometimes used.-History:...
professor at the University of Texas at Austin
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
. He was also an accomplished classical pianist
Pianist
A pianist is a musician who plays the piano. A professional pianist can perform solo pieces, play with an ensemble or orchestra, or accompany one or more singers, solo instrumentalists, or other performers.-Choice of genres:...
.
Biography
Gillman was born in Cleveland, OhioCleveland, Ohio
Cleveland is a city in the U.S. state of Ohio and is the county seat of Cuyahoga County, the most populous county in the state. The city is located in northeastern Ohio on the southern shore of Lake Erie, approximately west of the Pennsylvania border...
in 1917. His family moved to Pittsburgh, Pennsylvania
Pittsburgh, Pennsylvania
Pittsburgh is the second-largest city in the US Commonwealth of Pennsylvania and the county seat of Allegheny County. Regionally, it anchors the largest urban area of Appalachia and the Ohio River Valley, and nationally, it is the 22nd-largest urban area in the United States...
in 1922. It was there that he started taking piano
Piano
The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...
lessons at age six. They moved to New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
in 1926, and he began intensive training as a pianist. Upon graduation from high school
High school
High school is a term used in parts of the English speaking world to describe institutions which provide all or part of secondary education. The term is often incorporated into the name of such institutions....
in 1933, Gillman won a fellow
Fellow
A fellow in the broadest sense is someone who is an equal or a comrade. The term fellow is also used to describe a person, particularly by those in the upper social classes. It is most often used in an academic context: a fellow is often part of an elite group of learned people who are awarded...
ship to the Juilliard Graduate School of Music
Juilliard School
The Juilliard School, located at the Lincoln Center for the Performing Arts in New York City, United States, is a performing arts conservatory which was established in 1905...
.
After one semester at Juilliard, he enrolled in evening classes in French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
. He received a diploma in piano from Juilliard in 1938, then continued his studies at Columbia, graduating with a B.S. in mathematics in 1941. He stayed on as a graduate student, and completed the coursework
Coursework
Coursework is the name for work carried out by students at university or middle/high school that contributes towards their overall grade, but which is assessed separately from their final exams. Coursework can, for example, take the form of experimental work, or may involve research in the...
for a mathematics Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
by 1943.
In 1943 Gillman accepted a position at Tufts College, working on a special project for the Navy Department. While there he wrote a thesis
Thesis
A dissertation or thesis is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings...
based on their work on pursuit curves, and he received his master's degree
Master's degree
A master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...
from Columbia in 1945. He moved to Washington, D.C.
Washington, D.C.
Washington, D.C., formally the District of Columbia and commonly referred to as Washington, "the District", or simply D.C., is the capital of the United States. On July 16, 1790, the United States Congress approved the creation of a permanent national capital as permitted by the U.S. Constitution....
where he continued doing Navy work for the Operations Evaluation Group (OEG), affiliated with the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
. After five years he took a one-year sabbatical at MIT to write a doctoral thesis. Originally he intended to it to be on game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, but he happened to read a book by Wacław Sierpiński and became suddenly interested in set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
. With no specialists to advise him, Gillman wrote and published a paper that became his thesis: "On Intervals of Ordered Sets". He also sent the paper to Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
, beginning a correspondence that led Tarski to claim Gillman as "my Ph.D. by mail". In 1952 Gillman accepted an instructorship at Purdue University
Purdue University
Purdue University, located in West Lafayette, Indiana, U.S., is the flagship university of the six-campus Purdue University system. Purdue was founded on May 6, 1869, as a land-grant university when the Indiana General Assembly, taking advantage of the Morrill Act, accepted a donation of land and...
, and in 1953 he finally received his Ph.D. in mathematics from Columbia.
At Purdue he began to do research in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, in collaboration with Melvin Henriksen, Meyer Jerison
Meyer Jerison
Meyer Jerison was an American mathematician known for his work in functional analysis and rings, and especially for collaborating with Leonard Gillman on one of the standard texts in the field: Rings of Continuous Functions.-Biography:...
, and others. This work concentrated on the ring
Ring (mathematics)
In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations usually called addition and multiplication, where the set is an abelian group under addition and a semigroup under multiplication such that multiplication distributes over addition...
of all real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
-valued continuous function
Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous".Continuity of...
s whose domain
Domain (mathematics)
In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined...
is a given topological space
Topological space
Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
. They explored the relationships between topological properties of the space and algebraic properties of the ring. Gillman & Henriksen defined and characterized the classes of P-spaces and F-spaces, and Gillman & Jerison published an entire textbook on the subject: Rings of Continuous Functions, ISBN 0387901981.
In 1958 Gillman was awarded a Guggenheim Fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
, and he spent the next two years as a visiting member at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
. He and former OEG colleague Nathan Fine
Nathan Fine
Nathan Jacob Fine was a mathematician who worked on basic hypergeometric series. He is best known for his lecture notes on the subject which for four decades served as an inspiration to experts in the field until they were finally published as a book...
defined remote points and showed that if the continuum hypothesis
Continuum hypothesis
In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1874, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900...
holds, then the real line
Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line is the set of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one...
(or any separable Tychonoff space
Tychonoff space
In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.These conditions are examples of separation axioms....
that is not pseudocompact
Pseudocompact space
In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded.-Properties related to pseudocompactness:...
) has remote points.
In 1960 he became chairman of the department of mathematics at the University of Rochester
University of Rochester
The University of Rochester is a private, nonsectarian, research university in Rochester, New York, United States. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The university has six schools and various interdisciplinary programs.The...
. He was active in recruiting top mathematicians to the department, including Arthur Harold Stone
Arthur Harold Stone
Arthur Harold Stone was a British mathematician born in London, who worked mostly in topology. His wife was American mathematician Dorothy Maharam...
and his wife Dorothy Maharam
Dorothy Maharam
Dorothy Maharam Stone is an American mathematician who made important contributions to measure theory. Her husband was British mathematician Arthur Harold Stone....
. At Rochester, Gillman also became involved in activities of the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
(MAA). In 1969 he was appointed a regional Associate Secretary of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, but he had to give it up after moving to the University of Texas that same year. He chaired the UT mathematics department until 1973, when he was elected Treasurer
Treasurer
A treasurer is the person responsible for running the treasury of an organization. The adjective for a treasurer is normally "tresorial". The adjective "treasurial" normally means pertaining to a treasury, rather than the treasurer.-Government:...
of the MAA. He held this office for 13 years. Gillman retired from UT in 1987 and served as President of the MAA for the term 1987–1988.
Gillman was involved in local classical music
Classical music
Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...
everywhere he worked, and performed four times at the Joint Mathematics Meeting
Joint Mathematics Meeting
The Joint Mathematics Meetings are a mathematics conference hosted annually in early January by the American Mathematical Society and the Mathematical Association of America . Frequently, several other national mathematics organizations also participate...
, twice with William Browder
William Browder (mathematician)
William Browder is an American mathematician, specializing in algebraic topology, differential topology and differential geometry...
. Gillman died on April 7, 2009 in Austin, Texas
Austin, Texas
Austin is the capital city of the U.S. state of :Texas and the seat of Travis County. Located in Central Texas on the eastern edge of the American Southwest, it is the fourth-largest city in Texas and the 14th most populous city in the United States. It was the third-fastest-growing large city in...
.