Gian-Carlo Rota
Encyclopedia
Gian-Carlo Rota was an Italian
-born American
mathematician
and philosopher.
, Italy
. Gian-Carlo's family left Italy when he was 13 years old, initially going to Switzerland.
Rota attended the Colegio Americano de Quito
in Ecuador
, and earned degrees at Princeton University
and Yale University
. Much of his career was spent as a professor at the Massachusetts Institute of Technology
, where he was and remains the only person ever to be appointed Professor of Applied Mathematics and Philosophy. Rota was also the Norbert Wiener
Professor of Applied Mathematics.
Rota was one of the teachers at MIT. He taught a difficult but very popular course in probability
, 18.313, which MIT has not offered again. He also taught 18.001 (Applications of Calculus), 18.03 (Differential Equations), and 18.315 (Combinatorial Theory
). His philosophy course in phenomenology was offered on Friday nights to keep the enrollment manageable. Among his many eccentricities, he would not teach without a can of Coca-Cola, and handed out prizes ranging from Hershey bars to pocket knives to students who asked questions in class or did well on tests.
Rota could be tempermental at times: in 1976, he abruptly stopped teaching 18.313 in mid-semester. He felt that some students in the class were being disrespectful to him. He arrived one day to class, passed out a long examination, and said that due to the students' behavior, he would not be returning to the class this semester. A junior faculty member was assigned by the math department to finish out the class.
From 1966 until his death he was a consultant at Los Alamos National Laboratory
, frequently visiting to lecture, discuss, and collaborate, notably with his friend Stan Ulam
.
He began his career as a functional analyst
, but changed directions and became a distinguished combinatorialist
. His series of ten papers on "Foundations of Combinatorics" in the 1960s is credited with making it a respectable branch of modern mathematics. He said that the one combinatorial idea he would like to be remembered for is the correspondence between combinatorial problems and problems of the location of the zeroes of polynomial
s. He worked on the theory of incidence algebra
s (which generalize the 19th-century theory of Möbius inversion
) and popularized their study among combinatorialists, set the umbral calculus
on a rigorous foundation, unified the theory of Sheffer sequences and polynomial sequence
s of binomial type, and worked on fundamental problems in probability theory
. His philosophical work was largely in the phenomenology of Edmund Husserl
.
He died in his sleep, after failing to arrive in Philadelphia for lectures he had planned to give on April 19, 1999.
A reading room (2-285) in MIT's Department of Mathematics
is dedicated to Rota.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
-born American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
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....
and philosopher.
Life
Rota was born in VigevanoVigevano
Vigevano is a town and comune in the province of Pavia, Lombardy, northern Italy, which possesses many artistic treasures and runs a huge industrial business. It is at the center of a district called Lomellina, a great rice-growing agricultural centre...
, Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
. Gian-Carlo's family left Italy when he was 13 years old, initially going to Switzerland.
Rota attended the Colegio Americano de Quito
Colegio Americano de Quito
The Colegio Americano de Quito is a secondary school in Quito, Ecuador. It was founded by former president of Ecuador Galo Plaza in 1940....
in Ecuador
Ecuador
Ecuador , officially the Republic of Ecuador is a representative democratic republic in South America, bordered by Colombia on the north, Peru on the east and south, and by the Pacific Ocean to the west. It is one of only two countries in South America, along with Chile, that do not have a border...
, and earned degrees at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
. Much of his career was spent as a professor at 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...
, where he was and remains the only person ever to be appointed Professor of Applied Mathematics and Philosophy. Rota was also the Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...
Professor of Applied Mathematics.
Rota was one of the teachers at MIT. He taught a difficult but very popular course in probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, 18.313, which MIT has not offered again. He also taught 18.001 (Applications of Calculus), 18.03 (Differential Equations), and 18.315 (Combinatorial Theory
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
). His philosophy course in phenomenology was offered on Friday nights to keep the enrollment manageable. Among his many eccentricities, he would not teach without a can of Coca-Cola, and handed out prizes ranging from Hershey bars to pocket knives to students who asked questions in class or did well on tests.
Rota could be tempermental at times: in 1976, he abruptly stopped teaching 18.313 in mid-semester. He felt that some students in the class were being disrespectful to him. He arrived one day to class, passed out a long examination, and said that due to the students' behavior, he would not be returning to the class this semester. A junior faculty member was assigned by the math department to finish out the class.
From 1966 until his death he was a consultant at Los Alamos National Laboratory
Los Alamos National Laboratory
Los Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico...
, frequently visiting to lecture, discuss, and collaborate, notably with his friend Stan Ulam
Stanislaw Marcin Ulam
Stanisław Marcin Ulam was a renowned mathematician of Polish-Jewish origin. He participated in America's Manhattan Project, originated the Teller–Ulam design of thermonuclear weapons, invented the Monte Carlo method of computation, and proposed the idea of nuclear pulse propulsion...
.
He began his career as a functional analyst
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, but changed directions and became a distinguished combinatorialist
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
. His series of ten papers on "Foundations of Combinatorics" in the 1960s is credited with making it a respectable branch of modern mathematics. He said that the one combinatorial idea he would like to be remembered for is the correspondence between combinatorial problems and problems of the location of the zeroes of polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s. He worked on the theory of incidence algebra
Incidence algebra
In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for any locally finite partially ordered setand commutative ring with unity.-Definition:...
s (which generalize the 19th-century theory of Möbius inversion
Möbius inversion formula
In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius. Other Möbius inversion formulas are obtained when different local finite partially ordered sets replace the classic case of the natural numbers ordered by...
) and popularized their study among combinatorialists, set the umbral calculus
Umbral calculus
In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to 'prove' them. These techniques were introduced by and are sometimes called Blissard's symbolic method...
on a rigorous foundation, unified the theory of Sheffer sequences and polynomial sequence
Polynomial sequence
In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial...
s of binomial type, and worked on fundamental problems in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. His philosophical work was largely in the phenomenology of Edmund Husserl
Edmund Husserl
Edmund Gustav Albrecht Husserl was a philosopher and mathematician and the founder of the 20th century philosophical school of phenomenology. He broke with the positivist orientation of the science and philosophy of his day, yet he elaborated critiques of historicism and of psychologism in logic...
.
He died in his sleep, after failing to arrive in Philadelphia for lectures he had planned to give on April 19, 1999.
A reading room (2-285) in MIT's Department of Mathematics
MIT Mathematics Department
The Department of Mathematics at the Massachusetts Institute of Technology is one of the leading mathematics departments in the USAand the world...
is dedicated to Rota.
See also
- Rota–Baxter algebraRota–Baxter algebraIn mathematics, a Rota–Baxter algebra is an algebra, usually over a field k, together with a particular k-linear map R which satisfies the weight-θ Rota–Baxter identity. It appeared first in the work of the American mathematician Glen Baxter in the realm of probability theory...
- List of American philosophers
- Joint spectral radiusJoint spectral radiusIn mathematics, the joint spectral radius is a generalization of the classical notion of spectral radius of a matrix, to sets of matrices. In recent years this notion has found applications in a large number of engineering fields and is still a topic of active research.-General description:The...
, introduced by Rota in the early 1960s
External links
- The Forbidden City of Gian-Carlo Rota (a memorial site) This page at www.rota.org was not originally intended to be a memorial web site, but was created by Rota himself with the assistance of his friend Bill Chen in January 1999 while Rota was visiting Los Alamos National Laboratory.
- Mathematics, Philosophy, and Artificial Intelligence: a dialogue with Gian-Carlo Rota and David Sharp
- "Fine Hall in its golden age: Remembrances of Princeton in the early fifties" by Gian-Carlo Rota.
- Tribute page by Prof. Catherine Yan (Texas A&M University), a former student of Rota
- Scanned copy of Gian-Carlo Rota's and Kenneth Baclawski's Introduction to Probability and Random Processes manuscript in its 1979 version.}}, ISBN 0-8176-3866-0; review at MAA.org
- The Digital Footprint of Gian-Carlo Rota: International Conference in memory of Gian-Carlo Rota, organized by the University of MilanUniversity of MilanThe University of Milan is a higher education institution in Milan, Italy. It is one of the largest universities in Europe, with about 62,801 students, a teaching and research staff of 2,455 and a non-teaching staff of 2,200....
(Italy)