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Errett Albert Bishop (1928-1983) was an American mathematician known for is work on analysis. He is the father of constructivist analysis, by virtue of his 1967 Foundations of constructive analysis, where he proved most of the important theorems in real analysis by constructive methods. 1928 (MCMXXVIII) was a leap year starting on Sunday (link will take you to calendar). ...
1983 (MCMLXXXIII) was a common year starting on Saturday of the Gregorian calendar. ...
This article is in need of attention from an expert on the subject. ...
In mathematics, constructive analysis is mathematical analysis done according to the principles of constructivist mathematics. ...
In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ...
A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ...
Real analysis is that branch of mathematical analysis dealing with the set of real numbers and functions of real numbers. ...
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct) a mathematical object to prove that it exists. ...
Life
Errett Bishop's father, Albert T Bishop, graduated from the United States Military Academy at West Point, ending his career as professor of mathematics at Wichita State University in Kansas. Although he died when Errett was only 5 years old, he influenced Errett's eventual career by the math texts he left behind, which is how Errett discovered mathematics. Errett grew up in Newton, Kansas. He and his sister were apparent math prodigies. The United States Military Academy, also known as West Point, or simply USMA or Army is a U.S. service academy and Army fort. ...
Alternate meanings: West Point (disambiguation). ...
Wichita State University (WSU), an American university, was founded as a Congregational institution in 1895. ...
Newton is a city and county seat of Harvey County, Kansas. ...
Bishop entered the University of Chicago in 1944, obtaining both the BS and MS in 1947. The doctoral studies he began in that year were interrupted by two years in the US Army, 1950-52, doing mathematical research at the National Bureau of Standards. He completed his Ph.D. in 1954 under Paul Halmos; his thesis was titled Spectral Theory for Operations on Banach Spaces. Paul Halmos Paul Richard Halmos (born March 3, 1916) is a Hungarian-born American mathematician who has done research in the fields of logarithm theory, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). ...
Bishop taught at the University of California, 1954-65. He spent the 1964-65 academic year at the Miller Institute for Basic Research in Berkeley. From 1965 until his death, he was professor at the University of California at San Diego. The University of California (UC) is a public university system in the state of California. ...
The University of California, San Diego (popularly known as UCSD) is a public, coeducational university located in La Jolla, California. ...
Work Bishop's wide-ranging work falls into five categories: - Polynomial and rational approximation. Examples are extensions of Mergelyan's approximation theorem and the theorem of Frigyes Riesz and Marcel Riesz concerning measures on the unit circle orthogonal to polynomials.
- The general theory of function algebras. Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures. Bishop wrote a 1965 survey "Uniform algebras," examining the interaction between the theory of uniform algebras and that of several complex variables.
- Banach spaces and operator theory, the subject of his thesis. He introduced what is now called the Bishop condition, useful in the theory of decomposable operators.
- The theory of functions of several complex variables. An example is his 1962 "Analyticity in certain Banach spaces." He proved important results in this area such as the biholomorphic embedding theorem for a Stein manifold as a closed submanifold in Cn, and a new proof of Remmert's proper mapping theorem.
- Constructive mathematics. Bishop become interested in foundational issues while at the Miller Institute. His now-famous Foundations of constructive analysis (1967) aimed to show that a constructive treatment of analysis is feasible, something about which Weyl had been pessimistic. A 1985 revision, called Constructive analysis, was completed with the assistance of Douglas Bridges.
In 1972, Bishop (with Henry Cheng) published Constructive measure theory. Frigyes Riesz Frigyes Riesz (January 22, 1880 – February 28, 1956) was a mathematician who was born in Győr, Austria-Hungary (now Hungary) and died in Budapest Hungary. ...
Marcel Riesz (November 16, 1886 – September 4, 1969) was a mathematician who was born in Györ, Austria-Hungary (now Hungary) and died in Lund in Sweden. ...
In functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. ...
In mathematics, Banach spaces, named after Stefan Banach who studied them, are one of the central objects of study in functional analysis. ...
In mathematics, operator theory is the branch of functional analysis which deals with bounded linear operators and their properties. ...
Complex analysis is the branch of mathematics investigating holomorphic functions, i. ...
In mathematics, a Stein manifold in the theory of several complex variables and complex manifolds is a closed, complex submanifold of the vector space of n complex dimensions. ...
This is a glossary of terms specific to differential geometry and differential topology. ...
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct) a mathematical object to prove that it exists. ...
Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ...
See also In mathematics, constructive analysis is mathematical analysis done according to the principles of constructivist mathematics. ...
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct) a mathematical object to prove that it exists. ...
Reference - Rosenblatt, M., ed., 1985. Errett Bishop: Reflections on him and his research. Proceedings of the memorial meeting for Errett Bishop held at the University of California-San Diego, September 24, 1983. Contemporary Mathematics 39. AMS.
Quotation - "(A) Mathematics is common sense;
- (B) Do not ask whether a statement is true until you know what it means;
- (C) A proof is any completely convincing argument;
- (D) Meaningful distinctions deserve to be preserved. " (from his 1973 Schizophrenia in contemporary mathematics, reprinted in Rosenblatt 1985)
External links - Biography of Errett Bishop
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