Errett Albert Bishop (July 14, 1928 – April 14, 1983)[1] was an American mathematician known for his work on analysis. He is best known for developing constructive analysis in his 1967 Foundations of Constructive Analysis, where he proved most of the important theorems in real analysis using "constructivist" methods.
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 less than 4 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. Errett and his sister were apparent math prodigies.
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.
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. He was a visiting scholar at the Institute for Advanced Study in 1961–62.[2] From 1965 until his death, he was professor at the University of California at San Diego.
Bishop's work falls into five categories:
In 1972, Bishop (with Henry Cheng) published Constructive Measure Theory.
In the later part of his life, Bishop was seen as the leading mathematician in the area of constructivist mathematics. In 1966, he was invited to speak at the International Congress of Mathematicians on that theme. His talk was titled "The Constructivisation of Abstract Mathematical Analysis."[4] The American Mathematical Society invited him to give four hour-long lectures as part of the Colloquium Lectures series. The title of his lectures was "Schizophrenia of Contemporary Mathematics." Abraham Robinson wrote of Bishop's work in constructivist mathematics: "Even those who are not willing to accept Bishop's basic philosophy must be impressed with the great analytical power displayed in his work." [5] Robinson, however, wrote in his review of Bishop's book that Bishop's historical commentary is "more vigorous than accurate".
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