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Errett Bishop
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Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) 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 Bishop was less than 4 years old, he influenced Bishop's eventual career by the math texts he left behind, which is how Bishop discovered mathematics. Bishop grew up in Newton, Kansas. Bishop 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. From 1965 until his death, he was professor at the University of California at San Diego.
Bishop's thoughts were started by two main events and they are mentioned during the conversation with Douglas S. Bridges. The events are retold by Bridges as follows:
"A burning question for me, as for many who have read his work, was 'How did Errett come to constructive mathematics in the first place?' He told me of two events that helped to precipitate him in that direction. The first was when he had been lecturing on truth tables in one of those low-level courses that he described unforgettably as 'mathematics for gracious living'. A couple of bright students had come to him after the lecture, to argue against his definition of (material) implication and in favour of the notion that the truth of the antecedent in some sense causes that of the consequent; this got Errett thinking about implication, a topic that bothered him right up to his death. The second event occurred in his own research in several complex variables, a subject in which he had a huge reputation before entering the constructive domain: in trying to visualise some hypersurfaces, he had come to the conclusion (perhaps through some kind of Brouwerian example?) that those surfaces could not be constructed in any real sense; from which he was led to ask what it meant to assert their existence."
Bishop's work falls into five categories:
In 1972, Bishop (with Henry Cheng) published Constructive Measure Theory.
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Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) 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 Bishop was less than 4 years old, he influenced Bishop's eventual career by the math texts he left behind, which is how Bishop discovered mathematics. Bishop grew up in Newton, Kansas. Bishop 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. From 1965 until his death, he was professor at the University of California at San Diego.
Bishop's thoughts were started by two main events and they are mentioned during the conversation with Douglas S. Bridges. The events are retold by Bridges as follows:
"A burning question for me, as for many who have read his work, was 'How did Errett come to constructive mathematics in the first place?' He told me of two events that helped to precipitate him in that direction. The first was when he had been lecturing on truth tables in one of those low-level courses that he described unforgettably as 'mathematics for gracious living'. A couple of bright students had come to him after the lecture, to argue against his definition of (material) implication and in favour of the notion that the truth of the antecedent in some sense causes that of the consequent; this got Errett thinking about implication, a topic that bothered him right up to his death. The second event occurred in his own research in several complex variables, a subject in which he had a huge reputation before entering the constructive domain: in trying to visualise some hypersurfaces, he had come to the conclusion (perhaps through some kind of Brouwerian example?) that those surfaces could not be constructed in any real sense; from which he was led to ask what it meant to assert their existence."
Bishop's work falls into five categories:
In 1972, Bishop (with Henry Cheng) published Constructive Measure Theory.