×

A tale of mathematical myth-making: E. T. Bell and the ‘arithmetization of algebra’. (English) Zbl 1342.01022

Although most remembered for his dubious biographies of mathematicians, Bell specialized in algebra. This article focuses on his approach to abstraction in that area. The author supplies several examples from Bell’s expository writing that espouse the “modern” abstract viewpoint. But this paper contends that Bell was less aligned with contemporaries, such as Emmy Noether and Emil Artin, than with the postulate theorists of the preceding generation, like Huntington and Veblen. The author also sees the abstraction in Bell’s research as at times half-hearted, finding Bell ultimately to be more comfortable working in concrete settings.

MSC:

01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Bell, Eric Temple

References:

[1] Archibald Raymond Clare, Semicentennial addresses of the American Mathematical Society (1938)
[2] Bell E T, University of Washington Publications in Mathematics and Physical Science 1 pp 1– (1915)
[3] DOI: 10.1090/S0002-9947-1921-1501156-4 · JFM 48.0135.02 · doi:10.1090/S0002-9947-1921-1501156-4
[4] DOI: 10.1090/S0002-9947-1923-1501234-1 · doi:10.1090/S0002-9947-1923-1501234-1
[5] DOI: 10.1090/S0002-9947-1927-1501407-1 · doi:10.1090/S0002-9947-1927-1501407-1
[6] DOI: 10.2307/2298209 · JFM 53.0121.05 · doi:10.2307/2298209
[7] Bell E T, Algebraic arithmetic (American Mathematical Society Colloquium Publications, vol VII) (1927)
[8] DOI: 10.2307/2298430 · JFM 56.0150.01 · doi:10.2307/2298430
[9] DOI: 10.1090/S0002-9947-1931-1501623-X · doi:10.1090/S0002-9947-1931-1501623-X
[10] DOI: 10.2307/1968419 · Zbl 0001.11802 · doi:10.2307/1968419
[11] DOI: 10.1073/pnas.19.5.577 · Zbl 0007.00201 · doi:10.1073/pnas.19.5.577
[12] Bell E T, Men of mathematics (1937)
[13] DOI: 10.2307/2371481 · Zbl 0024.00203 · doi:10.2307/2371481
[14] Bell E T, The development of mathematics, 2. ed. (1945) · Zbl 0061.00101
[15] Bell E T, Mathematics: queen and servant of science (1952) · Zbl 0633.00001
[16] Boyer Carl B, A history of mathematics (1968)
[17] Cahen Eugene, Éléments de la théorie des nombres: congruences, formes quadratiques, nombres incommensurables, questions diverses (1900)
[18] Clifford A H, Arithmetic of ova (1933)
[19] Corry Leo, Modern algebra and the rise of mathematical structures, 2. ed. (1996) · Zbl 0858.01022
[20] Corry Leo, Modern Logic 8 (1) pp 5– (2000) · Zbl 1044.01008
[21] DOI: 10.1090/S0002-9947-1903-1500620-0 · doi:10.1090/S0002-9947-1903-1500620-0
[22] DOI: 10.1090/noti1009 · Zbl 1322.01045 · doi:10.1090/noti1009
[23] Grattan-Guinness I, The search for mathematical roots, 1870–1940: logics, set theories and the foundations of mathematics from Cantor through Russell to Gödel (2000) · Zbl 0962.03002
[24] DOI: 10.1080/17498430.2014.858202 · Zbl 1293.01012 · doi:10.1080/17498430.2014.858202
[25] Hollings Christopher, Mathematics across the Iron Curtain: a history of the algebraic theory of semigroups (History of Mathematics, vol 41) (2014) · Zbl 1317.20001
[26] DOI: 10.1090/S0002-9904-1902-00898-7 · JFM 33.0142.02 · doi:10.1090/S0002-9904-1902-00898-7
[27] DOI: 10.2307/2013678 · doi:10.2307/2013678
[28] Mac Lane, Saunders, ’Mathematics at the University of Chicago: a brief history’, in Duren, Peter (ed),A century of mathematics in America, Part II (History of Mathematics, vol 2), Providence, RI: American Mathematical Society, 1989, 127–154.
[29] DOI: 10.1090/S0002-9947-1902-1500616-8 · doi:10.1090/S0002-9947-1902-1500616-8
[30] Moore E H, General analysis (1935)
[31] DOI: 10.1080/00033798400200291 · Zbl 0556.01021 · doi:10.1080/00033798400200291
[32] Parshall Karen Hunger, Mathematics in Victorian Britain pp 339– (2011)
[33] Poole A R, Finite ova (1935)
[34] Reid Constance, The search for E. T. Bell, also known as John Taine (1993) · Zbl 0859.01015
[35] DOI: 10.2307/2695793 · Zbl 1067.01011 · doi:10.2307/2695793
[36] DOI: 10.2307/2320923 · Zbl 0499.01017 · doi:10.2307/2320923
[37] DOI: 10.2307/2275066 · Zbl 0739.01024 · doi:10.2307/2275066
[38] DOI: 10.1007/s11229-009-9667-9 · Zbl 1235.00015 · doi:10.1007/s11229-009-9667-9
[39] DOI: 10.1007/s004070050010 · Zbl 0890.01013 · doi:10.1007/s004070050010
[40] DOI: 10.2307/2323362 · Zbl 0561.01024 · doi:10.2307/2323362
[41] Ward Morgan, The foundations of general arithmetic (1928)
[42] Worth Carleton R, The subvarieties of a field (1933)
[43] Wussing Hans, Die Genesis des abstrakten Gruppenbegriffes: ein Beitrag zur Entstehungsgeschichte der abstrakten Gruppentheorie (1969)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.