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Robert Daniel Carmichael

January 20, 2023

"Robert Carmichael" redirects here. For the Scottish footballer, see Robert Carmichael (footballer).

Robert Daniel Carmichael (March 1, 1879 – May 2, 1967) was an American mathematician.

Robert D. Carmichael
Born(1879-03-01)March 1, 1879
Goodwater, Alabama, US
DiedMay 2, 1967(1967-05-02) (aged 88)
Merriam, Kansas, US
NationalityAmerican
Alma materPrinceton University
Lineville College
Scientific career
FieldsMathematics
InstitutionsUniversity of Illinois
Indiana University
Doctoral advisorG. D. Birkhoff
Doctoral studentsWilliam Martin

Biography

Carmichael was born in Goodwater, Alabama. He attended Lineville College, briefly, and he earned his bachelor's degree in 1898, while he was studying towards his Ph.D. degree at Princeton University. Carmichael completed the requirements for his Ph.D. in mathematics in 1911. Carmichael's Ph.D. research in mathematics was done under the guidance of the noted American mathematician G. David Birkhoff, and it is considered to be the first significant American contribution to the knowledge of differential equations in mathematics.

Carmichael next taught at Indiana University from 1911 to 1915. Then he moved on to the University of Illinois, where he remained from 1915 until his retirement in 1947.

Carmichael is known for his research in what are now called the Carmichael numbers (a subset of Fermat pseudoprimes, numbers satisfying properties of primes described by Fermat's Little Theorem although they are not primes), Carmichael's totient function conjecture, Carmichael's theorem, and the Carmichael function, all significant in number theory and in the study of the prime numbers. He found the smallest Carmichael number, 561, and over 50 years later, it was proven that there are infinitely many of them. Carmichael also described the Steiner system S(5,8,24) in his 1931 paper Tactical Configurations of Rank 2 and his 1937 book Introduction to the Theory of Groups of Finite Order, but the structure is often named after Ernst Witt, who rediscovered it in 1938.

While at Indiana University Carmichael was involved with the special theory of relativity.[1]

Mathematical publications

 
Wikisource has original works by or about:
Robert Daniel Carmichael
  • The Theory of Relativity, 1st edition, New York: John Wiley & Sons, Inc., pp. 74, 1913.
  • The Theory of Numbers, New York: John Wiley & Sons, Inc., pp. 94, 1914.[2]
  • Diophantine analysis, 1st edition, New York: John Wiley & Sons, Inc., pp. 118, 1915.[2]
  • The Theory of Relativity. 2nd edition, New York: John Wiley & Sons, Inc., pp. 112, 1920.[3]
  • A Debate on the Theory of Relativity, with an introduction by William Lowe Bryan, Chicago: Open Court Pub. CO., pp. 154, 1927.
  • The calculus, Robert D. Carmichael and James H. Weaver, Boston/New York: Ginn & company, pp. 345, 1927.
  • The Logic of Discovery, Chicago/London: Open Court Publishing CO., pp. 280, 1930;[4][5] Reprinted of Arno press, New York, 1975
  • Mathematical Tables and Formulas, Robert D. Carmichael and Edwin R. Smith, Boston: Ginn & company, pp. 269, 1931; Reprint of Dover Publications, Inc., New York, 1962.
  • The calculus, revised edition by Robert D. Carmichael, James H. Weaver and Lincoln La Paz, Boston/New York: Ginn & company, pp. 384, 1937.
  • Introduction to the Theory of Groups of finite order, Boston/New York: Ginn & company, pp. 447, 1937;[6] Reprint of Dover Publications, Inc., New York, 1956.

See also

Notes and references

  1. ^ For original papers on special theory of relativity see wikisource:Author:Robert Daniel Carmichael.
  2. ^ a b Dickson, L. E. (1916). "Review of The Theory of Numbers by R. D. Carmichael & Diophantine Analysis by R. D. Carmichael". Bull. Amer. Math. Soc. 22: 303–310. doi:10.1090/S0002-9904-1916-02783-2.
  3. ^ "Review: The Theory of Relativity by R. D. Carmichael, 2nd edition". The American Mathematical Monthly. 28: 175. April 1921. doi:10.2307/2972290. JSTOR 2972290.
  4. ^ Northrop, F. S. C. (1931). "Book Review: The Logic of Discovery". Bulletin of the American Mathematical Society. 37 (11): 807–809. doi:10.1090/S0002-9904-1931-05262-9.
  5. ^ Dubs, Homer H. (1931). "Reviewed work: The Logic of Discovery by R. D. Carmichael". The Journal of Philosophy. 28 (23): 637–639. doi:10.2307/2015687. JSTOR 2015687.
  6. ^ Weisner, Louis (1938). "Book Review: Introduction to the Theory of Groups of Finite Order". Bulletin of the American Mathematical Society. 44 (3): 178–179. doi:10.1090/S0002-9904-1938-06700-6.

External links

January 20, 2023
robert, daniel, carmichael, robert, carmichael, redirects, here, scottish, footballer, robert, carmichael, footballer, march, 1879, 1967, american, mathematician, robert, carmichaelborn, 1879, march, 1879goodwater, alabama, usdiedmay, 1967, 1967, aged, merriam. Robert Carmichael redirects here For the Scottish footballer see Robert Carmichael footballer Robert Daniel Carmichael March 1 1879 May 2 1967 was an American mathematician Robert D CarmichaelBorn 1879 03 01 March 1 1879Goodwater Alabama USDiedMay 2 1967 1967 05 02 aged 88 Merriam Kansas USNationalityAmericanAlma materPrinceton UniversityLineville CollegeScientific careerFieldsMathematicsInstitutionsUniversity of IllinoisIndiana UniversityDoctoral advisorG D BirkhoffDoctoral studentsWilliam Martin Contents 1 Biography 2 Mathematical publications 3 See also 4 Notes and references 5 External linksBiography EditCarmichael was born in Goodwater Alabama He attended Lineville College briefly and he earned his bachelor s degree in 1898 while he was studying towards his Ph D degree at Princeton University Carmichael completed the requirements for his Ph D in mathematics in 1911 Carmichael s Ph D research in mathematics was done under the guidance of the noted American mathematician G David Birkhoff and it is considered to be the first significant American contribution to the knowledge of differential equations in mathematics Carmichael next taught at Indiana University from 1911 to 1915 Then he moved on to the University of Illinois where he remained from 1915 until his retirement in 1947 Carmichael is known for his research in what are now called the Carmichael numbers a subset of Fermat pseudoprimes numbers satisfying properties of primes described by Fermat s Little Theorem although they are not primes Carmichael s totient function conjecture Carmichael s theorem and the Carmichael function all significant in number theory and in the study of the prime numbers He found the smallest Carmichael number 561 and over 50 years later it was proven that there are infinitely many of them Carmichael also described the Steiner system S 5 8 24 in his 1931 paper Tactical Configurations of Rank 2 and his 1937 book Introduction to the Theory of Groups of Finite Order but the structure is often named after Ernst Witt who rediscovered it in 1938 While at Indiana University Carmichael was involved with the special theory of relativity 1 Mathematical publications Edit Wikisource has original works by or about Robert Daniel Carmichael The Theory of Relativity 1st edition New York John Wiley amp Sons Inc pp 74 1913 The Theory of Numbers New York John Wiley amp Sons Inc pp 94 1914 2 Diophantine analysis 1st edition New York John Wiley amp Sons Inc pp 118 1915 2 The Theory of Relativity 2nd edition New York John Wiley amp Sons Inc pp 112 1920 3 A Debate on the Theory of Relativity with an introduction by William Lowe Bryan Chicago Open Court Pub CO pp 154 1927 The calculus Robert D Carmichael and James H Weaver Boston New York Ginn amp company pp 345 1927 The Logic of Discovery Chicago London Open Court Publishing CO pp 280 1930 4 5 Reprinted of Arno press New York 1975 Mathematical Tables and Formulas Robert D Carmichael and Edwin R Smith Boston Ginn amp company pp 269 1931 Reprint of Dover Publications Inc New York 1962 The calculus revised edition by Robert D Carmichael James H Weaver and Lincoln La Paz Boston New York Ginn amp company pp 384 1937 Introduction to the Theory of Groups of finite order Boston New York Ginn amp company pp 447 1937 6 Reprint of Dover Publications Inc New York 1956 See also EditPseudoprimesNotes and references Edit For original papers on special theory of relativity see wikisource Author Robert Daniel Carmichael a b Dickson L E 1916 Review of The Theory of Numbers by R D Carmichael amp Diophantine Analysis by R D Carmichael Bull Amer Math Soc 22 303 310 doi 10 1090 S0002 9904 1916 02783 2 Review The Theory of Relativity by R D Carmichael 2nd edition The American Mathematical Monthly 28 175 April 1921 doi 10 2307 2972290 JSTOR 2972290 Northrop F S C 1931 Book Review The Logic of Discovery Bulletin of the American Mathematical Society 37 11 807 809 doi 10 1090 S0002 9904 1931 05262 9 Dubs Homer H 1931 Reviewed work The Logic of Discovery by R D Carmichael The Journal of Philosophy 28 23 637 639 doi 10 2307 2015687 JSTOR 2015687 Weisner Louis 1938 Book Review Introduction to the Theory of Groups of Finite Order Bulletin of the American Mathematical Society 44 3 178 179 doi 10 1090 S0002 9904 1938 06700 6 External links EditWorks by Robert Daniel Carmichael at Project Gutenberg Works by or about Robert Daniel Carmichael at Internet Archive O Connor John J Robertson Edmund F Robert Daniel Carmichael MacTutor History of Mathematics archive University of St Andrews Robert Daniel Carmichael at the Mathematics Genealogy Project MAA presidents Robert Daniel Carmichael Retrieved from https en wikipedia org w index php title Robert Daniel Carmichael amp oldid 1092168442, wikipedia, wiki, book, books, library,

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