Leonard Carlitz (December 26, 1907 – September 17, 1999) was an American
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. Carlitz supervised 44 doctorates at
Duke University and published over 770 papers.
Chronology
* 1907 Born
Philadelphia, PA
Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...
, USA
* 1927 BA,
University of Pennsylvania
The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...
* 1930 PhD, University of Pennsylvania, 1930 under Howard Mitchell, who had studied under
Oswald Veblen
Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...
at
Princeton
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...
* 1930–31 at
Caltech
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
with
E. T. Bell
* 1931 married Clara Skaler
* 1931–32 at
Cambridge
Cambridge ( ) is a College town, university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cam ...
with
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
* 1932 Joined the faculty of Duke University where he served for 45 years
* 1938 to 1973 Editorial Board
Duke Mathematical Journal (Managing Editor from 1945.)
* 1939 Birth of son Michael
* 1940 Supervision of his first doctoral student E. F. Canaday, awarded 1940
* 1945 Birth of son Robert
* 1964 First
James B. Duke Professor in Mathematics
* 1977 Supervised his 44th and last doctoral student, Jo Ann Lutz, awarded 1977
* 1977 Retired
* 1990 Death of wife Clara, after 59 years of marriage
* 1999 September 17 Died in Pittsburgh, PA
Mathematical work
* The
Carlitz module is generalized by the
Drinfeld module In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of complex ...
*
An identity regarding
Bernoulli numbers
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...
* Carlitz wrote about
Bessel polynomials
* He introduced
Al-Salam–Carlitz polynomials.
*
Carlitz' identity for bicentric quadrilaterals
* He conjectured the
Carlitz-Wan conjecture, later proved by
Daqing Wan.
Publication
Leonard Carlitz published about 771 technical papers comprising approximately 7,000 pages. The effort to edit his collected works, undertaken originally by Professor John Brillhart, is ongoing.
[Joel V. Brawley, John Brillhart, and Henry W. Gould (editors), "The publications of Leonard Carlitz", ''Acta Arithmetica''. Vol. 152(2012), No. 4, 373–405. Annotated Catalogue of Carlitz's 773 publications.]
See also
*
Bateman polynomials
*
Carlitz exponential
In mathematics, the Carlitz exponential is a characteristic ''p'' analogue to the usual exponential function studied in real and complex analysis. It is used in the definition of the Carlitz module – an example of a Drinfeld module.
Definition
...
*
Carlitz polynomial (disambiguation)
*
Maillet's determinant
*
Reciprocal Fibonacci constant
The reciprocal Fibonacci constant, or ψ, is defined as the sum of the reciprocals of the Fibonacci numbers:
:\psi = \sum_^ \frac = \frac + \frac + \frac + \frac + \frac + \frac + \frac + \frac + \cdots.
The ratio of successive terms in this s ...
References
^ Joel V. Brawley, John Brillhart and Henry W. Gould, "Recollections of Leonard Carlitz", Acta Arithmetica, Vol. 152(2012), No. 4, 361–372.
^ Joel V. Brawley, John Brillhart, and Henry W. Gould (editors), "The publications of Leonard Carlitz", Acta Arithmetica. Vol. 152(2012), No. 4, 373–405. Annotated Catalogue of Carlitz's 773 publications.
*
*
*
*
External links
*Obituary a
Duke's Math Newsletter*
*
zbMATH.org author profile
{{DEFAULTSORT:Carlitz, Leonard
20th-century American mathematicians
Duke University faculty
University of Pennsylvania alumni
Institute for Advanced Study visiting scholars
Combinatorialists
1907 births
1999 deaths