# Carol Ruth Karp

### Quick Info

Born
10 August 1926
Forest Grove, Ottawa County, Michigan, USA
Died
20 August 1972
Arlington, Virginia, USA

Summary
Carol Karp was an American mathematical logician whose research was closely linked to algebra. She made a reputation both as a teacher and researcher, and she was undertaking important work on infinitary logic and recursion theory when she died at the age of 46.

### Biography

Carol Karp was born Carol Ruth van der Velde or Carol Ruth Vander Velde. Her parents were Peter Nelson Vander Velde (15 December 1901 - 8 September 1980) and Janet Lucy Keizer (7 January 1900 - 4 November 1949). Peter Vander Velde, originally named Pieter van der Velde, was the son of Weybe van der Velde and Nellie Stoel. He was baptised into the Dutch Christian Reformed Church on 10 April 1902, becoming a member on 11 June 1906. He married Janet Keizer in Ottawa, Kent, Michigan on 24 June 1925. Janet Keizer had been born in Forest Grove, Ottawa County, Michigan, the daughter of Cyrus Keizer and Renzena Strick. Peter Vander Velde was a fertiliser salesman at the time of the 1930 census living in Jamestown, Ottawa County, Michigan, and manager of Sunshine Stores, a feed and grain store in Alliance, Stark, Ohio, at the time of the 1940 census [4]:-
Both of [Carol's] parents had strong family ties to the conservative and devout Dutch farming community centred around Holland, Michigan.
Carol had a brother Wallace Earl Vander Velde (born in 1929). He was awarded B.Sc. in aero engineering from Purdue University in 1951, and a Ph.D. from the Massachusetts Institute of Technology in 1956 for his thesis A Nonlinear Method of Automatic Control in the Presence of Random Noise. He joined the faculty of the Massachusetts Institute of Technology in 1957 becoming professor of aeronautics and astronautics there in 1965. He died on 16 May 2019. Carol also had a brother Myron Dale Vander Velde (born 11 March 1939), known as Mike, who was awarded a degree in electrical engineering from Michigan State University in 1966. He became the manager of a computer centre and died on 6 August 2000 in Newport, Cocke County, Tennessee.

Having given some information about Carol's parents and her brothers, let us return to her biography. The family lived in Forest Grove for the first eleven years of her life and she attended a small school with only three rooms, each room having pupils from four of five different grades. When she was eleven, the family moved to Alliance, Ohio, where Carol attended Alliance High School. Home life, however, was rather restricted as she was growing up [4]:-
Even away from the Dutch community in Michigan, [Carol's] teenage activities were subject to the severe restrictions of the Dutch Reformed Church: dancing and movie-going were strictly forbidden, and card-playing was frowned upon.
We can see that Carol was a very successful student at Alliance High School from information in Red and Blue, the Alliance High School student newspaper. Her name appears in 31 of the Red and Blue newspapers between 1942 and 1944, see [9]. We learn that, among other things, she became an officer of the Latin Club (6 March 1942), entered the Columbus instruments contest (24 April 1942), served as Program Chairman of the Latin Club (22 May 1942), became a new member of the Fine Arts Club (9 October 1942), became a new member of the Blue Domino Club (12 March 1943), was a member of a string quartet performing Hungarian Dance No 5 (30 April 1943), was selected for the National Honor Society (28 May 1943), was elected secretary of the Forum Club (1 October 1943), was elected secretary of the Fine Arts Club (11 February 1944), took part in District Scholarship Tests (10 March 1944), performed in the play by George S Kaufman and Moss Hart "The Man Who Came to Dinner" (24 March 1944), took part in a string trio at Fine Arts' assembly and was first viola at the Mount Union Music Festival (5 May 1944), was received into the National Thespian Honor Society (19 May 1944), and came 14th in English in the District Scholarship Test (2 June 1944).

The most impressive activity reported in Red and Blue, however, was her success in the "Quiz Kid" competition. See the reports at THIS LINK.

Carol graduated from Alliance High School in 1944. The report on her High School years described her as:-
The girl who knows all the answers.
In the summer of 1945 the Vander Velde family moved from Alliance to Bremen, Indiana [4]:-
[Carol's] parents were not educated beyond high school, but they encouraged their children to pursue a college education.
She attended Manchester College in North Manchester, Indiana, abut 65 km south east of Bremen. This small college, run by the United Brethren Church, had been founded in 1860. She received her BA from there in 1948. Also in 1948 the Vander Velde family moved from Bremen, Indiana, to Ionia, Grand Rapids, Michigan. Around the same time Carol moved to Michigan too, enrolling for a Master's degree at Michigan State College (now Michigan State University) in East Lansing.

Her Master's Degree in mathematics was obtained two years later, in 1950, from Michigan State University and, following this, she spent the summer as an instructor at Michigan State University, and then for a time travelled around the United States as a violinist in an all-female orchestra. She then continued her studies at the University of Southern California, enrolling a postgraduate student in 1951. On 21 June 1952 she married Arthur Louis Karp in Los Angeles, California. Arthur Karp (1930-2020) had been born in the Bronx, New York City on 20 June 1930. He received a B.S. in Physics from the Massachusetts Institute of Technology, an M.S. in Mathematics from New Mexico State University, then studied Mathematics at the University of California (Berkeley). After qualifying as a Doctor of Jurisprudence from Georgetown University Law Center he served in the United States Army Signal Corps Agency followed by a post as a Systems Analyst at the Center for Naval Analyses. After her marriage to Arthur Karp, Carol was known as Carol Karp.

Her doctoral thesis was on mathematical logic. The thesis, Languages with expressions of infinite length, was supervised by Leon Henkin (1921-2006) and submitted to the University of Southern California in 1959. It was examined by Henkin and Henry Abel Dye (1926-1986). However Karp was teaching several years before the award of her Ph.D. having accepted a position as instructor at New Mexico College of Agriculture and Mechanic Arts in 1953. In 1960 the name of the New Mexico College of Agriculture and Mechanic Arts was changed to its present name of New Mexico State University. Karp spent a year at the College in Las Cruces, New Mexico.

Her thesis advisor had moved to Berkeley in 1953 and Karp was appointed as a teaching assistant there from 1954 to 1956 while she worked on her doctoral thesis [3]:-
In the fall of 1956 Henkin and Alfred Tarski organised a seminar at Berkeley on infinitary logic, where Karp presented her work on the syntax of predicate logic with infinitely long expressions. While other logicians had previously used expressions of infinite length, hers was the first comprehensive work on the extension of first order logic to languages that allow infinite conjunctions and disjunctions, as well as quantification over infinite sets of variables.
In 1957, she moved to Japan with her husband who, as we have indicated above, was in the US Navy. On her return from Japan, Karp accepted a post as an instructor at the University of Maryland. Before she submitted her thesis, Karp published four abstracts in Volume 5 of the Notices of the American Mathematical Society. Two had the title Formalizations of functional languages with wffs of infinite length, and the other two were Formalisms for $P_{\alpha}, F_{\alpha\beta}$ and $\alpha$-complete Boolean algebras, and Split semantic models.

Soon after the award of her doctorate Karp was promoted, in 1960, to assistant professor at the University of Maryland. She was to remain at the University of Maryland until her early death from cancer in 1972 but there she was promoted again, to associate professor in 1963 and then to full professor in 1966. Tiffany Wayne writes [11]:-
Her work was internationally recognised, and she was able to recruit other faculty [such as James Owings and Edgar G K López-Escobar] and a steady stream of graduate students [R J Gauntt, J Gregory, J Green, and E Cunningham] to the University of Maryland. She was instrumental in bringing several important participants to the colloquia that she sponsored, and she and he husband even had a home with an extra apartment in which visiting logicians were frequently housed.
We have seen that Karp was a mathematical logician but, as noted in [6], her work was closely related to algebra:-
Karp considered herself to be principally an 'algebraic logician'. Her inclination towards algebra was never completely forgotten and she always seemed to draw results concerning Boolean algebras from her results about infinitary languages.
In 1962 she published the paper Independence Proofs in Predicate Logic with Infinitely Long Expressions. Karp writes in the introduction to the paper:-
The systems of predicate logic considered here are extension first-order predicate logic. They were obtained by first admitting infinite conjunctions, disjunctions, and quantifications into formulas, and then adjusting the axiom schemata and rules of inference to accommodate them. In this paper, only systems with formulas of denumerable length and "formal proofs" with denumerably many steps will be discussed, though such restrictions are hardly essential. A precise treatment of these and other systems appears in the author's doc dissertation, Languages with expressions of infinite length, presented to the faculty of the University of Southern California in partial fulfilment of requirements for the Ph.D. degree. It is being prepared for publication in monograph form. The author wishes to thank her thesis supervisor, Professor Leon Henkin, for his encouragement and support over the years, as well as for specific suggestions relating to this paper. Thanks are due also to Professor Alfred Tarski for suggestions offered when an early version of some of this material was presented at a seminar in Berkeley in 1956. This paper was prepared with the aid of a faculty grant from the University of Maryland, and National Science Foundation grant GI 1294.
In 1964 she published a book on her research Languages with expressions of infinite length. You can read the Preface of that work at THIS LINK.

She had hoped to write another work which would take her ideas considerably further. She lectured on this later work as described in [6]:-
Karp did give lectures at Maryland in the Fall of 1970 on infinitary logic and recursion theory. Basically Karp wanted to return to Gödel's original proof-theoretic definitions of recursive sets but of course using more liberal notions of proof so as to obtain generalisations of recursion theory.
Edgar G K Lopez-Escobar writes in [7]:-
Carol Karp died on August 20, 1972 after a brave battle against cancer which had lasted for three long years. To her, teaching had always been more than a duty, and even during her illness she taught all her classes in addition to carrying out her administrative tasks. Her research, too, was pushed forward with her usual determination, but unfortunately the planned new monograph on infinitary languages remained unfinished. Her early work was collected in her one published book, but she realised that it very much needed to be brought up to date. Towards the end she was rather apprehensive that her doctoral students would not be able to complete their studies; but her fears were unfounded ... To them as to us the memory of the conduct of her life, exceptional spirit and warm personality persists as a lasting inspiration. The new book was intended for the Springer series 'Perspectives in Mathematical Logic'. Carol Karp was in the habit of doing most of her own research work during the summer months. Unfortunately the necessary treatment in 1972 left her exhausted and vulnerable to virus infections, so that there was barely time for her to organise the material for the beginning chapters. The final chapter was to be based on her lectures Generalized Recursion Theories at the Manchester Summer School (1969, unpublished), and from her notes it is apparent that she viewed it as the greatest contribution of the monograph. The gist of the programme was to show that the most natural way of generalising recursion theory was through representability in formal theories with infinitely long formulas.
It was both as a teacher and researcher that Karp made her reputation. She cared personally for her students and worried greatly for their futures during her illness.

Judy Green, who was one of Karp's doctoral students, wrote the article in [2]. In it she writes:-
Karp's intellectual standards were extremely high, and she was unfailingly honest in applying them. Although she showed almost familial concern for her students and younger colleagues, she was consistently candid in appraising their mathematical contributions and promise. In particular, she advised working towards a doctorate only if one expected to make research the most important part of one's professional career, and she refused to allow her students to graduate until their results met her own high standard for publishability.

### References (show)

1. A Guide to the Carol Karp Papers, 1949-1987, Briscoe Center for American History, University of Texas at Austin.
https://legacy.lib.utexas.edu/taro/utcah/00521/cah-00521.html
2. J Green, Carol Karp (1926-1972), in L S Grinstein and P J Campbell (eds.), Women of Mathematics (Westport, Conn., 1987)86-91.
3. J Green, Carol Karp, in John R Shook (ed.) Dictionary of Modern American Philosophers (A&C Black, 2005), 1276-1277.
4. J Green, Carol Karp (1926-1972), in Louise Grinstein and Paul Campbell (eds.), Women in Mathematics: A Biobibliographic Sourcebook (Westport, Conn., 1987), 86-91.
5. Karp Prize, Prizes and awards, Association for Symbolic Logic.
https://aslonline.org/other-information/prizes-and-awards/
6. D W Kueker (ed.)Infinitary Logic: In memoriam Carol Karp, Lecture Notes in Mathematics 492 (Springer-Verlag, Berlin - Heidelberg - New York, 1975).
7. E G K Lopez-Escobar, "Introduction," Infinitary Logic: In Memoriam Carol Karp, Lecture Notes in Mathematics 492 (Springer-Verlag, 1975).
8. M B Ogilvie, Carol Karp, in Marilyn Bailey Ogilvie and Joy Dorothy Harvey (eds.), The Biographical Dictionary of Women in Science: Pioneering Lives from Ancient Times to the Mid-20th Century 1 (Routledge, 2000), 677-678.
9. Red and Blue, Good News Well Told, Alliance High School, Alliance, Ohio XVII (12 December 1941) - XIX (2 June 1944).
10. L Riddle, Carol Karp, Biographies of Women Mathematicians, Agnes Scott College (25 February 2016).
https://www.agnesscott.edu/lriddle/women/karp.htm
11. T K Wayne, Karp, Carol Ruth (Vander Velde), American Women of Science Since 1900 Volume 1 (ABC-CLIO, 2011), 565-566.
12. M B Williams, Obituary, Association for Women in Mathematics Newsletter 3 (1) (1973), 2-3.