# Jeremiah Chappelle Certaine

### Quick Info

Born
6 June 1920
Died
30 July 1993
Mount Vernon, Westchester, New York, USA

Summary
Jeremiah Certaine was an African American mathematician who was awarded a Ph.D. by Harvard University for a thesis on algebra in 1945. He taught at Howard University for a few years but for most of his career he was an applied mathematician for Nuclear Development Associates and the United Nuclear Corporation.

### Biography

Jeremiah Certaine was an African American, the son of Lawrence Certaine (1884-1966) and Sadie M Hall (1885-1956). Lawrence Certaine, born in Hansometown, Duval, Florida, USA, worked as a carrier for the US Government, then later as a postman for the US Mail. He married Sadie Hall, born in Maryland, USA, and they had nine children, five boys and four girls, with Jeremiah, the subject of this biography, being their sixth child.

Jeremiah was brought up and attended school in Philadelphia. Graduating from High School, he continued to study in Philadelphia, entering Temple University. This university had been founded as Temple College in 1888:-
... primarily for the benefit of Working Men; and for men and women desirous of attending the same.
Certaine was awarded a B.A. by Temple University in 1940 and was accepted to continue studying mathematics at Temple University for a Master's Degree which he was awarded in 1941. While he was a student, Certaine completed a World War II Draft Card on 1 July 1941. It gives the following details. Name: Jeremiah Certaine; Race: Black; Age: 21; Birth Date: 6 June 1920; Birth Place: Philadelphia, Pennsylvania, USA; Residence Place: Philadelphia, Philadelphia, Pennsylvania, USA; Registration Date: 1 July 1941; Registration Place: Philadelphia, Philadelphia, Pennsylvania, USA; Height: 5 ft 11 ins; Weight: 150 lbs; Complexion: Light Brown; Hair Colour: Black; Eye Colour: Brown; Next of Kin: Sadie Certaine.

After the award of his Master's Degree, Certaine went to Harvard University where he began research advised by Garrett Birkhoff. In 1942-43 he was a member of the Harvard Math Club and presented the paper Groups as algebras of a single operation at one of its meetings. In 1943 he published the paper The ternary operation $(abc) = ab^{-1}c$ of a group which was reviewed by Dan Rutherford [11]:-
Let G be a set of elements on which there is defined a ternary operation (abc) satisfying the following postulates: (i) ((abc)de) = (ab(cde)), (ii) (abb) = a, (iii) (bba) = a. These postulates are shown to be independent and consistent. It is proved that any element u of G may be chosen as the identity of a group $G_{u}$ defined by ab=(aub) and that $(abc)=ab^{-1}c$. Further, the groups $G_{u}$ are isomorphic. Equivalent and weaker postulates are also considered. A geometrical interpretation of the ternary operation leads to an abstract definition of a set of free vectors. It is proved that any group may be converted into a group of free vectors and conversely.
In the paper Certaine writes:-
I wish to express my gratitude to Garrett Birkhoff for his kind assistance and encouragement, without which this note would probably not have been written.
In 1945 Certaine was awarded a Ph.D. from Harvard University for his 69-page thesis Lattice-Ordered Groupoids and Some Related Problems. The Abstract of the thesis begins as follows [7]:-
Lattice-ordered Groupoids and Some Related Problems. The idea of ideals in a commutative ring is a well-known one. We are able to multiply two ideals. For a given set of ideals we are able to find a unique smallest ideal containing any member of the set (greatest common divisor or g.c.d.) and a unique maximal ideal contained by any member of the set (least common multiple or l.c.m.). Under the operations of l.c.m. and g.c.d., the ideals form a lattice; and we find that multiplication distributes over g.c.d., i.e. A, B, C are three ideals, and (B, C) is the g.c.d. or join of B and C, then A · (B, C) = (A · B, A · C), This is merely a special example of a lattice-ordered groupoid, defined as follows. Let G be a lattice with join (a, b) and meet [a, b], with a multiplication a · b be defined over G such that a · (b, c) = (ab, ac), (b, c)a = (ba, ca). (This is called an operator lattice.) If multiplication is associative and an identity exists, then G is called a lattice-ordered groupoid.
Robert Nowland is in error when he records Certaine's Ph.D. being from the University of Michigan [10]:-
Jeremiah Certaine was the fourteenth African American to earn a Ph.D. in Mathematics (University of Michigan). At this time half of all African American Ph.Ds in Mathematics were earned by students of the University of Michigan.
In 1945, Certaine was appointed to the Radiation Laboratory at the Massachusetts Institute of Technology on a one year position. This Laboratory, which undertook microwave and radar research, had been created in 1940 and only operated to the end of 1945 when it was broken up. At the end of the year, in 1946, he was appointed as a Research Mathematician at the Nuclear Radiation Laboratory. On 19 July 1946 he married Carlotta Laura Henderson in Manhattan, New York City. Carlotta, born 31 May 1922, was the daughter of the Post Office worker Edgar Henderson and his wife Madeline Pearce who was an elementary school teacher.

In 1947 Certaine was appointed as an Assistant Professor of Mathematics at Howard University [3]:-
In 1947 Woodard was retired, Blackwell was chair, and two new regular faculty members had been added. One was Claytor, whose mathematical work, beginning with his 1933 doctoral thesis under Kline at Pennsylvania, had attracted considerable attention. It is generally agreed that his very promising career had been blunted by the racial restrictions he encountered .... Claytor was appointed as an associate professor. The new assistant professor was Jeremiah Certaine, who had just received his Ph.D. from Harvard, and who remained at Howard until 1951.
While at Howard University, Certaine became a member of the Mathematical Association of America in 1949. He attended the International Congress of Mathematicians which was held in Cambridge, Massachusetts, from 30 August to 6 September 1950. Among the many students he taught at Howard University, we mention Eleanor Jones who said [8]:-
My teachers at Howard included Dr Elbert Cox, who was the first Black person in the United States to receive the PhD degree in mathematics. He received his doctorate from Cornell University in 1925. I also studied under Dudley Woodard and William Claytor who had PhD degrees from the University of Pennsylvania and David Blackwell, who was eminent enough to occupy later positions at Stanford University and the University of California at Berkeley. It was Jeremiah Certaine, the Black Harvard PhD, who helped me see the beauty of algebraic structure.
Certaine left Howard University in 1951 when he was appointed as Senior Mathematician for the Nuclear Development Associates at White Plains, New York. He had published little after his time undertaking research at Harvard University, but once in this new position with Nuclear Development Associates he became very research active, publishing reports on work undertaken under contract from the United States Atomic Energy Commission. For example in 1953 his reports: Angular Distribution of Photons from Pane Monoenergetic Sources; Integral Term for Elastic Scattering of Particles; and Some Remarks on Plane Conical Sources appeared. One of his reports in 1954 was A Solution of the Neutron Transport Equation which begins:-
We present in this report the fundamental mathematical results upon which the NDA (Nuclear Development Associates) neutron calculational program has been based. All our results are derived from the neutron transport equation for a plane source, from which it is also possible to obtain certain results about point sources.
The authors of [5] write:-
About 1955, J Certaine proposed a method for the numerical integration of the Boltzmann transport equation, which found its fruition in a code known as NIOBE [Numerical Integration of the Boltzmann Equation] for the lBM7090 series of computers. Basically, the transport part of the equation was evaluated in terms of the standard method of characteristic rays while a discrete energy treatment was used with the slowing clown integrals determined by Gauss- Legendre quadratures. The results of some NIOBE-calculated problems have been published and a good number more were performed in the early 1960s, but remain unpublished. After that the method sort of faded away, and is practically unknown today.
Certaine continued to produce many reports, some single authored, others co-authored with other workers at Nuclear Development Associates. His excellent work led to a new appointment in 1958. The American Mathematical Monthly reported [9]:-
Dr Jeremiah Certaine, Howard University, has accepted the position of Manager, Department of Mathematics, Nuclear Development Corporation of America, White Plains, New York.
His publications over the following few years included On sequences of pseudo-random numbers of maximal length (1958), The solution of ordinary differential equations with large time constants (1960), and, with several co-authors, Minimum Weight Shield Synthesis for Space Vehicles (1964).

From 1964 Certaine worked as Science Advisor for the Office of the Manager, Research and Development Division, United Nuclear Corporation. With Lambros Lois he published A Round-Off Free Solution of the Boltzmann Transport Equation in Slab Geometry in the journal Advances in Nuclear Science and Technology (1969). This paper has the following summary:-
This chapter discusses the methods employed for the solution of the transport equation in slab geometry, transformation of the monoenergetic transport equation, a round-off free solution for the monoenergetic one-velocity single-region transport equation, the multi-region solution of the slab problem, and applications of the round-off free solution. The nuclear engineer or shield designer usually associates the Monte Carlo method with very long computing times. It turns out that at large distances from the source, very few particles can be expected to reach and to be recorded in some specific angular direction or energy range. For a reliable statistical answer, a sufficient number of particles are needed. This necessitates the tracing of the histories of an immensely large number of particles. Techniques like biased sampling and splitting and Russian roulette that increase the probability of an initial particle contributing to the final answer have been used to considerably decrease the time required for a solution. Monte Carlo calculations are resorted to only when the complications of geometry of the source and the region make it impossible to find an answer by other means. This method is particularly useful for the calculation of integral rather than differential quantities.
He died at Mount Vernon, Westchester, New York, at the age of 73 years.

### References (show)

1. J Certaine, On Sequences of Pseudo-Random Numbers of Maximal Length, Journal of the Association for Computing Machinery 5 (4) (1958), 353-356.
2. B A Chartres, Review: On sequences of pseudo-random numbers of maximal length, by Jeremiah Certaine, Mathematical Reviews MR0127511 (23 #B557).
3. J A Donaldson and R J Fleming, Elbert F Cox: An Early Pioneer, The American Mathematical Monthly 107 (2) (2000), 105-128.
4. P Henrici, Review: The solution of ordinary differential equations with large time constants, by Jeremiah Certaine, Mathematical Reviews MR0117917 (22 #8691).
5. D T Ingersoll and J K Ingersoll, Early Test Facilities and Analytic Methods for Radiation Shielding (Oak Ridge National Laboratory, 1992).
6. Jeremiah Chappell Certaine, ancestry.co.uk.
7. Jeremiah Certaine, Summaries of Theses Accepted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Graduate School of Arts and Sciences, Harvard University, 1947).
8. A Leggett and S Greenwald, Remembering Eleanor Green Dawley Jones, Association for Women in Mathematics Newsletter 51 (5) (2021), 25-28.
9. News and Notices, The American Mathematical Monthly 65 (7) (1958), 539-542.
10. R A Nowlan, Masters of Mathematics: The Problems They Solved, Why These Are Important, and What You Should Know about Them (Springer, 2017).
11. D E Rutherford, Review: The ternary operation $(abc) = ab^{-1}c$ of a group, by Jeremiah Certaine, Mathematical Reviews MR0009953 (5,227f).
12. J Taylor (ed.), Negro in Science (Morgan State College Press, Baltimore, MD, 1955).
13. S W Williams, Jeremiah Certaine, Mathematicians of the African Diaspora (2008).