Who are the greatest Black Mathematicians?

Often I am asked the questions:

1. Is [or was] there a Black Gauss?

2. Should a Black Mathematician have been awarded the Fields Medal?

3. Who is [or was] the most important Black Mathematician?

4. Who are the greatest Black Mathematicians?

5. Who are the young mathematicians whose careers exhibit extraordinary promise?

I believe all but the last two questions to be foolish. However, I hope to address these questions on this web page - in reverse order. For a history of African Americans in science research read Kenneth R. Mannings article, "Can History Predict the Future?" For a description of Blacks in Mathematics Research see Research Mathematicians of the African Diaspora. As usual, underlined words are hyperlinks in this website to more information on the individuals below.

CONTENTS

Who are the young mathematicians whose careers exhibit extraordinary promise?

Who are the greatest Black Mathematicians?

5. Who are the young mathematicians whose careers exhibit extraordinary promise?

Mathematicians of the 21st Century

I had anticipated delaying this section until 2007 and young folks had begun to publish. However, as a winner of the AMU/ICMS 2003 Young African in Mathematics Medals, one individual has changed my mind.

Oguntuase: Currently in Italy, Nigerian born and soley Nigerian trained, James Adedayo Oguntuase earned his Ph.D. in 2001, but has published 18 papers in mathematics since 1998. This promises to be a stelar career.

Mathematicians of the 1990s:

Seven mathematicians of the 1990s, Adebisi Agboola, Jonathan Farley, Wilfrid Gangbo, Abba Gumel, Trachette Jackson, Katherine Okikiolu, and Arlie Petters show extraordinary promise, "should be" (but are not necessarily) located at the very best institutions, and may be the Fields medal candidates of the future.

Petters: Belize born American citizen Arlie Petters, the most senior of the group is a member of Duke University's Bass Fellows. He is Full Professor of Mathematics and of Physics (their first tenured Black professor in the sciences - congratulations Duke). He is chiefly interested in the mathematical theory of gravitational lensing and related areas (differential geometry, singularity theory, general relativity, Astrophysics). Though Petters received his Ph.D. about ten years ago, he has published 30 papers and a book, chiefly in the area Gravitational Lensing. Petters's book on Gravitational Lensing is considered a tour de force in mathematical physics. In 1998, Petters was awarded the most prestigious award for "young" mathematicians, the three year Sloan Research Fellowship. In 2002, he was recipient of the first Blackwell-Tapia Prize.

K. Okikiolu: Born to Nigerian and British parents, but educated in the U.S., Katherine Okikiolu (was once on Princeton's faculty) received special distinction in 1997 when she was the first Black to win a Sloan Research Fellowship. Later in 1997, she won the Presidential Early Career Awards for Scientists and Engineers for "Innovative research in geometric analysis, particularly the determinant of the Laplacian under smooth perturbations, and developing student workshops and mathematics curricula for inner-city children." This particular award is worth $500,000 and is only granted 60 scientists and engineers in the U.S. per year. Okikiolu's work on elliptical differential operators is considered a major contribution, going well beyond what experts had considered feasible, given the current state of knowledge. Her 2001 publication Critical metrics for the determinant of the Laplacian in odd dimensions in the Annals of Mathematics, is receiving high acclaim. She is Associate Professor of Mathematics at the University of California at San Diego.

Farley: Born in an extremely successful academic family of Rochester, New York, Jonathan Farley, graduated second in his class with an A.B. from Harvard University and obtained a mathematics Ph.D. from Oxford University where he was awarded the Senior Mathematical Prize and Johnson Prize for his research. During a two year visit to the Mathematical Sciences Research Institute [MSRI] in 1996, Farley solved very important old problems in the Theory of Ordered Sets. He also works in Lattice Theory. He is currently publishing at an average of more than three papers a year, and in 2003 was a Distinguished Fulbright Scholar at Oxford University in England. Currently is Visiting Professor of Mathematics at Massachusettes Institute of Technology.

Gangbo: In just nine years from a Ph.D. to a Full Professor - this is incredible. Wilfrid Gangbo was born in Benin and in 1992 earned a Ph.D. from Swiss Federale Institute of Technology. Among his twelve papers is his 1996 The geometry of optimal transportation remains the single publication by a Black in the Mittag-Leffler Institute's Acta Mathematica, one of the world's strongest mathematics journals. In 2001 he was appointed Full Professor by Georgia Institute of Technology.

Agboola: In mathematics, one does not always know of young persons working in fields outside their own, and it is a great honor to the individual if the case is otherwise. Adebisi Agboola's work in Number Theory and Arithmetic Algebraic Geometry has been mentioned to me as very good by Kevin Corlette and two of my non-Black colleagues whose area of research is mutually exclusive with Agboola, Corlette, and each other. Agboola is Full Professor of Mathematics at the University of California at Santa Barbara

Gumel: Born in Nigeria, Ph.D. in England. Abba Gumel is an extremely prolific in the areas Mathematical Biology, Non-linear Dynamical Systems, and Computational Mathematics. Currently he is a Full Professor at the University of Manitoba in Canada.

Jackson: American Trachette Jackson was a mathematics major at Arizona State in Tempe. Four years later she earned a Ph.D. in Mathematical Biology. Five years later she had ten articles under her belt and a Sloan Fellowship. Currently, Associate Professor at the Department of Mathematics University of Michigan

Johnson: British born Mathematical Physicist Clifford V. Johnson has over 60 publications since his 1992 Ph.D. Since that time he has immersed himself within String Theory (also see Sylvester James Gates) with papers and books. He is currently on leave at USC.

Great Mathematicians of the 1980s:

This is a group of mathematicians, nearing or just past Fields medalist years (before the age of 40), whose careers are very strong, and we expect them to have careers stronger than many of those who came before. They are Idris Assani, Johnny Brown, Nathaniel Dean, Carl Graham, Overtoun Jenda, and William Massey. There are a few more Mathematicians who could be mentioned here.

Massey: During Princeton University's inclusive period, William Massey enrolled and obtained a B.S. in Mathematics. From there he went to Stanford University for the Ph.D. and to industry, but his location in the Mathematics Department of Lucent Technologies has given him the opportunity to publish an average of 2.5 papers a year. In addition to the application of many papers in Queueing Theory and Stochastic Processes to problems in the Modelling of Telecommunication Systems, Massey, most importantly, has been involved with the mentoring African American students of Mathematics. Those who pay attention do very well; one of these is Arlie Petters (see young mathematicians above). Massey is a co-founder of CAARMS, the annual Conference for African Americans Researchers in the Mathematical Sciences. In 2001, Massey became the first tenured African American Mathematician at an Ivy League Univrsity. He is Full Professor in Princeton University's department of Operations Research and Financial Engineering.

Dean: Applied Algebraist Nathaniel Dean has recently moved from Bell Labs and Lucent Technologies to academia in order to strengthen an already strong Applied Mathematics program at Rice University which included the Mexian American Richard Tapia. Currently he is Full Professor of Mathematics and Chairman of Mathematics at the HBCU Texas Southern University in Houston. Nearly half of his 50 publications are in Computer Science. Dean, along with Massey, were featured on the Public Broadcasting System 5-Part 1998 Mathematics Series Life by the Numbers.

Assani: Benin born, French educated Idris Assani studies Ergodic Theory and Dynamics. Assani has written very strong papers; read, for example, the 1997 Strong laws for weighted sums of independent identically distributed random variables. (which extends with new methods results obtained jointly by (1994 Fields medalist) J. Bourgain, H. Furstenberg, Y. Katznelson and D. Ornstein. Another one is the 1998 Multiple recurrence and almost sure convergence of weakly mixing dynamical systems. gives the best possible result to date on H. Furstenberg famous conjecture on a.e. multiple recurrence for dynamical systems. Fern Hunt also says Assani is her candidate for the greatest Black Mathematician.

Graham: American Carl Graham, the most junior of this group and a professor at École Polytécnic in Paris, was born in the U.S. but his African American mathematician father Eugene Graham emigrated to France where Graham was raised. One of his papers which particularly brought attention is The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary.

Makinde: Nigerian born Oluwole D. Makinde once said "Being a Black man in the World of Mathematics especially in Africa is not a

very pleasant experience. One has to learn how to work with little or no facility." He published 50 papers in a variety of pure mathematcs subjects on the way to becoming Professor and Head of Applied Mathematics Depatment, University of the North, South Africa.

Jenda: Malawi born Overtoun M. Jenda continues to produce good Algebra inspite of involvement with administration.

4. Who are the greatest Black Mathematicians?

Great Black Mathematicians of the 1970s& 1960s:

There are quite a few well established Black mathematicians, in Africa, the Americas, Asia, and Europe, who are internationally known as leaders in their respective fields though past the midpoint of their careers and never quite reaching the accomplishment/recognition of "the masters." Ethelbert Chukwu (Differential Equations, Control Theory, and Mathmatical Economics), Francisco Antonio Doria (mathematical physics, logic, the philosphy of science, and the mathematical theory of communications), Nöel Lohoue (Functional Analysis), Donald Richards (Statistics), and Floyd Williams (Homological Algebra & Lie Groups) are probably the best of the group.

Others are Olusola Akinyele (Ordinary Differential Equations), Augustin Banyaga (Differential Topology), Earl Barnes (Linear & Non-linear Programming), Heneri Dzinotyiweyi (Topological Semigroups), G. O. S. Ekhaguere (Mathematical Physics), John A. Ewell (Number Theory), Aderemi Kuku (Algebraic K-theory), and Scott Williams (Set-Theoretic Topology, Set Theory, Topological Dynamics). There are at least 10 other good mathematicians who could be mentioned here, you can find them on the web page Research Mathematicians of the African Diaspora: http://www.math.buffalo.edu/mad/ResearchMathematicians.html.

Though Black Women in Mathematics form 25% of all Black Mathematicians, it has not escaped this author that the above response to question 4 discusses no woman. I am only aware of a hand full of Black women active ly engaged at forwarding the science significantly beyond a thesis. The most senior is Fern Hunt who has at least 20 papers - recall the most junior, Kate Okikiolu is discussed in section 5 (above).

The Masters

Until the mid 1980s, Charles Bell, David Blackwell, A. T. Bharucha-Reid, and J. Ernest Wilkins had published more mathematics than the entire rest of the entire African American community. Though this no longer the case, The Masters, a slight expansion of the group has published more papers than the entire Black Mathematics community in the 20th century. I believe The Masters are David Blackwell, J. Ernest Wilkins, George O. Okikiolu, James Ezeilo, Albert T. Bharucha-Reid, Ronald E. Mickens, and Charles Bell.

no thumb photos Bharucha-Reid G. Okikiolu Ezeilo Mickens Bell

Blackwell: There have been few black mathematicians who, prior to the late 1960s, have had the freedom and opportunity to work relatively unfettered. Of this group, David Blackwell is the only Black mathematician whose work is clearly within the "extraordinary mathematician" rank. There are others not far behind, we discuss them below .

When he was 22, David Blackwell earned a Ph.D. (University of Illinois, 1941) within 5 years of high school. As only Black institutions with very high teaching loads (20 to 30 hours per week as opposed to the standard 6 hours of today) would hire him, one would think his early career would lag somewhat. Although his work caught the eye of great mathematicians of the time, it took another 13 years and 20 papers before Blackwell was hired permanently at a research oriented institution, the University of California at Berkeley. By the time he was 40 (in 1959), David Blackwell had accomplished that which most mathematicians would consider a lifetime's work, he had written a book considered a classic, published 35 papers (three in the Annals of Mathematics), and had been an invited speaker all over the world. In 1965 he became the first African American named to the National Academy of Sciences (he is still the only Black mathematician to be so honored). In 1979 Blackwell won the von Neumann Theory Prize (the Operations Research Society of America). Though most (but not all) of Blackwell's work was in Statistics, his work exhibits a strong "theoretical"mathematics background. In 2002, the Mathematical Sciences Research Institute in Berkeley and Cornell University has established the Blackwell-Tapia Award in honor of David Blackwell and Richard A. Tapia, distinguished mathematical scientists who have been inspirations to more than a generation of African American and Hispanic American students and professionals in the mathematical sciences.

Wilkins: J. Ernest Wilkins was a contemporary of David Blackwell, though his experience with racism was clearer. Both Wilkins' parents were graduates of the University of Chicago. At the age of 13, Wilkins entered the University of Chicago. He received his B.S. in Mathematics three and a half years later and at the age of 19 he earned a Ph.D. in Mathematics from the University of Chicago (1942) for a thesis in the area of Calculus of Variations. J. Ernest Wilkins, Jr. was described in national newspapers as "the Negro genius." Wilkins, though a very able mathematician, was interested in applications of mathematics, and after his Ph.D., he went back to school earning degrees in Mechanical Engineering from New York University.

Meanwhile, he experienced racism from the AMS (American Mathematics Society): In 1947 Wilkins received a letter from the AMS Associate Secretary for the Southeastern region urging him to come to the AMS meeting, and saying that very satisfactory arrangements had been made with which they were sure he'd be pleased; they had found a "nice colored family" with whom he could stay and where he would take his meals! No hotels would admit him and the hospitality of the University of Georgia (and of the AMS) was not for him. Thus, AMS meetings continued to be all white.

Though he has published nearly 100 papers (under 50 in Mathematics), Wilkins' impact on applications of mathematics to Mechanical and Nuclear Engineering is significant. He worked as a Physicist for several companies: from 1960-70, Wilkins was Assistant Chairman of the Theoretical Physics Department and Assistant Director (1960-65) of the Atomic Division of General Dynamics Corporation. J. Ernest Wilkins, Jr. was the second African American member of the National Academy of Engineers (1965). One of Wilkins' major achievements has been the development of radiation shielding against gamma radiation, emitted during electron decay of the Sun and other nuclear sources. He developed mathematical models by which the amount of gamma radiation absorbed by a given material can be calculated. In 1999 he is Distinguished Professor of Mathematics and Physics at Clark-Atlanta University.

Bharucha-Reid: To me, Albert T. Bharucha-Reid's work was, mathematically, nearly has great as Blackwell's and Wilkins, but for points of recognition, his career suffered one major fault - he resolutely refused to obtain a Ph.D. I have known several good mathematicians (e.g., James Joseph, and Andrew Gleason, an ex-chair of Harvard University's Mathematics Department) who have found themselves in a similar position.

In 1949 at the age of 19, Albert Turner Reid (he later shared the surname, Bharucha, of his India born wife) earned a B.S. in Mathematics and a B.S. in Biology from the University of Iowa. By the time he was 23, he produced mathematics for eight published papers, but did not produce a Ph.D. thesis (he said, in 1953, it was a waste of his time) at his graduate school - the University of Chicago. Bharucha-Reid published six books and nearly 80 papers in algebra, analysis, mathematical biology, statistics, and topology, and was an undisputd leader in the area of Random Polynomials. With the exception of short stays at many institutions, he spent the majority of his career at Wayne State University in positions from Professor to Chair to Dean. He completed his career at Clark-Atlanta University a few years before, despondent with the death of his wife and taking his own life in 1990.

G. Okikiolu: The excellence of Black persons in Mathematics has not been limited to Americans, the Nigerian George O. Okikiolu works in London and has published 3 books and at least 190 papers, more than any other Black mathematician. He is also the father of Katherine Okikiolu discussed above.

Ezeilo: Another Nigerian, James Ezeilo made an enormous contribution. This 1958 Ph.D. (University of Cambridge) has also received numerous honorary doctorates. His early research deals mainly with the problem of stability, boundedness, and convergence of solutions of third order ordinary differential equations. Apart from extending known results and techniques to higher order equations, the main thrust of his work was the construction of Lyapunov-like functions, which he did elegantly and used to study the qualitative properties of solutions. In addition he was a pioneer in the use of Leray-Schauder degree type arguments to obtain existence results for periodic solutions of ordinary differential equations. Finally, with two other mathematicians, Ezeilo built mathematics to the fine degree it exists in Nigeria today serving the entire African continent quite well. Ronald E. Mickens at Historically Black Clark-Atlanta University straddles two fields, Mathematics and Physics, and from 1970 to 1999, Dr. Mickens published over 200 papers and 5 books. Recently, Mickens was honored with an election to Fellowship in the American Physical Society, a rare position limited to .5% of the membership of the society. With all of this Mickens has worked directly at the effort to bring African Americans into Physics and to improve Physics in Africa.

Here we note Charles Bell, who though, far from the rank of contemporaries Blackwell and Bharucha-Reid in Mathematical Statistics or Ezeilo and Mickens, had an exellent life-time career.

3. Who is [or was] the most important Black Mathematician?

I believe the answer is vaguely fathomable? Assuming "importance" refers to impact upon the community. Do we mean on mathematics, on the world community in general, or just in the African Diaspora community? In the first case, we discussed individuals in the masters above. In the last case the answer might be the first Black Math Ph.D., a mathematician influential with governement (as Percy A. Pierre), a great teacher (such as Etta Falconer or Clarence Stephens), a research mathematician, or some part or combination of the four (like Adegoke Olubummo or Raymond Johnson). You must decide; to learn more click on the underlined words.

2. Should a Black Mathematician have been awarded the Fields Medal?

OR

1. Is [or was] there a Black Gauss?

Carl F. Gauss and Archimedes are the greatest mathematicians of all time, and those not even close have won Mathematics' Fields Medal or the Nevanlinna Prize. Though a relatively recent award, the Fields Medal is sometimes known to the public as Mathematics' Nobel Prize, but that is a misnomer as the medal is only awarded to for work completed prior to the age of 40. In 2002, Cornell University and the Mathematical Sciences Research Institute (in Berkeley) established a biannual prize, the Blackwell-Tapia Prize in honor of David Blackwell and Richard A. Tapia, distinguished mathematical scientists who have been inspirations to more than a generation of African American and Hispanic American students and professionals in the mathematical sciences.

Less than 1% of all mathematicians are Black, but a high1 percentage, 15%, of Black Mathematicians do mathematics research.. Extreme obstacles (also see struggles) prior to 1970 often blocked mere participation of Blacks within the advanced mathematical community and may have had an effect on possible candidates for the Fields; however, a few slipped through the blockade. Further, we, the mathematics community, have had a generation, since 1970, to grow a Black prize winner and, to my knowledge, no Black mathematician of Fields Medal caliber has been totally ignored. Finally, since the beginning of the eighties, there have been enough journals so that a journal change can avoid a bad or racialist editor or referee. Not all published mathematics is good or even correct [see Fermat's Last Theorem]; however, no good mathematics goes unpublished unless its author desires it that way. I, therefore, believe the answer to question 1 is "NO!" and to question 2, "Maybe?"

(1 high compared with well under 10% in the general mathematical community)

R EFERENCES

[agwu & nkwanta], [akinyele & olubummo], [deGroot], [Donaldson], [Falconner], [Grinstein & Campbell], [Ferguson, Shapeley & MacQueen], [Hill], [Kenschaft3], [Mayes], [Newell, et al], [Williams, Statistics], [74-93 survey], [Fields and Nevanlinna winners], [Fields Medal]

The address of this webpage is http://www.math.buffalo.edu/mad/madgreatest.html

A different version of this web page appeared in print elsewhere.

December 31, 1998

revised: January 7, 1999

revised: April 30, 2000

revised: July 24, 2001

revised: April1, 2002

Scott W. Williams

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