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Who are the greatest Black Mathematicians?

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 awardedthe FieldsMedal?

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

4. Who are the greatest Black Mathematicians?

5. Who are the young mathematicians whose careersexhibit extraordinary promise?

I believe all but the last two questions tobe foolish. However, I hope to address these questions on thisweb page - in reverse order. For a history of AfricanAmericans in science research read Kenneth R. Mannings article,"CanHistory Predict the Future?" For a description ofBlacks in Mathematics Research see ResearchMathematicians of the African Diaspora. As usual, underlinedwords are hyperlinks in this website to more information on theindividuals below.

CONTENTS

Who are the young mathematicians whose careersexhibit extraordinary promise?

Mathematicians of the 1990s

Mathematicians of the 1980s

Who are the greatest Black Mathematicians?

Great Black Mathematicians of the 1970s & 1960s

The Masters

5. Whoare the young mathematicians whose careers exhibit extraordinarypromise?

Mathematicians of the 21st Century

I had anticipated delaying this section until 2007 and youngfolks had begun to publish. However, as a winner of the AMU/ICMS2003 Young Africanin Mathematics Medals, one individual has changed my mind.

Oguntuase: Currently in Italy, Nigerian born and soleyNigerian trained, JamesAdedayo Oguntuase earned his Ph.D. in 2001, but has published18 papers in mathematics since 1998. This promises to be a stelarcareer.

Mathematicians of the1990s:

Seven mathematicians of the 1990s, Adebisi Agboola, JonathanFarley, Wilfrid Gangbo, Abba Gumel, Trachette Jackson, KatherineOkikiolu, and Arlie Petters show extraordinary promise, "shouldbe" (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 ArliePetters, the most senior of the group is a member of DukeUniversity's Bass Fellows. He is Full Professor of Mathematicsand of Physics (their first tenured Black professor in the sciences- congratulations Duke). He is chiefly interested in the mathematicaltheory of gravitational lensing and related areas (differentialgeometry, singularity theory, general relativity, Astrophysics).Though Petters received his Ph.D. about ten years ago, he haspublished 30 papers and a book, chiefly in the area GravitationalLensing. Petters's book on Gravitational Lensing is considereda tour de force in mathematical physics. In 1998, Petters wasawarded the most prestigious award for "young" mathematicians,the three year Sloan Research Fellowship. In 2002, he wasrecipient of the first Blackwell-TapiaPrize.

K. Okikiolu: Born to Nigerian and British parents, buteducated in the U.S., KatherineOkikiolu (was once on Princeton's faculty) received specialdistinction in 1997 when she was the first Black to win a SloanResearch Fellowship. Later in 1997, she won the PresidentialEarly Career Awards for Scientists and Engineers for "Innovativeresearch in geometric analysis, particularly the determinant ofthe Laplacian under smooth perturbations, and developing studentworkshops and mathematics curricula for inner-city children."This particular award is worth $500,000 and is only granted 60scientists and engineers in the U.S. per year. Okikiolu's workon elliptical differential operators is considered a major contribution,going well beyond what experts had considered feasible, giventhe current state of knowledge. Her 2001 publication Criticalmetrics for the determinant of the Laplacian in odd dimensionsin the Annals of Mathematics, is receiving high acclaim. She isAssociate Professor of Mathematics at the University of Californiaat San Diego.

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

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

Agboola: In mathematics, one does not always know ofyoung persons working in fields outside their own, and it is agreat honor to the individual if the case is otherwise. Adebisi Agboola's workin Number Theory and Arithmetic Algebraic Geometry has been mentionedto me as very good by KevinCorlette and two of my non-Black colleagues whose areaof research is mutually exclusive with Agboola, Corlette, andeach other. Agboola is Full Professor of Mathematics at the Universityof California at Santa Barbara

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

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

Johnson: British born Mathematical Physicist Clifford V. Johnsonhas over 60 publications since his 1992 Ph.D. Since that timehe has immersed himself within String Theory (also see SylvesterJames Gates) with papers and books. He is currently on leaveat USC.

Great Mathematicians ofthe 1980s:

This is a group of mathematicians, nearing or just past Fieldsmedalist years (before the age of 40), whose careers are verystrong, and we expect them to have careers stronger than manyof 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 Masseyenrolled and obtained a B.S. in Mathematics. From there he wentto Stanford University for the Ph.D. and to industry, but hislocation in the Mathematics Department of Lucent Technologieshas given him the opportunity to publish an average of 2.5 papersa year. In addition to the application of many papers in QueueingTheory and Stochastic Processes to problems in the Modelling ofTelecommunication Systems, Massey, most importantly, has beeninvolved 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 theMathematical Sciences. In 2001, Massey became the first tenuredAfrican American Mathematician at an Ivy League Univrsity. Heis Full Professor in Princeton University's department of OperationsResearch and Financial Engineering.

Dean: Applied Algebraist NathanielDean has recently moved from Bell Labs and Lucent Technologiesto academia in order to strengthen an already strong Applied Mathematicsprogram at Rice University which included the Mexian AmericanRichard Tapia. Currently he is Full Professor of Mathematics andChairman of Mathematics at the HBCU Texas Southern Universityin Houston. Nearly half of his 50 publications are in ComputerScience. Dean, along with Massey, were featured on the PublicBroadcasting System 5-Part 1998 Mathematics Series Life bythe Numbers.

Assani: Benin born, French educated IdrisAssani studies Ergodic Theory and Dynamics. Assani haswritten very strong papers; read, for example, the 1997 Stronglaws for weighted sums of independent identically distributedrandom variables. (which extends with new methods resultsobtained jointly by (1994 Fields medalist) J. Bourgain, H. Furstenberg,Y. Katznelson and D. Ornstein. Another one is the 1998 Multiplerecurrence and almost sure convergence of weakly mixing dynamicalsystems. gives the best possible result to date on H. Furstenbergfamous conjecture on a.e. multiple recurrence for dynamical systems.Fern Hunt alsosays Assani is her candidate for the greatest Black Mathematician.

Graham: American CarlGraham, the most junior of this group and a professorat cole Polytcnic in Paris, was born in the U.S.but his African American mathematician father EugeneGraham emigrated to France where Graham was raised. Oneof his papers which particularly brought attention is The martingaleproblem with sticky reflection conditions, and a system of particlesinteracting at the boundary.

Makinde: Nigerian born OluwoleD. Makinde once said "Being a Black man in the Worldof Mathematics especially in Africa is not a very pleasant experience. One has to learn how to work with littleor no facility." He published 50 papers in a variety of puremathematcs subjects on the way to becoming Professor and Headof Applied Mathematics Depatment, University of the North, SouthAfrica.

Jenda: Malawi born OvertounM. Jenda continues to produce good Algebra inspite ofinvolvement with administration.

4. Who are the greatestBlack Mathematicians?

Great Black Mathematiciansof the 1970s& 1960s:

There are quite a few well established Black mathematicians,in Africa, the Americas, Asia, and Europe, who are internationallyknown as leaders in their respective fields though past the midpointof their careers and never quite reaching the accomplishment/recognitionof "the masters." Ethelbert Chukwu(Differential Equations, Control Theory, and Mathmatical Economics),Francisco Antonio Doria(mathematical physics, logic, the philosphy of science, and themathematical theory of communications), NelLohoue (Functional Analysis), DonaldRichards (Statistics), and FloydWilliams (Homological Algebra & Lie Groups) are probablythe best of the group.

Others are OlusolaAkinyele (Ordinary Differential Equations), AugustinBanyaga (Differential Topology), EarlBarnes (Linear & Non-linear Programming), HeneriDzinotyiweyi (Topological Semigroups), G.O. S. Ekhaguere (Mathematical Physics), JohnA. Ewell (Number Theory), AderemiKuku (Algebraic K-theory), and ScottWilliams (Set-Theoretic Topology, Set Theory, TopologicalDynamics). There are at least 10 other good mathematicians whocould be mentioned here, you can find them on the web page ResearchMathematicians of the African Diaspora: http://www.math.buffalo.edu/mad/ResearchMathematicians.html.

Though Black Women in Mathematicsform 25% of all Black Mathematicians, it has not escaped thisauthor that the above response to question 4 discusses no woman.I am only aware of a hand full of Black women active ly engagedat forwarding the sciencesignificantly beyond a thesis. The most senior is FernHunt 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 theentire rest of the entire African American community. Though thisno longer the case, The Masters, a slight expansion of the grouphas published more papers than the entire Black Mathematics communityin the 20th century. I believe The Masters are David Blackwell,J. Ernest Wilkins, George O. Okikiolu, JamesEzeilo, 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 mathematicianswho, prior to the late 1960s, have had the freedom and opportunityto work relatively unfettered. Of this group, David Blackwellis the only Black mathematician whose work is clearly within the"extraordinary mathematician" rank. There are othersnot 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' parentswere 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 of19 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 "theNegro 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 Engineeringfrom New York University.

Bharucha-Reid: To me, AlbertT. Bharucha-Reid's work was, mathematically, nearly hasgreat as Blackwell's and Wilkins, but for points of recognition,his career suffered one major fault - he resolutely refused toobtain a Ph.D. I have known several good mathematicians (e.g.,James Joseph, andAndrew Gleason, an ex-chair of Harvard University's MathematicsDepartment) who have found themselves in a similar position.

In 1949 at the age of 19, Albert Turner Reid (he later sharedthe surname, Bharucha, of his India born wife) earned a B.S. inMathematics and a B.S. in Biology from the University of Iowa.By the time he was 23, he produced mathematics for eight publishedpapers, but did not produce a Ph.D. thesis (he said, in 1953,it was a waste of his time) at his graduate school - the Universityof Chicago. Bharucha-Reid published six books and nearly 80 papersin 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 spentthe majority of his career at Wayne State University in positionsfrom Professor to Chair to Dean. He completed his career at Clark-AtlantaUniversity a few years before, despondent with the death of hiswife and taking his own life in 1990.

G. Okikiolu: The excellence of Black persons in Mathematicshas not been limited to Americans, the Nigerian GeorgeO. Okikiolu works in London and has published 3 booksand at least 190 papers, more than any other Black mathematician.He is also the father of Katherine Okikiolu discussedabove.

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 CharlesBell, who though, far from the rank of contemporariesBlackwell and Bharucha-Reid in Mathematical Statistics or Ezeiloand Mickens, had an exellent life-time career.

3. Who is [orwas] 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 Diasporacommunity? In the first case, we discussed individuals in the masters above. In the last case theanswer might be thefirst Black Math Ph.D., a mathematician influential withgovernement (as Percy A.Pierre), a great teacher (such as EttaFalconer or ClarenceStephens), a researchmathematician, or some part or combination of the four(like Adegoke Olubummoor Raymond Johnson).You must decide; to learn more click on the underlined words.

2. Should a Black Mathematician have beenawarded the Fields Medal?

OR

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

CarlF. Gauss and Archimedesare the greatest mathematicians of all time, and those not evenclose have won Mathematics' Fields Medal or the NevanlinnaPrize. Though a relatively recent award, the Fields Medalis sometimes known to the public as Mathematics' Nobel Prize,but that is a misnomer as the medal is only awarded to for workcompleted prior to the age of 40. In 2002, Cornell Universityand the Mathematical Sciences Research Institute (in Berkeley)established a biannual prize, the Blackwell-TapiaPrize in honor of David Blackwell and Richard A. Tapia,distinguished mathematical scientists who have been inspirationsto more than a generation of African American and Hispanic Americanstudents and professionals in the mathematical sciences.

Less than1% of all mathematicians are Black, but a high1 percentage, 15%, of Black Mathematiciansdo mathematics research.. Extremeobstacles (also see struggles)prior to 1970 often blocked mere participation of Blacks withinthe advanced mathematical community and may have had an effecton possible candidates for the Fields; however, a few slippedthrough the blockade. Further, we, the mathematics community,have had a generation, since 1970, to grow a Black prize winnerand, to my knowledge, no Black mathematician of Fields Medal caliberhas been totally ignored. Finally, since the beginning of theeighties, there have been enough journals so that a journal changecan avoid a bad or racialist editor or referee. Not all publishedmathematics is good or even correct [see Fermat'sLast Theorem]; however, no good mathematics goes unpublishedunless its author desires it that way. I, therefore, believe theanswer to question 1 is "NO!" and to question 2, "Maybe?"

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

REFERENCES

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

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, 1998revised: January 7, 1999revised: April 30, 2000revised: July 24, 2001revised: April1, 2002

Scott W. WilliamsE-mail

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