Two of the first African Americans to earn a Ph.D. in mathematics, Dudley Weldon Woodard and William Waldron Schieffelin Claytor worked on fundamental problems in the field of topology and supported graduate-level math education for minority students.
Dudley Weldon Woodard (left) and William Waldron Schieffelin Claytor, who earned their Ph.D.s in mathematics in 1928 and 1933, respectively.
Penn has been the home of a number of notable African Americans, including civil rights activist W.E.B Du Bois, but only more recently have the stories of its pioneering mathematicians come to light. As two of the first African Americans to earn a Ph.D. in mathematics, Dudley Weldon Woodard and William Waldron Schieffelin Claytor were both talented researchers as well as devoted supporters of math education for minority students. Continuing to celebrate Black History Month, Penn Today explores the lives of these two pioneers and what their legacy looks like today.
Dudley Weldon Woodard
Woodard was born in Galveston, Texas, in 1881. While there is little information about his childhood, segregation and a “separate but equal” doctrine likely made it difficult for any African Americans who sought higher education. Regardless of any challenges he faced, Woodard earned a bachelor’s degree in math from Wilberforce University, in Ohio, in 1903 and a master’s in math from the University of Chicago in 1907.
After teaching at Tuskegee University and Wilberforce, Woodard joined the faculty at Howard University in 1920. Around that time, he began taking advanced math courses at Colombia University under the mentorship of Elbert Frank Cox, the first African American to earn a Ph.D. in mathematics. Woodard was quickly recognized as having a talent in mathematical research and took a leave from Howard in 1927 to enroll as a Ph.D. student at Penn. He worked under John R. Kline on Jordan curves, the topic of a well-known theorem in topology.
Woodard’s Ph.D. thesis was the first research paper published in an accredited mathematics journal by an African American, and Woodard became only the second African American to earn a Ph.D. in math. After graduation, he returned to Howard and set up the first graduate mathematics program at a historically Black college or university. Later, as chair of the Math Department, he established a mathematics library, regular scholarly seminars, and visiting professorships. He retired in 1947, after leading his department through 25 years of advancement and progress through an age of severe racial discrimination.
William Waldron Schieffelin Claytor
One of Woodard’s most promising students was Claytor, who was born in 1908 and raised in Virginia. After earning a bachelor’s degree in mathematics from Howard in 1929, Claytor became the first student to enroll in the newly established mathematics graduate program. Woodard recommended Claytor to the Ph.D. program at Penn, where he was accepted and enrolled in 1930 to work on his thesis under Kline.
Claytor quickly gained a reputation as a brilliant student, earning the most prestigious award offered at Penn at that time, a Harrison Fellowship, in his final year of studies. Of Claytor’s Ph.D. thesis, Kline told his advisor Robert L. Moore that “Claytor wrote a very fine thesis. In many ways I think that it is perhaps the best that I have ever had done under my direction.”
In 1934, Claytor further developed theories based on work by prominent mathematician Kuratowski. Professional mathematicians began to refer to this work as “Claytor curves” (Image: Annals of Mathematics)
Mathematician Ryan Hynd says that the publication of Claytor’s thesis in the Annals of Mathematics, one of the field’s most prestigious journals, is a testament to the quality of his work. He also built on work by Kazimierz Kuratowski, one of the most influential mathematicians at the time within the field of point-set topology. “Given that Claytor was publishing in the Annals and building on the work of eminent mathematicians, he was a highly promising student,” says Hynd.
Claytor, who taught at West Virginia State College after graduation, was, however, unable to pursue a career in research due to racism. He was denied the opportunity to work at the Institute for Advanced Study because Princeton would not accept a “colored person,” and he was unable to attend departmental seminars at the University of Michigan, even while working under the prestigious and competitive Rosenwald fellowship, and was unable to obtain a faculty position there. While presenting at a 1936 meeting hosted by the American Mathematical Society in Durham, North Carolina, Claytor was not allowed to stay overnight in the hotel where the conference sessions were being held.
Claytor went on to serve in the Army during World War II as an instructor in Anti-Aircraft Artillery Schools, and a chance meeting with statistician David Blackwell led Claytor to joining the math faculty at Howard after teaching stints at Southern University, in Baton Rouge, Louisiana, and the Hampton Institute, now Hampton University, in Virginia. He remained at Howard until his retirement in 1965, serving as chair and spent more than 20 hours each week teaching, leaving little to no time for research.
A mathematical legacy
This month, the Math/Physics/Astronomy Library curated a display of works authored by African American mathematicians, physicists, and astronomers. Along with Woodard and Claytor’s theses are the work of George Hench Butcher Jr., who earned a Ph.D. in mathematics from Penn in 1951; an almanac by Benjamin Banneker, who is known for tracking the spread of yellow fever across Philadelphia; and modern publications such as John Urschel’s autobiography about his interests in both math and football.
The book display featured the theses of Woodard and Claytor as well as Benjamin Banneker’s almanac, Shirley Ann Jackson’s visions for a 21st century workforce, and Thomas Urschel’s memoir. (Image: Kathryn Schaeffer)
Librarian and display curator Lauren Gala sees the collection as a way to celebrate both the work and the lives of pioneering African American men and women from Penn and from the surrounding community. “It’s important to connect the person and their experiences with their scholarship because that deepens your appreciation for both,” she says.
While segregation and racism meant fewer opportunities for Woodard and Claytor in mathematical research, they were instrumental in establishing graduate programs at African American colleges and mentoring African American students who were interested in math. Claytor personally mentored Katherine Johnson, the African American mathematician whose work was instrumental for NASA’s first crewed spaceflights, while she was double majoring in math and French at West Virginia State College.
“Dr. Claytor told me—I guess I was a freshman, he said, ‘you’d make a good research mathematician.’ I said, ‘what do they do?’ He said, ‘you’ll have to find that out.’ But he said, ‘I’m going to prepare you to be a research mathematician.’” Johnson said in a 2012 interview for “The History Makers.”
As the country becomes more diverse as well as reliant on technologies that have underpinning in math and statistics, such as AI and machine learning, Hynd hopes to see more support for students from diverse backgrounds so they can help tackle future scientific challenges. “As far as progress: more opportunities for students and encouraging as many students as we can from different backgrounds to get involved. Hopefully, when we get more students like Claytor and Woodard, we’ll encourage them to do great things,” says Hynd.
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