The IBM 650 was a marvellous beast. The world’s first mass-produced (and first profitable) computer, it was the mainstay machine of the 1950s, its magnetic drum capable of storing up to four thousand words in its memory as it rotated at a rate of 12,500 revolutions per minute, allowing what was for the time a blazing capacity for computational speed. Marvellous as it was, it required a distinct and rare group of core competencies to operate, and the maestros of the device were in high demand by both government and private industry, which fell over themselves to attract people with the right combination of abstract numerical analytic abilities, practical computational rigor, and raw engineering instincts to make the 650 hum.

One of the great luminaries from this exciting era, when the world’s first mass computer met humanity’s first attempts to find its way into space, was Evelyn Boyd Granville (b. 1924). The second black American ever to earn a PhD in mathematics, she harnessed her knowledge of numerical analysis to her pioneering interest in the application of computers to scientific problems to garner for herself a succession of positions at IBM, NASA and the NAA, working on her era’s biggest computational puzzles.

Born on 1 May 1924, the dizzying heights of Evelyn Boyd’s future academic success were anything but assured. Her birth town of Washington DC was segregated, her father left the family while Boyd was a child, and the Great Depression struck her family when she was but 5 years old. Her single mother, Julia Walker Boyd, was left to raise Boyd and her sister, during a time of economic destitution, in a city of institutionalised racial discrimination, on the income she could manage from her work as first a maid, and then later as a stamp and currency examiner for the Bureau of Engraving and Printing.

Arrayed against these lingering adversarial forces, however, were a number of supports that proved crucial for Boyd’s ultimate success. First, her aunt, Louise Walker, who was a graduate of the Miner Normal Teachers’ College, was devoted to the cause of education as the black population’s best way to lift themselves out of their economic hardship, and was willing to put her own savings on the line to ensure that the Boyd sisters had an education that would nurture their gifts. Second, though Washington DC was segregated in many of its facets, it also happened to boast one of the nation’s elite academic institutions for black children: Paul Laurence Dunbar High School.

Founded in 1870 as M Street High School, it was the first public high school in the United States to serve the black population. In 1916, the school moved, and changed its name to Paul Laurence Dunbar High School in honour of the poet who had passed away in 1906. Whereas other high schools in the city were categorised as vocational in focus, Dunbar was designated as an academic achievement school, and attracted a crop of highly trained, deeply competent teachers, some of whom possessed doctorates in their fields, devoted to the principle of black educational excellence. As a result, over the subsequent years, Dunbar alumni included a robust roster of some of the nation’s most famous and influential trailblazers, from Senator Edward Brooke, to the discoverer of blood plasma, Charles R. Drew, to John Aubrey Davis, who played a key role in the *Brown v. Board of Education *Supreme Court case that ended school segregation.

As educational opportunities for a brilliant young black woman went, this was the jackpot, and its assembly of successful, enthusiastic teachers served as constant inspiration for young Boyd, who wanted nothing more than to become like one of them. Her mathematical abilities were noted by teachers Ulysses Basset (a graduate of Yale University) and Mary Cromwell (a graduate of the University of Pennsylvania), who both encouraged her to apply to top-level colleges. Cromwell in particular suggested that she apply to Smith College and Mount Holyoke, both of which accepted her, but neither of which offered any type of scholarship. Fortunately, Aunt Louise offered up $500 from her savings to help Boyd meet the expenses of her first year at her chosen school, Smith, and she supplemented this money by taking summer work at the National Bureau of Standards, earning scholarships from Smith, and economising by living in a co-op for her last three years at the college.

While at Smith, she studied mathematics, theoretical physics and astronomy, the latter of which nearly tempted her to switch majors. Ultimately, the prospect of sitting in isolation for long observational stretches overcame her enthusiasm for the mind-expanding scope of a career in astronomy, and she settled in to a future as a mathematician. Boyd graduated *summa cum laude* in 1945 with honours in mathematics, and was accepted to both the University of Michigan and Yale for graduate studies. Boyd chose Yale, because it offered additional scholarships that Michigan did not, and worked there under Einar Hille, who was president of the American Mathematical Society from 1947–48, and whose name lives on in functional analysis textbooks in the form of the Hille-Yosida Theorem.

Boyd’s research under Hille concentrated on Laguerre series, which are sums of the polynomials that solve the differential equation xy’’ + (1-x)y’ + y = 0, and which have importance in the realm of quantum mechanics. She received her PhD for this work in 1949, becoming only the second black woman in the United States to receive a Mathematics PhD (Euphemia Hayes was the first, in 1943, and Marjorie Lee Browne would be the third, also in 1949, while the fourth, Argelia Velez-Rodriguez, would not occur until 1960). Though she found research interesting, she was also profoundly pulled by the personal fulfilment of teaching, and spent two years as Associate Professor of Mathematics at Fisk University in Nashville, Tennessee, where she taught future PhD students Vivienne Malone-Mayes and Etta Zuber Falconer.

In 1952, she took the fateful step of accepting a position at the National Bureau of Standards in Washington DC. Here, she worked on mathematical analysis of problems related to the creation of missile fuses; more importantly, she met a group of mathematicians who were working at the NBS as computer programmers, using the power of the new machines to analyse problems arising from scientific research. She found the prospect fascinating, and when a chance arose in 1955 to work for computer industry leader IBM, she grasped it.

Joining in 1956, Boyd was just in time for the computing revolution created by the IBM 650, which was introduced in 1954 and would continue production until 1962. She learned how to work with SOAP, which was the assembler that attempted to semi-automate the optimisation of instruction addresses on the 650’s magnetic drum. As mentioned, the drum rotated at 12,500 revolutions per minute, meaning that one revolution took about 4.8 milliseconds to complete. Part of the trick of writing code for the 650, then, meant placing instructions in memory so that, when one was completed, the part of the drum that contained the next instruction was in place to be read right away. If you randomly placed instruction addresses on the drum, you stood to vastly slow down computation speed, by having instructions finish, and then having to wait up to 4.8 milliseconds for the drum to rotate around to the location of the next instruction. SOAP helped this process to a degree by automating the placement of instructions so that, when one completed, the drum was exactly where it needed to be for the next instruction to be read.

Boyd learned how SOAP worked, and learned how to improve upon its automated assignments, while creating programs for the 650, and ultimately becoming a numerical analysis consultant for the Service Bureau Corporation, which was a subsidiary of IBM. This was the time when NASA realised the vast potential of computers to aid in trajectory computations, and awarded IBM a contract to essentially run the Vanguard Computing Center in Washington DC. Boyd saw the chance to apply her experience with computers and expertise in mathematical analysis to problems related to space travel, and volunteered to join the IBM group that would be overseeing Vanguard, working on the programs that calculated trajectories and mission models for Project Vanguard and Project Mercury. Her marriage in 1960 caused her to leave IBM and take up a job in Los Angeles for the Computation and Data Reduction Center of Space Technology Laboratories, where she worked on refining computational methods for determining orbits.

As the space race grew in intensity, so did NASA’s need to farm out work to private industry, and in 1962 Boyd joined the North American Aviation Company, which had just received a NASA contract for design work related to the upcoming Apollo missions. Boyd worked as a specialist there, focusing on problems of celestial mechanics, orbital computations, digital computation methods, and numerical analysis – work she continued until 1963 when she rejoined IBM to continue her research in using numerical analysis to improve trajectory computation. This work continued until 1967, when IBM began cutting staff at its Los Angeles divisions, and Boyd’s first marriage ended in divorce. After years of working at a breakneck pace for government and industry during the hectic days of the Soviet–US Space Race, a change was in order.

Perhaps unsurprisingly, Boyd at this point pivoted back to the career that had motivated her to excel academically in the first place: that of teacher. She took up an Assistant Professor position at California State University, Los Angeles. This was in the middle of the revolution in mathematics teaching known as New Math (famously satirised by Tom Lehrer with the phrase, ‘Where the important thing is to understand what you’re doing, rather than to get the right answer’). Boyd devoted herself not only to teaching classes but also to training new mathematics teachers in the methods of the New Math, even taking up teaching two elementary classes herself as part of the Miller Mathematics Improvement Program. In 1989, Boyd looked back on this time fondly:

*I wonder how I was able to handle a full-time load at CSULA, an evening class at the University of Southern California and the elementary school classes. I was happy in my work and I felt that I was a good teacher; hence, the full schedule was not a burden to me.*

As an outgrowth of her work helping new teachers learn the New Math, she collaborated with Jason Frand to create a new textbook for teachers, *Theory and Applications of Mathematics for Teachers *(1975), which went into a second edition in 1978, and then disappeared as mathematics teaching moved away from the New Math in its perpetual quest after the Next Big Method that, surely, this time, will fix America’s declining performance in mathematics.

In 1970, Boyd married real estate broker Edward V. Granville, with whom she moved to Texas in 1984, and subsequently took up a position at Texas College, which she held until her retirement in 1997. The intervening years have seen Granville honoured with medals, degrees and titles in recognition of her long service not only to the nation’s space program, but to the cause of improving American mathematical education at its most foundational, important, and often-neglected levels. As of the time of this writing, she has eighteen months to go to her hundredth birthday, and let us hope that it is a day full of even a fraction of the wonder and happiness that she has brought to students and science lovers over the decades.

FURTHER READING: In 1989, Evelyn Boyd Granville wrote a reminiscence of her life for *SAGE: A Scholarly Journal on Black Women* which is an important source for clarifying her various changes of employment throughout the 1950s and early 1960s. To learn more about the machine that she did most of her seminal work on and the relationship between computing and NASA, you can pick up Emerson Pugh’s *Building IBM: Shaping an Industry and its Technology* or James Cortada’s *IBM: The Rise and Fall and Reinvention of a Global Icon *(2019).

If you'd like to read more about women mathematicians like this one, check out my History of Women in Mathematics, launching in October 2023 from Pen and Sword Books!

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