The National Association of Mathematicians (NAM) proudly celebrates Dr. Emery N. Brown, an innovative neuroscientist, statistician, and anesthesiologist, for receiving the prestigious National Medal of Science—the highest honor bestowed upon scientists and engineers in the United States. Dr. Brown, a trailblazer in computational neuroscience, was recognized at a White House ceremony on January 3, 2025, where he was presented the medal by Arati Prabhakar, Director of the White House Office of Science and Technology Policy.
Dr. Brown’s work exemplifies the intersection of mathematics, neuroscience, and medicine, making groundbreaking contributions to the understanding of brain function and anesthesia. As a professor at MIT and Harvard Medical School, and an anesthesiologist at Massachusetts General Hospital, he has led innovative research in signal processing and statistical methods that have advanced multiple fields of science.
His research has focused on how neurons encode signals, how anesthesia affects brain function, and how mathematical models can enhance patient care. His pioneering work has not only revolutionized anesthesiology but has also provided fundamental insights into human consciousness, learning, and memory. These contributions continue to impact mathematical biology, computational neuroscience, and biomedical engineering.
Brown’s official citation at the White House ceremony highlighted his transformational work in neuroscience and anesthesiology, stating:
“Emery Brown's neuroscientific approach to understanding anesthesia’s exact impact on the brain has been transformational for relieving patient suffering and has provided a new foundation for how we think about the very thing that makes us human, our consciousness.”
His research into EEG monitoring during surgery has provided precise methods for anesthetic dosing, leading to improved patient safety and reducing post-operative side effects. In 2023, his lab demonstrated a closed-loop EEG system that adjusts anesthesia levels in real time, paving the way for future clinical applications. His work is also being applied to fields such as sleep medicine, psychiatry, and coma recovery, showing the far-reaching implications of his discoveries.
As a Black mathematician and scientist, Dr. Brown’s achievements are particularly inspiring to the NAM community. His career exemplifies the power of mathematical and statistical reasoning in solving real-world problems, a core principle that NAM seeks to promote among students and early-career researchers.
His success also underscores the critical role of mentorship and representation in STEM fields. Brown is a member of the National Academies of Science, Engineering, and Medicine and has received numerous accolades, including the Gruber Prize in Neuroscience, the Swartz Prize in Theoretical and Computational Neuroscience, and the Pierre Galletti Prize of the American Institute for Medical and Biological Engineering.
Dr. Brown’s latest initiative, the Brain Arousal State Control Innovation Center, is poised to unify anesthesiology research with broader neuroscience applications, including the treatment of depression and the development of improved sleep aids. His ability to bridge mathematical modeling with medical applications continues to set new standards for interdisciplinary research.
The National Association of Mathematicians extends its heartfelt congratulations to Dr. Emery N. Brown for this well-deserved honor. His work stands as a testament to the transformative power of mathematics in neuroscience, medicine, and beyond. As NAM continues its mission to uplift and support Black mathematicians, Brown’s success serves as an inspiration for the next generation of scholars and innovators.
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Articled written by Zerotti Woods, Ph.D. and Michole Washington, Ph.D.
Photo from Phillips Exeter Academy
We are thrilled to recognize the outstanding achievements of Dr. Olivia (Prosper) Feldman, a valued member of the National Association of Mathematicians, as she is named the 2025 Etta Z. Falconer Lecturer by the Association for Women in Mathematics (AWM) and the Mathematical Association of America (MAA).
Dr. Feldman is widely known for her expertise in mathematical modeling with a strong emphasis on epidemiology. Her research spans topics such as parasite-borne infections, population dynamics, and the societal and economic impacts of emerging diseases. Her work is particularly notable for its focus on real-world applications—developing intervention strategies to control outbreaks and improve experimental data collection.
From 2020 to 2024, Feldman published 14 peer-reviewed articles and authored three preprints. Many of these works were collaborative efforts, including projects supported by the American Institute of Mathematics Structured Quartet Research Ensemble (AIM SQuaRE). Her ability to lead and connect researchers across disciplines is a hallmark of her approach.
In addition to her research excellence, Feldman has shown a deep commitment to mentoring and expanding access in mathematics. At the University of Tennessee, she launched the Junior Modelers Program (JuMP)—a program that introduces undergraduates, as early as their first semester, to data-driven modeling and coding.
Her mentorship has guided four Ph.D. students, one Master’s student, and numerous undergraduates. In 2021, she received the Ann Keith Rea Faculty Teaching Award, a testament to her dedication to student growth and inclusive pedagogy.
Feldman’s talent for communicating complex concepts clearly and compassionately has not gone unnoticed. She has spoken on national webinar panels about COVID-19’s impact on the Black community and was interviewed by The New York Times for her epidemiological expertise. Her ability to reach diverse audiences speaks to her strength as both an educator and public scholar.
Dr. Feldman is currently an Associate Professor in the Department of Mathematics at the University of Tennessee at Knoxville. She holds a B.S., M.S., and Ph.D. in mathematics from the University of Florida and completed a postdoc at Dartmouth College. Prior to her current role, she was an assistant professor at the University of Kentucky.
Her accolades include:
In 2021, she also served as an organizer for an American Mathematical Society Mathematical Research Community, supporting early-career mathematicians in building collaborative research projects.
“It is an honor to be recognized by AWM and MAA as the 2025 Falconer Lecturer. AWM has played an important role in my career, providing support and opportunities to expand my collaborations and to provide opportunities for my graduate students.”
– Dr. Olivia (Prosper) Feldman
The Falconer Lectures honor the legacy of Dr. Etta Zuber Falconer (1933–2002), a trailblazer in mathematics education and an advocate for minority and women representation in STEM. These lectures spotlight women who have made significant contributions to the mathematical sciences and education.
We celebrate Dr. Feldman not only for the distinguished honor of being named the 2025 Falconer Lecturer, but also for her exemplary embodiment of the values Dr. Falconer championed—excellence, equity, and community.
Article reprinted with permission by the Association for Women in Mathematics and edited for NAM by Zerotti Woods, Ph.D. and Michole Washington, Ph.D.
Photo by Ben Walker, University of Tennessee
The United Negro College Fund Teaching + Learning Center is excited to invite Math teachers and professors to participate in a Gates Foundation-funded initiative aimed at improving student outcomes in college introductory-level math courses, with a particular focus on Calculus I.
The Gates Foundation is developing free, open-source digital courseware with the goal of mitigating high D/F/W/I rates among historically underrepresented students. This R&D initiative ensures that the perspectives of expert faculty help inform this tech-enabled product.
UNCF is conducting a series of virtual focus groups and interviews to assess what is working well on university campuses, unearth best pedagogical practices, and gauge interest in educational technology tools that leverage adaptive courseware and AI to promote student success.
Data collection activities will be conducted from Spring 2025, and faculty will receive a gift card for their participation
We are proud to recognize Dr. Johnny L. Houston, a founding member and lifelong leader within the National Association of Mathematicians (NAM), for his extraordinary legacy and his recent recognition at the 2025 Joint Mathematics Meetings (JMM) in Seattle, WA.
Dr. Johnny L. Houston is Professor Emeritus at Elizabeth City State University (ECSU) and has shaped the mathematics community for over five decades. He co-founded NAM in 1969 and served as its Executive Secretary from 1975 to 2000. His leadership has continued with his presence on NAM’s Board of Directors for an incredible 50 years.
Dr. Houston’s impact on mathematics and STEM education has been nationally acknowledged. Among his many honors:
The Joint Mathematics Meetings (JMM), the world’s largest annual math gathering, is hosted by the American Mathematical Society (AMS) along with 16 partner organizations—including NAM. Dr. Houston, a Life Member of AMS and also of NAM, MAA, and SIAM, was a significant figure at JMM 2025 in Seattle.
At this year's JMM, NAM held its annual National Meeting featuring the Claytor-Woodard Lecture, Cox-Talbot Address, and Haynes-Granville-Browne Presentations. The event also showcased a special project that Dr. Houston helped bring to life.
At both JMM 2024 and 2025, NAM and SLMATH (formerly MSRI) presented premiere screenings of The JBM Project: Journeys of Black Mathematicians, produced by ZALA Films:
Dr. Houston served as the primary consultant for the JBM Project and chaired the Advisory Group responsible for selecting participants. He appeared on both panels following the screenings and was instrumental in shaping the vision, focus, and authenticity of the films. His deep connections in the mathematical community and his decades of leadership through NAM were invaluable in identifying and connecting with contributors for the project.
At the conclusion of the JBM Panel on January 11, 2025, Dr. Houston was honored with a special recognition plaque from ZALA Films (Producer George Csicsery) and Tatiana Toro, Director of SLMATH. The tribute acknowledged his unmatched knowledge of the Black mathematical community, his commitment to documenting its legacy, and his unique ability to bring people together through NAM.
Dr. Houston’s lifelong service, mentorship, and storytelling have helped illuminate the journeys of countless Black mathematicians. We celebrate him—not only for what he has done but for who he continues to be in our community.
Article edited by Zerotti Woods, Ph.D. and Michole Washington, Ph.D.
Dr. Johnny L. Houston (second from left) pictured above during the JBM Project Panel at JMM 2025
For the past several months, PBS stations across the United States have been airing "Journeys of Black Mathematicians," a powerful two-part documentary that delves into the cultural evolution of Black scholars, scientists, and educators in the field of mathematics. The series, which has garnered widespread acclaim, brings to light the remarkable contributions of Black mathematicians while exploring the impact of Historically Black Colleges and Universities (HBCUs) in shaping the next generation of mathematical minds.
"Journeys of Black Mathematicians" is not just a historical account—it is a living testament to the perseverance, brilliance, and contributions of Black scholars in mathematics. The films follow the stories of pioneering mathematicians who, despite systemic barriers, carved paths of excellence that continue to inspire today’s mid-career professionals in the field. These individuals, in turn, serve as mentors and role models for college students and K-12 learners across the country, reinforcing the idea that they, too, belong in the world of mathematics and STEM.
The project behind this landmark documentary was initiated by Dr. Johnny Houston, one of the founding members of the National Association of Mathematicians (NAM). His vision for the series was to highlight the rich legacy of Black mathematicians and their enduring impact on the field, particularly through the role of HBCUs. Many NAM members are prominently featured in the series, sharing their experiences, insights, and perspectives on the progress and future of Black mathematicians in academia and beyond.
One of the central themes of "Journeys of Black Mathematicians" is the profound influence of HBCUs in cultivating Black talent in mathematics. The documentary underscores the indispensable role that these institutions have played in developing and nurturing mathematical excellence, often in the face of limited resources and institutional challenges. Throughout the series, students at these institutions emphasize the dedication of outstanding teachers who have been instrumental in advancing math and science programs, ensuring that future generations have access to the knowledge and mentorship needed to succeed.
Beyond celebrating past and present achievements, the series also looks forward, posing critical questions about how to increase representation and engagement in mathematics. How can the pipeline for Black mathematicians be strengthened? What strategies can be implemented to create more opportunities for young Black students in STEM? The films explore these pressing issues, offering insights into mentorship, community-building, and innovative approaches to education that seek to bring more students into the mathematical fold.
"Journeys of Black Mathematicians" is a landmark documentary that is not only a celebration of history but also a roadmap for the future. By sharing the personal and professional journeys of Black mathematicians, the series provides a compelling narrative that challenges stereotypes, fosters inspiration, and highlights the critical importance of diversity in mathematics.
With continued broadcasts on PBS and growing recognition, the impact of this series will undoubtedly resonate for years to come, encouraging educators, policymakers, and students to take an active role in advancing diversity and inclusion in mathematics.
For those who have yet to experience the power of this documentary, check local PBS listings or visit Journeys of Black Mathematicians | PBS for upcoming airings and streaming options.
The National Association of Mathematicians (NAM) had an impactful presence at the 2025 Joint Mathematics Meeting (JMM), showcasing a robust lineup of sessions, discussions, and celebrations that highlighted the contributions of Black mathematicians and fostered a sense of community within the profession. Held at The Seattle Convention Center and The Sheraton Grand, the JMM is the largest annual gathering of mathematicians in the world, and NAM’s events provided a vital platform for networking, mentorship, and scholarly exchange.
NAM's programming at JMM 2025 kicked off with “Quantitative Justice”, an insightful session held on January 8 where speakers explored the role of mathematics in social justice and policy-making. Attendees engaged in thought-provoking discussions on data-driven approaches to equity and justice.
On January 9, the Haynes-Granville-Browne Presentations offered a showcase of cutting-edge research by recent doctoral recipients. These presentations provided an opportunity for emerging scholars to share their work with the broader mathematical community, reinforcing NAM’s commitment to supporting early-career mathematicians.
That afternoon, the Legacy of Elbert Frank Cox session honored the first Black Ph.D. in mathematics, reflecting on his enduring impact and the continued efforts to build a more inclusive discipline.
One of the most anticipated events of NAM’s JMM programming was the Banquet and Cox-Talbot Address. This prestigious lecture, delivered by Dr. Omayra Ortega, celebrated the achievements of Black mathematicians and provided inspiration for the next generation of scholars.
On the morning of January 11, attendees gathered for the Claytor-Woodard Lecture, a distinguished talk given by Dr. Tai-Danae Bradley. This annual lecture, named after mathematical pioneers William W. S. Claytor and Dudley Weldon Woodard, highlights groundbreaking research and contributions by Black mathematicians.
Following the lecture, NAM members convened for the NAM Business Meeting to discuss organizational updates, upcoming initiatives, and ways to further NAM’s mission of fostering excellence and inclusion in the mathematical sciences.
The conference concluded with a special screening of George Csicsery’s film, “Journeys of Black Mathematicians: Creating Pathways,” followed by a panel discussion. This event provided a powerful reflection on the experiences of Black mathematicians, celebrating both historical figures and contemporary trailblazers who are shaping the future of the field.
NAM’s presence at JMM 2025 was a testament to the strength, resilience, and brilliance of Black mathematicians. As we look ahead to another year of mentorship, research, and advocacy, NAM remains dedicated to advancing diversity in mathematics and ensuring that the contributions of Black scholars continue to be recognized and celebrated.
Stay tuned for future NAM events and initiatives, and we look forward to gathering again next year!
Join Us for the 2025 Faculty Conference on Research and Teaching Excellence (FCRTE) at Medgar Evers College
Are you a faculty member at a Historically Black College or University (HBCU) or support education at HBCUs? Are you looking to connect with peers, share research, and explore strategies for teaching excellence? Mark your calendar for April 11-12, 2025, and join us at Medgar Evers College in Brooklyn, New York, for the Faculty Conference on Research and Teaching Excellence (FCRTE)!
The Faculty Conference on Research and Teaching Excellence is a premier two-day event designed to foster collaboration, innovation, and recognition within the academic community. Organized by the National Association of Mathematicians (NAM), this conference rotates across the country based on NAM’s regional structure, ensuring broad participation and engagement.
This year’s host institution, Medgar Evers College, provides a dynamic backdrop for faculty members to exchange ideas and celebrate achievements in research and pedagogy.
The FCRTE 2025 will offer four major components that cater to the interests and needs of faculty in mathematics, computer science, and related fields:
An esteemed tradition, this hour-long lecture will be delivered prior to the Friday evening banquet. It serves as a platform for an influential scholar to share insights and advancements in mathematical sciences and teaching methodologies.
Taking place on Friday evening, this celebratory dinner will honor distinguished faculty, recognize outstanding contributions, and provide a space for attendees to network and build lasting professional connections.
Eight selected faculty members will have the opportunity to present their research or teaching innovations. Each 20-minute talk, followed by a 5-10 minute Q&A session, will allow for knowledge sharing and intellectual exchange.
The conference will conclude on Saturday with a regional panel discussion addressing pressing academic and institutional issues relevant to faculty in the region. This interactive session will encourage dialogue, collaboration, and actionable takeaways for all participants.
Engage with fellow HBCU faculty and expand your professional network.
Showcase your research through contributed talks.
Gain insights from distinguished scholars and experts.
Celebrate excellence in teaching and research.
Participate in meaningful discussions on challenges and opportunities in higher education.
Don’t miss this enriching experience to grow professionally, share your expertise, and contribute to the advancement of research and teaching within the HBCU community.
Stay tuned for registration details and speaker announcements. We look forward to welcoming you to Brooklyn, NY, on April 11-12, 2025!
For more information, visit www.nam-math.org.
This memorial article, by Tasha R. Inniss, Ph.D. (Originally published by the American Mathematical Society) focuses on two African American women mathematicians/statisticians who not only had an enormous impact on her life, but who also played pivotal roles in diversifying the science, technology, engineering, and mathematics (STEM) fields. The first, Dr. Shirley Mathis McBay (May 4, 1935–November 27, 2021), was one of her mentors, and the second, Dr. Dionne Lynnette Price (August 29, 1971–February 22, 2024), was her best friend.
Shirley Mathis McBay, PhD was the dean for student affairs at MIT in the 1980s where she started the Quality Education for Minorities (QEM) Project to determine ways to increase minority participation in higher education. She authored “Education that Works: An Action Plan for the Education of Minorities”. She left MIT in 1990 to found the QEM Network (https://qem.org/) and served as its president until 2016. In an interview with Dr. Zerotti Woods for the article he wrote on Dr. McBay for the AMS Notices, she shared that her goal for establishing the QEM Network was “to implement the recommendations of the [1990] study”. Since its founding, the QEM Network has achieved Dr. McBay’s goal and has helped to shape the STEM landscape, particularly as it relates to federal funding to support historically underrepresented faculty in STEM and minority-serving institutions (MSIs).
Dionne Lynnette Price, PhD, at the time of her passing, was the deputy director of the Office of Biostatistics in the Office of Translational Sciences, Center for Drug Evaluation and Research at the Food and Drug Administration (FDA). “Dionne’s decision to work at the FDA as a statistician was driven by her desire to combine her love of teaching, her aspiration to apply her skills to real-world problems, and her unwavering determination to create meaningful impact in the lives of others.”Footnote1 She spent her entire career at the FDA where she rose through the ranks and made significant contributions both at the FDA and in the global statistics community. Dr. Price was an active member of the American Statistical Association (ASA), consistent attendee at the annual diversity workshop during the Joint Statistical Meetings (JSM), and faithful participant during the Fostering Diversity in Biostatistics meetings of the Eastern North American Region (ENAR) International Biometric Society. In an interview at the 2019 JSM Diversity & Leadership Conference, Dr. Price spoke about the value of the diversity workshop, saying “We get to impact everyone and build our pipeline so that we will have a bright future.”
I wanted to write this joint memorial not just because they were both important people in my life, but also because I met both of these phenomenal women at the same time during the David and Lucile Packard Foundation HBCU Graduate Scholars Program conference. In 1993, “Dee,” as those who were close to her affectionately called her, and I were each awarded a Packard graduate scholarship. We became Packard Graduate Scholars after we both completed our undergraduate degrees in mathematics from Historically Black Colleges & Universities (HBCUs); Dee from Norfolk State University and I from Xavier University of Louisiana. Dr. McBay was on the Advisory Committee for the program along with HBCU presidents such as the president of my alma mater, Dr. Norman C. Francis, as well as two president emeriti of Morehouse College, Dr. Hugh Gloster and Dr. Walter E. Massey. Every summer, the Packard Foundation would fly all Packard HBCU Graduate Scholars to Monterey, California, for the annual conference. The Foundation selected and supported graduate scholars from 1992 to 2002.
Dr. McBay along with other members of the Advisory Board had a keen interest in our experiences as Black students at Research I institutions. What was ascertained was that those of us who majored in mathematics at HBCUs and then pursued advanced degrees at highly ranked research-focused institutions experienced a more challenging road to our PhDs because we were perceived to be less prepared. The perception of our talent and ability to do mathematical research as Black women was at times disheartening, but we prevailed due to the mentorship and fierce advocacy we received from individuals such as Dr. McBay and because of the powerful network we had as Packard Graduate Scholars. Our experiences bring to mind the quote of Dr. Evelyn Boyd Granville, who was “an internationally recognized mathematician, computer scientist, scientist/engineer, scholar, educator, mentor, and pioneer/barrier breaker …”.
“I always smile when I hear that women cannot excel in mathematics.” — Dr. Evelyn Boyd Granville, 2nd African American woman to earn a PhD in Mathematics
In addition to being among the small number of African American women who earned doctoral degrees in the mathematical sciences, Dr. McBay and Dr. Price shared other parallels in their narratives and trajectories. They both graduated summa cum laude from their undergraduate HBCU institutions and were the first African Americans to earn a PhD in their field from their graduate institutions.
Dr. McBay graduated from Paine College with a BA degree in Chemistry in 1954 at the age of 19. In 1966, she became the first African American to earn a PhD from the University of Georgia (UGA) in any field and the first woman to earn a doctorate in mathematics.
Dr. Price graduated from Norfolk State University as valedictorian with a BS degree in mathematics in 1993 and was the first African American to earn a doctoral degree in Biostatistics from Emory University in 2001.
They were both honorees on Mathematically Gifted & Black, a website highlighting the careers of Black mathematicians. The website was begun by four Black women mathematicians (Dr. Erica Graham, Dr. Raegen Higgins, Dr. Candice Price, and Dr. Shelby Wilson) who are phenomenal in their own right. I am sure they would also make Dr. Granville smile as they exemplify women excelling in mathematics.
In January 2023, Dr. Price became the 118th, and first African American, president of the ASA. She took this role very seriously and served in excellence as she did with everything in her career and professional life. Every month, she would write a column, President’s Corner, for the AMSTAT News. In the February 2023 issue, she stated “There are still settings in which bias has the potential to negatively affect the careers and professional development of members. Thus, embracing JEDI [justice, equity, diversity, and inclusion] is embracing the intellect of all”.
Her parents, niece, and I, along with the ASA executive director, Ron Wasserstein, sat in the front row in amazement at the brilliant speech she delivered. In it she was not only able to pay homage to statistical scholars who were giants in the field, but also to honor those individuals who shaped her life and career trajectory in a STEM field. It was motivating as well as informative. She made great use of many types of media, including beginning with the Mission Impossible music since the title of her address was “Our Mission in Action: Past, Present, and Future.” In her ASA presidential address, Dr. Price stated the following: “my vision of our future is one that has 1) a rich pipeline of students in statistics and data science, 2) increased awareness and visibility of our community and our many efforts, and 3) ensuring our future leaders are prepared to lead with statistics”.
It was such a compelling address that both her niece and I wanted to jump up to give her a standing ovation.
Dr. McBay and Dr. Price were proud graduates of HBCUs. Dr. McBay also worked at an HBCU, Spelman College, between 1967 and 1975. Spelman is only one of two HBCUs for Black women and has been the number one HBCU as reported by US News & World Report 4 for 18 years in a row. According to Infobrief NCSES, produced by the National Center for Science and Engineering Statistics (NCSES),Footnote2 Spelman College is listed as second to Howard University as top US baccalaureate-origin institution of Black or African American doctorate recipients, which includes males, between 2010 and 2020. This is remarkable since Howard, classified as an R2 doctoral university, has more than four times the student enrollment of Spelman, which is classified as a Baccaulareate college with an arts and sciences focus. When the data was disaggregated for males and females by RTI International, Spelman is ranked number one for producing African American female doctorate recipients.
Dr. Price loved her alma mater and had enormous pride at having been a DNIMASFootnote3 5 Scholar. I recall her saying frequently to me “Behold, the Green and Gold.” We both felt strongly that our time and training at NSU (for Dee) and XULA (for me) really prepared us to be scholars and leaders. Our professors held high standards, but also instilled confidence in us to be able to pursue and persist to the finish line of doctorates in the mathematical sciences. Our trajectories and achievements are due to our supportive families, our encouraging mentors/professors, and our impactful HBCU experiences.
In a communication written for the February 2024 AMS Notices entitled “Making Journeys of Black Mathematicians,” the filmmaker Csicsery, stated, “I quickly learned that [HBCUs] were an integral part of the story for many African-American mathematicians.” He went on to say, “Several scholars mentioned that Black students with undergraduate backgrounds at an HBCU earn more PhDs in mathematics than those who completed their undergraduate studies at predominantly white institutions (PWIs)” 4.
In the tribute written by Spelman College after Dr. McBay’s passing 15, Dr. Sylvia Bozeman is quoted as saying,
It was also my good fortune, as I determined later, to be jointly interviewed by Dr. Shirley McBay, and Dr. Etta Falconer, chairperson of the Department of Mathematics [in 1974]. During my interview it became apparent that these two women were on a mission, determined to increase the number of African American women in science and mathematics, beginning with Spelman College.
This was precisely the case! In the Spelman College Archives, there is an article written by Dr. McBay, which is stamped as being received by the Office of the President on March 10, 1976 9. In this article, she begins by providing all the statistics that reflect the “Black Underrepresentation in Science,” both from a national perspective and a Spelman perspective. She outlines the “identified barriers,” lists “strategies to remove barriers,” and provides “evidence of success.” What is incredibly remarkable is that in 1976, Dr. McBay had created a comprehensive strategic plan for increasing participation of women and students of color in STEM, that was not only applicable for Spelman, but for the nation. The strategies that she outlined are still relevant today and perhaps served as the roadmap for her work at MIT on the QEM Project and her vision for the QEM Network. The QEM Network has been impactful not only on HBCUs, but other MSIs, including tribal colleges. QEM is most known for the QEM workshops that were organized by Dr. McBay for faculty and institutional teams from MSIs to participate in intensive sessions designed to assist in developing competitive proposals for funding opportunities at the National Science Foundation. In addition, the QEM Network has produced numerous reports that describe their work and beneficial resources.
Dr. Shirley M. McBay and Dr. Dionne L. Price were pioneers, trailblazers, mentors, and leaders who made significant impacts in the mathematical sciences community. Because of their influence in changing the face of STEM, their contributions are being recognized in momentous ways. On October 7, 2022, the University of Georgia dedicated the library they renamed in honor of Shirley Mathis McBay, PhD.
On April 26, 2024, the FDA held a memorial service for Dr. Price and announced the establishment of the “Dionne Price Memorial Award” by the FDA Statistical Association. The announcement stated that “this prestigious award aims to preserve Dionne’s legacy in a meaningful manner, and to recognize statisticians who have made significant contributions to advancing statistical methodologies in regulatory science.” ASA has also launched the “Dionne Price Public Lecture Series,” which will “showcase rising stars in statistics and data science.” Additionally, Norfolk State University has established the “Dr. Dionne Price Scholarship,” which accepts funds to support students following in Dee’s footsteps.
The legacy of these phenomenal women will be cemented for generations to come!
These Black women are true inspirations for me. I am both honored and humbled that I had the opportunity to interact with, learn from, be mentored by, and to share in decades-long friendships with them. Their presence here on earth is deeply missed. I will forever cherish their memories. I marvel at their lifelong commitments to and lasting legacies for diversifying STEM. They loved mathematics and statistics, understood the importance of mentorship, and had a strong commitment to increasing the representation in mathematics, and STEM more broadly.
In the March 2024 President’s Corner in AMSTAT NEWS 5, current ASA President, Dr. Ghosh-Dastidar, shared the words of former ASA President, Dr. Kathy Ensor, who introduced Dr. Price before her presidential address at JSM 2023:
Dionne Price’s journey as a leader has been defined by her passion for creating impactful change in the lives of others. Dionne has an innate ability to bring people together, empowering them to collaborate towards a common goal. Her inclusive approach ensures that diverse voices are heard. Beyond her role as ASA president, she continues to be a source of inspiration [emphasis by author] to countless individuals, mentoring and nurturing emerging leaders. Her commitment to empowering the next generation of change makers ensures a sustainable legacy of progress that will endure far beyond her tenure.
Though Dr. Price and Dr. McBay may have approached diversifying STEM in different ways, they were both committed to opening doors and ensuring that STEM professionals and leaders are reflective of this nation as a whole. It is indeed their legacy and lifelong inspiration.
“We will always have STEM with us. Some things will drop out of the public eye and go away, but there will always be science, engineering, and technology. And there will always, always be mathematics [emphasis by author].” — Katherine Johnson, NASA Research Mathematician
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This article was originally published on the American Mathematical Society's website on December 31, 2024. It is reprinted here with permission. The content remains unchanged except for formatting adjustments for this website.
Citation: First published in Notices Amer. Math. Soc. 71 (December 2024), published by the American Mathematical Society. ©2024 American Mathematical Society.
Editor's Note: References can be found in the original article print
NAM member Terrence Blackman joined fellow mathematicians on Capitol Hill to advocate for increased federal funding for mathematics education. Representing New York, Blackman engaged with key congressional staff, highlighting the vital role of math in advancing national STEM initiatives.
Last week, seven mathematicians went to Washington, DC, to visit their states’ delegations on Capitol Hill: an experience not unlike the first day of high school.
Armed with tight schedules to follow in a labyrinth of unfamiliar buildings, they set out in small teams, roaming the busy, noisy, marble halls of Congress. The goal: to advocate for funding for mathematics education, representing the American Mathematical Society (AMS), with the staff of their elected officials.
First-time Hill visitors were paired with helpful “upperclassmen,” mathematicians who had paid Hill visits before. The AMS Office of Government Relations (OGR) served as guidance counselors, providing orientation in advance and direction during the Hill visit day, as well as handouts for the congressional staffers.
In total, 18 congressional offices representing six states received AMS visitors: 12 senators and six representatives.
“I am very grateful that so many congressional offices made time to speak with representatives from the AMS,” said AMS CEO John Meier. “Mathematics is beautiful and of great importance to the nation, and I think we did a very good job of highlighting in particular the impact of federal funding on advancing the mathematical sciences.”
Before the visits, “I was unsure about the impact and importance,” said Sara Maloni, University of Virginia mathematics professor. “It was really great to do it, both to be able to explain how the money we receive from the NSF is used, tell stories about mathematics and mathematicians, but also to understand better how decisions are made.”
Karen Saxe, senior vice president, AMS OGR, said, “These visits are so important for mathematicians to do. Both because they learn how legislation is made, and also so that legislators hear from us about exciting projects that students and faculty are doing in their districts and states.
“Perhaps due to AI and quantum science, we see more and more legislative staff interested in mathematics and its role in these areas.”
At most, an individual Capitol Hill office visit lasts a half-hour. In contrast, prep for the AMS-hosted Hill visits began weeks beforehand with an orientation meeting via Zoom for the participants, most of whom are members of the AMS Committee on Education (CoE).
Tyler Kloefkorn, associate vice president, AMS OGR, explained that meetings would be taken not by the elected official but by staffers, whose job it is to take notes, ask follow-up questions, and brief their legislator about the meeting.
The visit format is somewhat scripted, with the constituent and nonconstituent mathematician in each pair assigned a role.
After introductions, the nonconstituent mathematician briefly describes the AMS to the congressional staffer and sets up the purpose of the visit: to discuss the importance of mathematical sciences education.
Then, the constituent mathematician makes the “ask”: in this case, strong NSF appropriations for fiscal year 2025, especially in STEM education. An optional ask, Kloefkorn noted, would be for support of the Math/Stats Modeling Education Act. Finally, the constituent shares evidence of the impact of government-funded math programs in the district or state of the staffer.
“Attendees must emphasize a connection to district or state,” Kloefkorn said. “Attendees must have clear talking points and asks: ‘We are here to talk about the importance of mathematical sciences education and ways that Congress can support students, educators, and the workforce.”’
In advance, the prospective Hill visitors researched the legislative staffers’ backgrounds and their bosses’ committee assignments, priorities, and general interests. They read the AMS one-pager on National Science Foundation (NSF) appropriations and prepared stories about programs funded by the NSF, to inform the congressional staffer.
The night before the Hill visits, the AMS OGR hosted a dinner meeting with a PowerPoint review of the steps each group would take the next day, right down to maps of congressional buildings and a review of the Byzantine numbering system of the Capitol offices.
Allow extra time to get through security, the group learned. Also, do not mention campaign support or elections. And for speedy transit, wear sneakers between meetings.
On a September morning of intermittent rain, the mathematicians walked up to Capitol Hill. They split up into smaller groups to cover their schedules, accompanied by OGR staff when available.
Maloni and Boris Hasselblatt (AMS Secretary and Tufts University professor) had six meetings scheduled, with the offices of Senators Elizabeth Warren and Edward Markey and Representative Ayanna Pressley of Massachusetts and Sens. Tim Kaine and Mark Warner and Rep. Bob Good from Virginia.
Christine Berkesch (professor at University of Minnesota Twin Cities) made her Hill debut paired with Terrence Blackman (professor and former dean of the School of Science, Health, and Technology at Medgar Evers College, City University of New York). They met with the staffs of New York Sens. Charles Schumer—the Senate Majority Leader—and Kirsten Gillibrand as well as House Minority Leader Hakeem Jeffries; plus Minnesota Sens. Tina Smith and Amy Klobuchar and Rep. Betty McCollum.
Professors Ravi Vakil (Stanford University) and Jesús De Loera (University of California, Davis) covered California: Reps. Mike Thompson and Anna Eshoo in the morning, Sens. Laphonza Butler and Alex Padilla in the afternoon.
AMS CEO John Meier represented Rhode Island and the AMS headquarters in meetings with the staffs of Sens. Jack Reed and Sheldon Whitehouse. “They are not only supportive of mathematics, they are also delighted that the AMS is based in Providence, Rhode Island,” Meier said.
“The engagement of the staffers with us was impressive given the number of such meetings they must be taking,” Hasselblatt said. “Although we all had to mind the available time, their focus on the conversation and us was exemplary.”
“I was surprised how many young people are involved in this job, how many interns,” Maloni said. Most have a political-science background, although “I’m a STEM kid,” said Sharif Long, legislative correspondent to Rep. Pressley. And Chris Mirabella in Sen. Smith’s office asked Berkesch and Blackman an actual math question: “What was Fermat thinking?”
The mathematicians delivered folders that contained a one-sheet explainer about NSF appropriations, a one-sheet about the AMS, math posters, and the 2025 AMS Calendar of Mathematical Imagery.
“Of course, I brought homework,” Blackman said to Senate staffer Alex Hsi, producing a foldable 3-D puzzle with the faces of mathematicians.
“Chuck Schumer always does his homework,” Hsi responded.
The halls of Congress bustle with interest groups, often in matching attire. OGR’s training came in handy, even for those with Hill experience, such as Hasselblatt, on his third round of Hill visits.
“Navigating the various buildings when there was little time between meetings took a little advance planning, and keeping the conversations with the staffers to the right length takes some concentration and the right improvisation or restraint depending on the direction in which time runs, long or short,” he said.
There was one legislator sighting in an office: Massachusetts Sen. Edward Markey appeared and exchanged pleasantries as Hasselblatt and Maloni were leaving their meeting with his staffer, Karina Bravo. “I said that we’d shaken hands when he received an honorary doctorate from Tufts, and he said that he loves Tufts,” Hasselblatt said.
With a short lunch break in the Senate’s Dirksen Cafeteria, where an observant few spotted New Jersey Sen. Cory Booker, the Capitol Hill visits made for a long day of walking and talking.
“I was able to discuss the value of mathematics and STEM education, while requesting strong appropriations for the NSF next year,” Berkesch said. “In these meetings, I stressed the importance of programs like the NSF GRFP and shared personal stories of the impact of NSF funding within my own department and university. This was both fun and gratifying work, thanks to the interest the staffers showed in mathematics and the excellent prep I received from AMS staff.”
Saxe said, “I love seeing mathematicians do this for the first time—to see them develop their stories over the day. This year watching Sara Maloni and Jesús De Loera make Hill visits for the first time was most gratifying; they were both terrific at delivering our message and making personal connections to the offices they visited.”
“My main takeaway is be focused and prepared enough: Know your representative,” De Loera said.
“I learned that Rep. Good’s office’s primary interest in education is around school choice, and I am wondering what we can do to engage in the conversation,” Maloni said. She added that she would return to the Hill and hopes that more colleagues will make Hill visits.
De Loera concurs. “Only by speaking out we will be heard,” he said. “We need allies and coalitions, with other organizations. Strength in numbers.”
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Citation: First published in Notices Amer. Math. Soc. 72 (January 2025), published by the American Mathematical Society. ©2025 American Mathematical Society.
Explore the groundbreaking contributions of Evelyn Boyd Granville, the second Black woman to earn a Ph.D. in mathematics in the U.S., whose pioneering programming work supported key space projects like Project Vanguard and Project Mercury. This article sheds light on her vital role in early space computing, bridging academia, government, and industry.
Article By Laura E. Turner (Originally published by the American Mathematical Society)
The second Black woman to earn a PhD in mathematics from an American university, Evelyn Boyd Granville (1924–2023) had a career that spanned academia, government, and industry, and included groundbreaking work in computing in the prehistory and early years of the US space program. Since most accounts of her life provide little information about the latter facets of her work, I aim to elaborate upon [Tur23] by shedding light on the sorts of programming in which Granville and her colleagues were engaged.
In what follows, I will first treat aspects of the early stages of space computing, with particular emphasis on the projects in which Granville was involved. Here, the primary focus is IBM work in relation to Project Vanguard and Project Mercury, though a limited treatment of other projects on which Granville worked, both at IBM and elsewhere, is included. I will then describe some of the roles Granville played in these connections and, when possible, some details of her individual involvement. Because her name rarely appears in scientific publications, it is difficult to determine her specific contributions to these projects; future work remains to uncover this information. In light of this, my foremost aim is to provide a new context in which to appreciate and understand this pioneering work.
International Business Machines (IBM) took its name in 1924. Founded in 1911 through the merger of three manufacturing businesses, the company initially sold punch card tabulating equipment and a variety of other products ranging from butcher scales and coffee grinders to time clocks and office furniture [Cor18, p. 121]. Although the demand for advanced office machinery increased during World War I and through the 1920s, the company faced challenges linked to patent issues, competition, and the increasing complexity of its machines. It reaped the benefits of its “optimistic strategy” for product development, however, in a lucrative contract with the US Social Security Administration for tabulating equipment. This set it on a path for growth even during the Great Depression. It shifted from tabulating equipment to computers during the late 1940s and into the 1950s, a transition supported by US government agencies. With a ready commercial market for computing products and a role as an important provider, IBM expanded dramatically. In 1950, its worldwide workforce numbered just over 30,000. By 1963, this number had more than quadrupled [Cor18, pp. 132– 133] 25 man-years to the project and wrote close to 50,000 instructions for the 704 and 709 [Mow60, pp. 120–126]. Predicting the course of a satellite was challenging due to its tremendous speed. Once a satellite was launched from the Cape Canaveral Missile Test Center, the VCC was tasked with calculating its orbit using data from the Minitrack stations around the world. Once a station received a signal, it sent a message in triplicate to the Vanguard Control Center at NRL for review. The information was then relayed, again in triplicate, by teletype (a precursor of the fax machine) to the VCC, where it was received on punched paper tape. There, an operator fed the tape into a machine that punched holes in IBM cards corresponding to the Minitrack observations. After these were fed into a card-reader that transferred the information to the 704, a master program processed the observations, calculating the predicted longitude and latitude of the satellite positions for each minute, one week to ten days in advance. Predictions could be entered on punch cards, converted to teletype, and sent back to the Control Center and Minitrack stations, providing advance information to observers concerning the time and angle at which to expect the satellite for the purpose of optical location. Output devices also included a cathode-ray tube visual display and a cathode-ray tube recorder [Hag58, pp. 48–50].
As the company grew, its tradition of equal employment opportunities became a point of pride. A 1953 employment policy letter states: “It is the policy of this organization to hire people who have the responsibility, talent and background necessary to fill a given job, regardless of race, color or creed” [IBM65]. A 1965 issue of IBM News indicated that the company had been actively recruiting Black employees [IBM65], and a 1957 brochure for women (titled “My Fair Ladies” after the recent hit on Broadway) encouraged women applicants for positions in computing. During the same period of growth, IBM also won government contracts for work on important new projects, pushing the boundaries of computing at that time. The US satellite program, called Project Vanguard, was one of them.
The period from July 1, 1957 to December 31, 1958 marked the International Geophysical Year (IGY), an international program of geophysical research initiated in the midst of the Cold War. Sixty-seven countries, including the United States and the Soviet Union, participated in this effort toward a comprehensive study of the earth’s atmosphere, surface, and interior, as well the measurement of nuclear radiation on land and in the air and sea.
Project Vanguard was one part of the US Scientific Satellite Program connected to IGY. Initiated in 1955, it aimed at launching a scientific satellite, to be designed and built by the US Naval Research Laboratory (NRL), during that 18-month period. The objectives of the project were threefold: to put a satellite into orbit about the earth, to prove that it was in orbit, and to conduct at least one scientific experiment using it. One requirement for this earth satellite program was a high-speed digital computer for calculating a satellite’s orbit. By 1956, the Office of Naval Research, which oversees NRL, invited bids from companies equipped to rent computer facilities and provide mathematical and programming services, and IBM won. For $900,000 (roughly $10,000,000 in 2023), IBM would supply its 704 computer for six weeks, plus orbital computations for the entire lifetime of the satellite or the Minitrack tracking system, whichever was shorter, for the first three successful satellites to be launched. In addition, it would furnish the services of mathematicians for programming (designing and creating programs), coding (writing programs in machine language), numerical analysis and related tasks, as well as 100 hours of computing time for checking programs, and a computing center in DC to be made available on demand [GM70, p. 160]. A. Robin Mowlem, who directed programming there, described the NRL decision to enter into this contract as “a leap into the future,” for “at that time one could not be sure that satellites would behave exactly the way they have or, indeed, that computers were suitable for orbital computation” [Mow60, p. 119].
The Vanguard Computing Center (VCC), as it would be called, opened in July 1957 in what was once a bus terminal. Its 704, a state-of-the-art computer with vacuum tube logic circuitry and magnetic-core memory capable of storing up to 32,768 words, was designed with scientific, industrial, business, and government calculations in mind; much faster than earlier models, its floating-point arithmetic hardware made it ideal for precise mathematical computations such as those involved in Project Vanguard.
Proof that a satellite was in orbit necessitated tracking it, computing its orbit, and establishing a predicted path over the earth’s surface. Tracking Vanguard satellites involved radio angle and optical methods, the latter of which were important in making precise measurements of the position of the satellite, and thereby obtaining the best determination of its orbit. These satellites had no selfcontained light source, but if one crossed the twilight belt, it could be viewed, if large enough, by the naked eye or through binoculars or telescopes by observers at that latitude [Hag58, p. 36]. The VCC was primarily concerned with processing positional information obtained through radio transmission via the Minitrack tracking system developed at NRL. Vanguard satellites were equipped with 108Mc signal sources, with Minitrack stations positioned in a worldwide network. When a station received a satellite transmission, it was subdivided into individual observations consisting of phase-difference readings for the northsouth and east-west antennas of that station [QJ58, p. 59]. The Minitrack system functioned as a radio interferometer calibrated against the stars, providing direction cosines of the position vector of a satellite (the cosines of the angles between the vector and the coordinate axes) relative to the tracking stations. Once transmitted to the Control Center, and then to the VCC, the information was ready to be processed by the 704.
Work on the orbit computation methods to be used began immediately, and once the algorithms were formulated mathematically, mathematicians and programmers at IBM translated them into programs, first to be run on the 704, and later the 709, a faster and more powerful vacuum tube successor. Elliptic or circular orbit programs were used to determine the main features of the orbit, and precise orbit programs were then used to find the precise orbit. There were two types of each program: for the former, it depended on whether or not the observations belonged to the same neighborhood in the sense of a Taylor series, and for the latter, one used numerical integration and the other the method of general perturbations (to be touched upon later) [Sir58].
Programming, which was generally machine symbolic (FORTRAN was incomplete when the project began, but was increasingly used later), was a task of enormous magnitude. Mowlem estimated that IBM devoted roughly
The VCC was responsible for satellite tracking and orbit determination, with IBM staff handling the programming. The system was highly automatic, with minor decisions governed by the algorithms, and based on collections of subroutines linked into macro-operations; this minimized duplication, allowed for easy modifications, and enabled programmers to work independently on the various parts of the system [Mow60, p. 126]. It was also card-controlled for greater flexibility. Upon receiving a transmission, subroutines loaded the message into the high-speed storage of the 704; compared the triplicate items for agreement; adjusted the data, converting phase readings into directional information; and fit a least-squares parabola to the direction components from the phase-difference readings. These were linked into the initial macro-operation, which produced a “smoothed” direction of the satellite from that Minitrack station for one instant of time, expressed according to a local coordinate system [QJ58, p. 60].
Another macro-operation used one of several different procedures based on Gauss’s method to compute a preliminary orbit and then improve it iteratively. Next, the approximate orbit was refined through numerical integration of the differential equations of motion relating (by Newton’s law) the components of the gravitational and atmospheric drag forces on the satellite to its acceleration components, providing the predicted position and velocity vectors for the satellite across time. A different macro-operation performed a differential correction method to the position and velocity vectors to bring predictions into closer agreement with observations. Separate macro-operations then “translated” the predicted position, height, and zenith-angle-acquisition for a specific time, latitude, and longitude into a form which was more meaningful to the general public.
An alternate technique for obtaining predicted positions was implemented by 1960 via a general oblateness perturbation program based on Hansen’s lunar theory,[1]which computed Fourier series representations of orbital characteristics like perturbations of the satellite due to the oblateness of the earth (which has an equatorial bulge) in terms of time, and a separate numerical integration technique treating drag perturbations [QJ58, p. 61]. One key advantage of this program was that it could be evaluated at any particular time in a satellite’s orbit, which prevents the possibility of cumulative errors. This process, together with differential correction, was used iteratively to minimize the corrections to the orbital elements, and because of its long-term accuracy, was instrumental in the determination, by NASA scientists, that the earth is actually slightly pear-shaped [Mow60, pp. 124–125]. In fact, in their report of this discovery in Science, John O’Keefe, Ann Eckels, and Ken Squires thanked “the Vanguard Minitrack Branch, the IBM Vanguard Computing Center [emphasis added], and Dr. Paul Herget, whose work in obtaining and processing the data made this study possible” [OES59, p. 566].
IBM staff began programming the 704 in 1956. When Sputnik I was launched in October 1957, their programs successfully computed its orbit using three satellite positions and, according to Donald A. Quarles, Jr., IBM’s chief mathematician for the project, when Vanguard 1 was launched the following spring, the VCC predictions were “accurate to within a small fraction of a minute of time ” [QJ58, p. 64]. Although the project experienced delays and launching and orbital failures, Project Vanguard met its scientific objectives. Three satellites were placed in orbit, and the data received by Vanguard 1, alone, established new findings about the shape of the earth; that the sun and the moon modified the orbit of earth satellites; that the orbital path of a satellite is affected by solar radiation pressure; and that magnetic drag dampens a metallic satellite’s rotational movement. As the orb continued its passage through space, it also provided information about the diameters of the earth’s equator and poles; the density of the upper atmosphere; and variations in atmospheric density with the rotation of the sun [GM70, p. 244].
Project Mercury was the first phase of the US manned satellite program. Its aims were to launch a manned satellite into orbit about the earth; recover the astronaut-pilot upon its return; and enable the study of human capabilities when subjected to the stresses of acceleration, weightlessness, deceleration, and landing. Alan Shepard became the first American in space under Project Mercury in May 1961, and IBM computers and staff were critical to this achievement, as well.
Although Western Electric won the contract for equipping and testing the Project Mercury Tracking and Ground Instrumentation System, based on its previous success in determining satellite orbits in Project Vanguard, IBM was awarded the subcontract for computers and software (this was later broadened to include designing and installing the Launch Monitor Subsystem). By then, the VCC had been renamed the IBM Space Computing Center (SCC), and featured the IBM 7090, a transistorized system 7.5 and six times faster, respectively, than the 704 and 709 (but far less powerful than a modern smartphone). The National Aeronautics and Space Administration (NASA) was founded in 1958, and when it opened the Goddard Space Flight Center in Greenbelt, Maryland, in 1959, its Computing and Communications Center housed duplexed 7090s, redundancies receiving the same input data and performing the same computations. They also served as the communications link between the Control Center and the remote radar stations, and were complemented by a 709 in Bermuda.
The 7090s were responsible for providing powered flight trajectory parameters (to be monitored for signs of a possible imminent abort) and a smoothed present position for Mercury capsules during the launch phase; predicting future positions and providing radar acquisition data; quantitatively monitoring radar and computer performance; and calculating and transmitting display information to the Control Center, with output data updated every half second during launch and abort, and 10 to 20 times per minute in other phases [Gas99, p. 42]. Programming for the different phases was integrated into a single automatically-sequenced package. Once the liftoff signal was received, programs performing launch computations were activated [Gas61, p. 40].
One role of the Goddard duplex during the launch phase was to make a “go” or “no-go” recommendation depending on whether the satellite had successfully attained an orbit. Doing so required computing the anticipated orbit lifetime and providing trajectory parameters needed for monitoring the launch status for any indications of the possible need to abort. Once the computers recommended a “go” decision and the flight controller had no external reason to recommend otherwise, the launch switch signaled the computers to execute the orbit program.
During the orbit phase, the 7090s calculated precisely when to fire the retro-rockets for reentry and landing. These times were recomputed after each new set of orbit parameters was determined, and position and time data were sent to Goddard from radar sites around the world. These data were used to predict the position of the capsule for acquisition and supervision by radar sites using methods like Cowell’s numerical integration to extrapolate and correct orbital parameters. Because its accuracy depended on the accuracy of the initial position and velocity vectors and the accuracy of the approximated perturbations due to the shape of the earth and its atmosphere, differential correction was used to improve the predictions [Gas61, pp. 40–41].
For reentry, the primary task was computing retrofire clock information and the capsule’s probable impact point (which was refined upon the arrival of new radar observations) using position and time data from the radar stations, and transmitting this information to the Control Center. Reentry trajectory data were then provided to radar stations in advance of the satellite’s passage [Gas61, p. 41].
Project Mercury was computationally demanding, and the significance of the achievement may be difficult for modern readers to appreciate. Real-time computing was incredibly rare at that time, and the sorts of programming methods required for the task of human spaceflight were previously nonexistent. Saul Gass, who managed the IBM Project Mercury Simulation Group in 1960, noted in a later description of Project Mercury’s computer system that his personal computer in 1999 had “greater computational ability and memory than all the combined computers used in a Project Mercury mission” [Gas99].
Aerospace Computing Beyond Vanguard and Mercury IBM was not the only US corporation engaged with orbit computations in the early years of the space age, nor were Vanguard and Mercury the only projects. Space Technology Laboratories (STL), for example, formerly the Guided Missiles Research Division of Ramo-Wooldridge Corporation (a private missile research firm), was then developing missile systems and spacecrafts and employed mathematicians, programmers, scientists, and engineers in this connection. In 1957, STL had developed a two-stage Advanced Reentry Test Vehicle (ARTV) for the US Air Force Ballistic Missile Division (AFBMD) that combined a Thor ballistic missile with the second stage propulsion system (the Able rocket stage) developed for Project Vanguard. This suggested the possibility of placing a probe in lunar orbit, and thus STL became involved in the first US effort toward a lunar mission; another part of IGY, this probe was intended to carry a camera and other scientific instruments.
Under AFBMD and NASA, STL was assigned important technical tasks which included not only engineering challenges but also computing and data processing to locate the payload in the event of a successful launch. Its Systems Research and Analysis Division was involved with managing space and missile systems studies and contained its Computation and Data Reduction Center (CDRC), which housed state-of-the-art IBM computers. There, staff performed functions including numerical analysis, applied mathematics, statistical analysis, scientific and computational systems programming, data processing analysis, and test evaluation programming and analysis.
North American Aviation (NAA) was another company active in the booming aerospace field. Incorporated in 1928 as a holding company, NAA developed as an aircraft manufacturer in the 1930s, and in the 1950s built aircraft for the US military and NASA for research on flight conditions beyond the earth’s atmosphere. By 1961, its newly developed Space and Information Systems Division (formerly its Missile Division) sought to accelerate the development of the NAA Hound Dog supersonic cruise missile, and engage in anti-ICBM (intercontinental ballistic missile) projects, manned and unmanned space exploration vehicles, and managing information processing systems. Notably, in 1961 it was also chosen as the prime NASA contractor to design, develop, and construct the spacecraft command and service modules for Project Apollo, which landed humans (Neil Armstrong and Buzz Aldrin) on the moon for the very first time in 1969.
IBM, too, took on new projects during the same period and in the years that followed. As one example, a team of its mathematicians was engaged in work on the US Air Force’s Athena spacecraft reentry research and development program at White Sands Missile Range. The Athena RTV (Reentry Test Vehicle) missile was developed within the Air Force Advanced Ballistic Missile Re-Entry System (ABRES) program, with the intention of improving ballistic penetration via smaller and less-expensive missiles than those launched from Cape Kennedy and Vandenberg Air Force Base. IBM was also involved in Project Gemini and Project Apollo, providing mainframes, software, and technical support, as well as Skylab (the first US space station) and the US Space Shuttle program.
Granville was involved in many of the projects described above as a mathematician and computer programmer. She was hired at IBM in 1956, having already distinguished herself academically and professionally. Born in DC, she attended segregated public schools with excellent teachers, and excelled at Smith College, graduating summa cum laude in 1945. She earned her doctorate from Yale in functional analysis in 1949 under the supervision of Einar Hille, and subsequently worked as a research assistant at NYU. She was a mathematics professor at Fisk University, where she taught Etta Zuber Falconer and Vivienne Malone Mayes,[2]from 1950 to 1952, and then returned to DC to take a position at the National Bureau of Standards (now the National Institute of Standards and Technology). By her own testament, this was where she met mathematicians working as programmers and contemplated a career in that field [Gra89].
When Granville (then Boyd) arrived at IBM, she had no experience with computers (this was not unusual), and attended a two-week training session at the Watson Computing Center in New York City. There, she became acquainted with the IBM 650 Magnetic Drum DataProcessing Machine, first introduced two years prior, and the Symbolic Optimal Assembly Program (SOAP) assembler language. She spent the next year in the IBM DC office writing programs [Gra89], though her activities were at least occasionally more varied. A 1957 feature in an IBM magazine describes how “Dr. Evelyn Boyd, assisted by Mr. [Saul] Gass, demonstrated basic Electronic Accounting Machines and the [IBM] 650 computer” to high school students during a seminar “designed to stimulate interest among high-school students in the new and important professions associated with the ever-expanding field of electronic computers” [IBM57].
Gass (the same man who would later manage the IBM Project Mercury Simulation Group), was a former Pentagon employee involved in scientific computation who left government when the Eisenhower administration cut funding for such work. In 1957, he was employed at IBM as an applied science representative, that is, as a technically trained professional who helped salespeople with customers. In this role, he described himself as an “...educator, as well as a pseudo-salesman,” and it was in this capacity that the local IBM applied science staff organized the seminar, busing 500 high school students from DC and nearby Maryland to the Mayflower Hotel [Gas99, pp. 38–39]. There, students had the opportunity to use the IBM 650 to evaluate a square root, with one student apparently remarking: “much better than a slide rule” [IBM57].
Granville moved to New York City as a research mathematician at the New York Data Processing Center of the Service Bureau Corporation, an IBM subsidiary which provided electric data processing services to customers. After IBM opened the VCC in Washington, DC, she transferred there, arriving around 1958. In doing so, she became involved with Project Vanguard.
Although her name does not appear in publications detailing IBM work on the project, Granville’s re´sume´ indicates she was engaged in “Computer programming” for the 704, and the “Formulation of orbit computations and computer procedures for Project Vanguard and Project Mercury.”[3] She marveled in a later interview that her work involved “writing programs for something up in the air the size of a grapefruit!” [Lam14].
This “grapefruit” was Vanguard 1 (officially 1958 Beta 2), launched on March 17, 1958. Vanguard 2(E), the first Vanguard satellite placed in orbit under NASA and a precursor to modern weather satellites, was launched in February 1959. It contained photocells to scan the earth and map its cloud cover. A wobble in its orientation made the interpretation of the data difficult, but it proved the feasibility of a weather satellite. With a 20-inch diameter, it was not the diminutive sphere Granville recounted in her interview, but she worked on this project, too, with her role as a “mathematician programmer” at the VCC highlighted by the Associated Press [Pre59].
Granville was also involved with Project Mercury, which began in May 1958 and concluded in May 1963. She left IBM in 1960 when she married Reverend G. Mansfield Collins and moved to Los Angeles. By that point, she served as an IBM Staff Assistant helping to solving trajectory problems [IBM66]. According to Ebony Magazine, which published a short profile of the “space computing mathematician,” she supervised the work of three people developing the calculations for tracking capsules [Mag60]. Attesting to the cutting-edge nature of this activity, in 1966 Granville indicated that her work on Project Mercury had involved “a constant learning process due to the ever improving mathematical techniques for trajectory calculations” and afforded her “the opportunity to stay abreast of the latest developments in the aerospace field.” She described this work as “most exciting because of the experience we had in formulating and implementing the calculations for the Mercury flights”—“one of the highlights” of her career with IBM [IBM66].
After she left IBM, Granville (now Collins) resumed work on the west coast. Since, she later recalled, IBM had no big projects in California in 1960, she was not able to transfer. Instead, she joined the technical staff of STL in Redondo Beach. There, she worked in its CDRC (Computation and Data Reduction Center) on “research studies on methods of orbit computations” [Gra89].
The CDRC contained an Applied Mathematics Department (AMD). STL was then under contract with NASA, and engaged in studies of earth satellite orbit computations and the effect of atmospheric density thereon. In this connection, AMD staff produced a final contractor report treating the Diliberto general perturbation method. In astronomy, perturbation refers to the deviation in motion or orbit of a celestial body from its trajectory due to forces such as (in the case of near-earth satellites) drag and the earth’s oblateness. General perturbation methods, important in the context of long-term motion, were analytical procedures used to express the deviations of a body from its unperturbed orbit, and allowed for the calculation of the perturbed position of the body at any point in time. By 1962, a number of general perturbation methods had been proposed. These included Hansen’s method, successfully used by IBM in Project Vanguard, and an adaptation of Delaunay’s method. The Diliberto method was a novel approach developed at STL based on Stephen P. Diliberto’s theory of periodic -surfaces ( -dimensional toruses composed of trajectories). In the AMD Report, the method was applied in a “new and more suitable” coordinate system, simplifying the analysis and results and, by introducing a change of variables, removing low eccentricity singularities. In addition to Diliberto, the five contributors to the report included E.B. Collins [STL62].
Granville left STL in 1962. By then, the American space program was dominated by manned spaceflight, first under Project Mercury, and then Project Apollo. Granville was involved in this latter project, too, at NAA, having been enticed there by a friend in August 1962. “It sounds like job jumping,” she later remarked, “but that was the way things were then. The whole field was exploding, and people needed workers. I was always moving on to more money and more interesting work” [Lam14, p. 26].
At NAA, Granville became a research specialist, giving technical support related to celestial mechanics, trajectory and orbit computations, numerical analysis, and digital computing to Apollo engineering departments [Gra89]. She left NAA in October 1963, however, after a call from IBM convinced her to return [Lam14]. She accepted a position in Los Angeles as Senior Mathematician in the Systems Development West Department of the Federal Systems Center (FSC) [IBM65], part of the IBM Federal Systems Division (FSD). There, she provided technical support in trajectory analysis, orbit computation, numerical analysis, and digital computer methods. In particular, she was engaged in data processing in the context of ballistic missile reentry and target recognition programs [IBM66] as a member of the IBM team of mathematicians working on the US Air Force Athena spacecraft reentry research and development program [IBM65]. By 1966, Granville worked in the IBM FSC-West Coast Operations’ Signal Analysis Department on a project for the space exploration program of the Jet Propulsion Laboratory treating the changes in velocity induced by the collision of particles [IBM66]. According to her own account in [Gra89], her work at the IBM FSD was “similar to that done at NAA—trajectory analysis and orbit computation using techniques of numerical analysis.”
When IBM reduced its staff in the L.A. area, Granville took a job at California State University, Los Angeles, in 1967 rather than transfer back to DC or elsewhere in the state. She and Collins divorced the same year. She married Edward Granville in 1970 and retired in 1984, at which point the couple moved to East Texas. Granville reentered the workforce there several times to teach at the junior high, high school, and university levels, and retired once and for all in 1997 [Lam14].
When asked, in 2015, about her “favorite job” across the span of her career, Granville cited her work related to the space program, referring to it as “something brand new.” “NASA was new,” she remarked. “And the idea of being able to write programs to track these satellites. That was really the most fascinating job I’ve had, yes” [PG15].
Granville’s work in the aerospace industry is now widely recognized and valued. Few accounts of the nature of this work and its broader context, however, have thus far accompanied descriptions of her life and trajectory, particularly in popular literature. While work remains to ascertain and explain her individual contributions to the US space program, it is the hope that the present account further illuminates and contextualizes this fascinating facet of her career, and the significance of the work of Granville and her colleagues at the vanguard of space computing.
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