History should not base an individual’s legacy on only what they attempted and accomplished in their lifetime: The record of their life should also include what is tried and achieved by succeeding generations that they enabled.
This biographical book is part of my tribute to an extraordinary individual, Richard Wesley Hamming (1915–1998), a gifted and celebrated Numerical Mathematician, Computational Scientist, and Educator. He was not only my Ph.D. dissertation advisor but also my mentor. Simply put, Hamming saved me by stepping in at a critical time and supporting my research vision, empowering my experimentation, and mentoring me toward a career and life path full of opportunities, achievements, and personal fulfillment.
He also taught me that scientists are responsible for documenting their findings in both papers and books, the latter being the preferable and longer-lasting in Hamming’s mind. Besides always continuing to learn, conducting research, and publishing your results, a scientist should also teach others, and Hamming made me promise to do all four.
I hope that the Richard Wesley Hamming Legacy Project, of which this biography serves as the core, similarly inspires generations to come as they learn both how and why they wish to continue to learn and how and why they want to teach. In this way, we humans better honor our teachers, official and unofficial, for, without outstanding mentors, many of us would not only wander but also be lost. In Einstein’s words, “It is the supreme art of the teacher to awaken joy in creative expression and knowledge[MM1] ”. Therefore, teachers’ life works naturally touch on the success—and tribulations—of their students.
Hamming was a world-renowned American mathematician most famous for his mathematics work as he helped form the foundation of modern computing science. While employed at the American Telephone & Telegraph (AT&T) Bell Telephone Laboratories (BTL or Bell Labs), he spent 30 years as a Research Mathematician primarily involved in computing, numerical analysis, and management of computer centers. During those three decades, he received wide recognition for developing Coding Theory, especially for inventing Error Correcting Codes (ECC), which enable the error-free digital communications and computing on which we all rely. ECC allows us, still today, to send a message around the globe and have the message received exactly as we sent it. ECC also enables reliable storage, transmission, and processing of data by providing a way to detect and rectify the errors caused by intervening noise and also allows for higher reliability with less reliable parts.
Hamming was an exceptional applied mathematician and numerical analyst. Besides ECC, he was best known for integrating differential equations and the Hamming spectral window used for smoothing data before Fourier analysis. In his lectures and textbooks, he propounded aphorisms like:
The purpose of computing is insight, not numbers, and
It is better to solve the right problem the wrong way than the wrong problem the right way.
Hamming received substantial awards for his ECC work, including the 1968 ACM Turing Award, the 1986 IEEE Hamming Award, and the 1996 Eduard Rhein Foundation Award. Besides these awards and other acknowledgments, many of his accomplishments over decades of work remain generally unknown to the generations of mathematicians, physicists, and engineers who follow.
For example, starting in 1944, before he reached his 30th birthday, Hamming was actively being recruited to work on the Manhattan Project in Los Alamos, New Mexico. When he accepted, his responsibilities included helping figure out how to use a room full of early IBM digital relay computers to perform crucial calculations related to the development and testing of the first atomic bombs. Few of the ideas examined in developing those atomic bombs served only that purpose. Instead, much of what happened in those years set the stage for the world of science on which we currently depend, including the transition from analog to digital computing advances in applied mathematics, and computer science, and the field of computer simulation.
Hamming’s early experiences observing and working with world-class scientists at Los Alamos, and later at Bell Labs, drove him to significant insights for the future and allowed him to choose to focus his energy on the most critical problems of the times. Without his efforts on essential issues, today’s world would likely function quite differently.
Another of Hamming’s significant contributions, possibly his most crucial, had yet to be described when I began this Legacy Project: Hamming was a Mentor in the most real sense of the word. He encouraged and enabled many individuals throughout his life, yet no formal biography existed when I began this effort in 2017.
So that others may also learn about Hamming’s work, experience, and teaching, this book presents Hamming as the man, mathematician, and mentor that he was. Almost three decades after he gave his last live class lecture, Richard Wesley Hamming’s accomplishments continue to stimulate students, teachers, scientists, inventors, and managers. Since his first publications in 1939, Hammings’ real influence is being rediscovered every few years.
My research for and writing of this unauthorized biography started 19 years after his death. Hamming did not get to know that I would choose to write his biography, nor do I believe he expected that anyone would ever write one. Except for his ten books and hundreds of articles/lectures, Hamming did not collect or document much of what I would eventually put in this book. Without any such guidance, I chose to follow the chronology of his life, including the places where he worked and taught. Two trips to Nokia Bell Labs in New Jersey, one to Los Alamos National Laboratory in New Mexico, and a dozen trips to NPS in Monterey California allowed me to build the outline of the story that appears in the following chapters.
I wish that I had started this legacy project when Richard and his wife Wanda Hamming were still alive to answer my many questions. Since that was not possible, I began by documenting my recollections from the nearly four years that I worked with Hamming. Reading much of his writings and viewing his recorded lectures provided a significant body of knowledge, that had to be distilled, organized, and paraphrased or referenced. From this point on, my research efforts became widespread in geography and substance.
I identified and assembled a significant collection of previously unpublished material concerning his family genealogy, role models, education, friends, co-workers, Manhattan Project involvement, 30-year career at Bell Labs, honors, and teaching - including several discoveries not discussed elsewhere. I also collected detailed information about his publications, presentations, and lectures from the period he was a professor at the Naval Postgraduate School (NPS). Persistence and fortune permitted me to conduct illuminating interviews with over a dozen of his contemporaries, former students, and relatives.
As permitted by these information sources rightful owners, all of the material I collected is being made available on the Calhoun Open Archive at the NPS Dudley Knox Library. My goals are to see that this project and book are well written, the research source information is made available, and that I have done justice in claiming, establishing, and perpetuating Richard Wesley Hamming's legacy.
Any historian writing a biography inevitably includes disclosures and judgments that, given the opportunity, the subject of the biography might dispute. I believe that in the case of Hamming, any of these are acts of omission, based on the paucity of verifiable information about a specific event. In his lectures, Hamming was known for recalling some details of his experiences to support a point, but to the best of my knowledge, he had never written any detailed memoirs about important periods of his life. I was able to fill in some of the blanks, thanks to the 15 individuals I was able to interview in person, or on the phone. Extracts of their comments and insights are inserted within the chronology story I have attempted to weave in this biography.
Most biographies start with the story of two families. Hamming’s father, Richard James Hamming, was a Dutch immigrant who came to America in 1900 and married Mabel Redfield from a middle-class family with ancestral roots back to the American Revolution. These young parents (Richard James Hamming and his wife Mable Redfield) worked through the challenges of the Great Depression to help build this country and make a better life for their children, ideals that remain genuinely relevant today.
“Remember, remember always, that all of us, and you and I especially, are descended from immigrants and revolutionists.”
- Franklin D. Roosevelt [3[MM2] ]
Richard Wesley Hamming would honor his ancestors, support international students, and develop revolutionary solutions. What drove Richard Wesley Hamming to traits and achievements worthy of tribute? We will see that financial need, positive role models, a supporting family, and a progressive education system—helped drive his ambition. underlying intelligence, determination, and persistence propelled his pursuit of knowledge and the development of his vision of the future. The insights I found while researching Hamming’s life and work renewed my own belief in the opportunities and responsibilities inherent within those who adopt the aspirations and put in the required efforts to achieve the American Dream.
Determination and focused effort—coupled with others' beneficial assistance and friendship—made this country’s exceptional growth possible. Immigrant families formed the United States' foundations, growing its idea into a reality for generations to come. As a second-generation American myself, with all my grandparents coming from Austria (1889) and Ukraince (1905) to the United States as children, I also benefited from the American Dream. In learning how to research, write, teach, and mentor others, I found my calling. I hope that others who find inspiration in Hamming’s story will do the same and that they also strive to work on important problems.
I welcome the involvements of others who may help describe Hamming’s legacy by sharing their own stories and thoughts for subsequent editions. Throughout this book, I have cited sources, including previously unpublished works, to the best of my ability. Any errors or misinterpretations are my responsibility alone. Please email comments, suggestions, and corrections to me at Martin.Mandelberg@RichardWesleyHamming.com.
 This is my vision for the Richard Wesley Hamming Legacy Project.
 The term mentor comes from Homer's Odyssey, in which a man named Mentor was assigned the task of educating the son of Odysseus.
 The Manhattan Project was the coded name for the American-led effort to develop a functional atomic weapon during World War II. The controversial creation and eventual use of the atomic bomb engaged some of the world’s leading scientific minds, as well as the U.S. military [ ].
 The American Dream is the belief that anyone, regardless of where they were born or what class they were born into, can attain their own version of success in a society where upward mobility is possible for everyone. The American Dream is achieved through sacrifice, risk-taking, and hard work, rather than by chance [ ].
 [MM1]Einstein, Albert, and Alice Calaprice. The Ultimate Quotable Einstein. Princeton, N.J: Princeton University Press, 2011, pages 99-101
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