Chapter One, Introduction
“If you don’t work on important problems, it’s not likely that you’ll do important work.” —Richard Wesley Hamming
The Man Who Taught Us to Think Great Thoughts
Richard Wesley Hamming (1915–1998) was an inspirational and visionary American engineer, mathematician, computer scientist, and scholar who contributed to the foundation of modern computational science and helped shape our contemporary world. His work on error-correcting codes (ECC), famously known as Hamming codes, revolutionized data transmission and storage, earning him international acclaim. While primarily known for ECC, Hamming also made foundational contributions across numerous fields, including information theory, digital filters, computational science, numerical methods, and the teaching of computer science. Hamming’s ability to bridge theoretical mathematics with practical applications in computing and communication systems displayed his versatility and depth of knowledge. He chose to work on what he referred to as “Important Problems,” and as the quote below this picture indicates, he encouraged others to do so as well.
The Hamming Legacy Project
Hamming inspired, encouraged, and enabled countless individuals throughout his life — yet no scholarly biography existed when I started my research on this tribute project in early 2017.
The articles I found and a video for a university class discussed only partial aspects of his life and work. Exhaustive research was necessary to gain a comprehensive understanding of this visionary man, beginning with what motivated Hamming to tackle significant problems, gain insights, and produce inventions. Time was a factor because we needed opportunities to document his specific influence on others, given the dwindling number of individuals who knew him well.
This book shares stories about how Hamming overcame challenges, developed his vision, drove himself to greatness, and empowered others. He influenced many individuals to learn how to conduct research, solve complex problems, formulate innovative solutions, and communicate effectively for future generations. Years ago, we didn't have TED Talks. However, we still long celebrated each other’s ability to bring forth the essence of our work in math, science, and computing to help the world.
After earning his college degrees in engineering and math, Hamming taught at leading universities, which gave him invaluable feedback on the effectiveness of the lessons he wished to make, including introducing concepts like the popular paraphrase of Ockham’s Razor, which is often attributed to Einstein: 4 “Everything must be made as simple as possible—but not simpler.” Hamming used this principle to motivate others to understand an idea’s heart, soul, and essence before clearly and concisely describing it to others.
Hamming left us with many valuable inspirational lessons through his books, articles, and lectures. His most well-known aphorism, “The Purpose of Computing is Insight, not Numbers,” is often quoted by those who wish to ensure they are effective when they use mathematics and computers to solve problems.
Over 27 years have passed since Hamming taught his last class in December 1997, yet his innovations, books, articles, and lectures continue to stimulate students, teachers, and scientists. Even today, researchers regularly cite his writings in books, articles, lectures, and college courses through the online repositories of the Institute of Electrical and Electronics Engineers (IEEE), the Association for Computing Machinery (ACM), and the American Mathematical Society (AMS).
One of Hamming’s significant contributions, his most crucial, had yet to be adequately chronicled when I began this biography — he was a mentor in the absolute sense of the word. As my doctoral advisor at NPS, Hamming stepped in at a crucial moment, supported my research vision, encouraged me to be innovative in my experimental approach, and mentored me in my scientific research career. He helped me do what he had also done in his life—evolve from an engineer to a mathematician and then to a philosopher-scientist. Treating me as a protégé, colleague, and friend, Hamming helped me develop transformative insight and conduct better research, which enhanced my career and significantly enriched my opportunities, achievements, and fulfillment in life.
Richard Hamming passed away on January 7, 1998. Neither he nor his wife, Wanda, knew that I, nor anyone else, would write his biography, and they did not leave any written guidance on how he wanted his legacy described. In books and lectures, he drew on numerous life experiences to support the points he wanted to make. Still, he neglected to leave details that would have been helpful in my research for this book. I wish I had started this legacy project when Richard or Wanda was still alive to answer my questions. Since that was impossible, I researched his publications, lectures, family genealogy, role models, education, teaching, and work at Los Alamos (1945–1946), the American Telephone and Telegraph (AT&T) Bell Laboratories (1946–1976), and NPS (1976–1998). I located historical archival photographs and videos to help describe the events and individuals who influenced him as he grew up in Chicago and worked in Los Alamos, New Jersey, and Monterey.
Persistence and fortune helped me discover and interview two dozen of his contemporaries, former students, and relatives. Many generously shared their memories and helped me synthesize what I wanted to write about — how Hamming empowered and encouraged us to ask essential questions, develop insights, find solutions, and document the results.
People Who and Opportunities That Influenced Hamming
What influences produced a genius like Richard Hamming? Role models, growing up in Chicago during significant world events and fortunate opportunities, played a substantial part in Hamming’s development. Family, teachers and professors affected his motivation and determination. Hamming studied the exceptional traits, styles, and techniques of individuals to increase his understanding and develop his wisdom. This book reveals over 24 influential individuals.
Challenges during the Depression and prospects provided by far-reaching leaders contributed to his development. Education is the foundation for advancement, and teachers are often the key to this process. Einstein almost certainly said, “It is the supreme art of the teacher to awaken joy in creative expression and knowledge.” Teachers’ work naturally touches on their students’ successes and tribulations. Hamming experienced many influential teachers. In late 1944, Hamming was a recent Ph.D. graduate with teaching experience and a few publications about his research in partial differential equations. This book reveals details of his recruitment and subsequent work on digital computing, advances in applied mathematics, and the new field of computational science. His work at Los Alamos, Bell Laboratories, and NPS drove him to significant insights and accomplishments. In his research and support for others, he identified critical issues, focused on developing practical solutions, and shared his wisdom.
While most known for his work on numerical methods and the invention of ECC, Hamming also did foundational work in many other areas. His earliest research publications contained new techniques for integrating differential equations. He helped create a spectral window used for smoothing data before Fourier Analysis, as well as contributed to other areas of applied mathematics, computer center operations, languages, operating systems, and education. Without his wisdom, insight and innovative work, today’s world would function quite differently.
Most biographies begin with the story of a family. Hamming’s father immigrated to America in 1900 at the age of twenty. Ten years later, he married into a family with roots in the American Revolution. He and his wife worked through challenges, including the Great Depression, to improve their children’s lives—ideals that remain relevant today. Immigrants formed the foundations of the United States, making its ideals a reality for generations. Strength of character and focused effort, coupled with beneficial help and hard work, made this country’s exceptional growth possible.
Hamming benefited from a supportive family, role models, financial needs, and a progressive education system that helped motivate him and develop his character. Influencing individuals propelled his pursuit of knowledge, and he strove to achieve his goal of a future with choices. The Greek philosopher Heraclitus may have stated that “character is destiny” and described outstanding character traits as trustworthiness, respect, responsibility, fairness, caring, and citizenship. Hamming’s family upbringing and role models contributed to his development of these traits, along with his determination to succeed and pursuit of excellence.
Many writers express the power that results from determination. Author, educator, diplomat, and Presbyterian clergyman Henry VanDyke (1852–1933) described this well when he said, “Some succeed because they are destined to, but most succeed because they are determined to.” Author and motivational speaker Zig Ziglar (1926–2012) said, “If you’re not willing to learn, no one can help you. If you are determined to learn, no one can stop you.” Regarding the drive for excellence, Vince Lombardi (1913–1970) said, “The quality of a person's life is in direct proportion to their commitment to excellence, regardless of their chosen field of endeavor.” Hamming was determined to overcome early obstacles and saw education, persistence, determination, and striving for excellence as the best methods to achieve his goals. He later encouraged coworkers and students to do the same.
Organization of This Book
Chapter Two: The Man begins with Hamming’s ancestry, role models, education, academic background, and work from 1915 to 1945. Overcoming many challenges, Hamming pursued knowledge, developed wisdom, and achieved insight for future opportunities.
Chapter Three: The Mathematician reveals how he supported the world’s brightest scientists, engineers, and mathematicians on the Manhattan Project to help end World War II. Hamming studied the traits that drove their success, and the lessons he learned would shape the rest of his life. The second part of this chapter presents his career as a Research Mathematician at Bell Labs (1946–1976), where he solved several fundamental problems, helped countless others, and earned his profession’s highest awards.
Chapter Four: The Mentor reveals how, after retirement from Bell Labs, Hamming moved to academia to inspire and empower others through his teaching, articles, and books. This chapter includes revealing memories of fifteen individuals who knew Hamming well from 1958 through 1998.
Chapter Five: hamming ripples presents my closing words as a final tribute to Richard Wesley Hamming and a challenge to readers.
I have included five appendices. Appendix A contains a previously unknown lecture by Wanda Hamming, his wife, about their time together in Los Alamos. Appendix B contains the full text of Hamming’s 1968 Turing Award lecture, One Man’s View of Computer Research. Appendix C contains the full text of Hamming’s exceptional 1986 Bellcore lecture, You and Your Research. Appendix D contains Hamming’s 1987 talk, A Scientist’s Life, and Appendix E includes some of his timeless lessons.
This book is my first attempt at writing a biography, and I found the project daunting. I endeavored to cite all of the sources I used, verify facts from multiple sources, paraphrase long quotes to the best of my ability, and provide links to relevant photographs and video clips. Any acts of omission are based on the need for more verifiable information about events long ago. Any errors are my responsibility alone, and I will strive to correct them in future editions. Please send any comments and suggestions via email to me at Martin.Mandelberg@RichardWesleyHamming.com.
To enable readers to benefit from understanding Hamming’s life and teachings, I now present the story of Richard Wesley Hamming as the Man, Mathematician, and mentor I know well and wish to honor.
3 Hamming video at https://www.youtube.com/watch?v=Z4NGQZ7Jatk