Who is Richard Hamming? Wisdom on the Art of Learning From The One of the World’s Most Impactful Engineers & Greatest Teachers.


Richard Hamming is one of the great minds of the 20th century. Below is an attempt to capture that wisdom in one shareable place.



“Courage, or confidence, is a property to develop in yourself. Look at your successes, and pay less attention to failures than you are usually advised to do in the expression, “Learn from your mistakes”. The courage to continue is essential since great research often has long periods with no success and many discouragements.”


Richard “Dick” Hamming, a longtime resident of Monterrey, California, is perhaps best known for his work on numerical methods, automatic coding systems, and error-detecting and error-correcting codes impacting projects of worldwide significance, from The Manhattan Project to nearly all of the Bell Laboratories’ most prominent achievements. His mathematical formulas allow computers to correct their own errors, making possible such innovations as modems, compact disks, satellite communications, and machine learning.

‘‘If you don’t work on important problems, it’s not likely that you’ll do important work,’’ was a favorite maxim of Hamming’s, and he noted that his discoveries were the high point of his life. ‘‘The emotion at the point of technical breakthrough is better than wine, women and song put together,’’ he said.

Hamming was an effective spokesman representing the user community in computing, particularly toward getting better human-machine interfaces through better languages, operating systems and programming practices. He had a central role in the development of computer and computing science, and contributed significantly to the area of information science, which includes his error-correcting codes. His codes, filters, and methods became indispensable parts of the digital engineer’s tool kit. ‘‘We were first-class troublemakers,’’ said Hamming. ‘‘We did unconventional things in unconventional ways and still got valuable results. Thus, management had to tolerate us and let us alone a lot of the time.’’

As a person Hamming was never dull. He had strong opinions, and he liked to express them. His voice comes through in his books in a way that few technical authors achieve. He liked to give people advice, especially young people, whom he would educate and entertain with his often-repeated lecture “You and Your Research”. He enjoyed the speaker’s platform, and on occasion he enjoyed, as he jokingly said, “hamming” with a small h.

Hamming cautioned that “the purpose of computation is insight, not numbers” suggesting that “a good theoretician can account for almost any result that is produced, right or wrong,” which makes it important to be able to tell if we have a sensible answer. In the end, there is still no substitute for Hamming’s emphasis on common-sense thinking.  

Besides his work in computing, information science and a variety of contributions to his professional associations, Richard is known for his fluent, multidisciplinary mind. Trained as a engineer during World War II and after 30 years at Bell Labs, Hamming transitioned to writing and teaching at the Naval Postgraduate School.

His insights on computer science, learning, and life are unique, rare, and correct with unusual consistency. Speeches and writings made long ago stand up in their logic and validity today as much as when they were written, given their basis in the deeply fundamental wisdom of the world.

Adopting the “Hamming” approach to thinking is difficult, as is imitating any genius, but utilizing its core tenets will very quickly begin to remove the cobwebs from your mind. Given our increasing reliance on data, in the form of artificial intelligence and machine learning, is driving much of our behavior through phone apps, social media conditioning, and an increasing reliance on gadgets, Hamming’s maxims for and warnings to users are more important than ever before.

Richard Hamming Quotes

“The purpose of computation is insight, not numbers.” 

“If you don’t work on important problems, it’s not likely that you’ll do important work.” 

“It is better to do the right problem the wrong way than the wrong problem the right way. “

“It is not easy to become an educated person.” 

“Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started. It requires a lovely balance.” 

“Beware of finding what you’re looking for.”

“I need to discuss science vs. engineering. Put glibly:
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.” 

“The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish.” 

“Vicarious learning from the experiences of others saves making errors yourself, but I regard the study of successes as being basically more important than the study of failures. There are so many ways of being wrong and so few of being right, studying successes is more efficient.”

“Newton said, ‘If I have seen further than others, it is because I’ve stood on the shoulders of giants.’ These days we stand on each other’s feet!” 

“What you learn from others you can use to follow.
What you learn for yourself you can use to lead.” 

“When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn’t the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you.” 


Suggested Readings on Richard Hamming

coming soon

Speeches & Videos

“Learning to Learn” by Richard Hamming – In 1995, Hamming spoke at the Naval Postgraduate School, offering some of his most incisive, cutting, and original thoughts while introducing his last work from the Introduction of The Art of Doing Science and Engineering: Learning to Learn.

You and Your Research (and Career) —This lecture was originally delivered to graduate students at the Naval Postgraduate School in Monterrey, California, on June 6, 1995. The lecture was the last lecture of a capstone course taught by Dr. Richard Hamming called “The Art of Doing Science and Engineering.”

Hamming’s Books

Numerical Methods for Scientists and Engineers, McGrawHill, 1962; 2nd ed. 1973; Dover reprint 1985; translated into Russian.

Calculus and the Computer Revolution, Houghton-Mifflin, 1968. Introduction to Applied Numerical Analysis, McGraw-Hill, 1971.

Computers and Society, McGraw-Hill, 1972. Digital Filters, Prentice-Hall, 1977; 2nd ed. 1983; 3rd ed. 1989; translated into several European languages.

Coding and Information Theory, Prentice-Hall, 1980; 2nd ed. 1986.

Methods of Mathematics Applied to Calculus, Probability and Statistics, Prentice-Hall, 1985.

The Art of Probability for Scientists and Engineers, AddisonWesley, 1991.

The Art of Doing Science and Engineering: Learning to Learn, Gordon and Breach, 1997.

Mental Models: The Power of Reframing Problems Through Inversion

An approach to problem-solving that starts with imagining worst-case scenarios – and then using those scenarios as the basis for developing solutions.


How might this apply to great teams and cultures?
One of the methods used in creative ideation sessions is reverse thinking. Instead of following the ‘normal, logical’ direction of a challenge, you turn it around (or an important element in the challenge) and look for opposite ideas.

How might this apply to great products?
For instance,  when designing a chair, you can list the assumptions of a chair (it needs to have legs)  and think its opposite (no legs?!) to trigger additional ideas: what if chairs were hanging from the ceiling? or be built as part of the table? or….

taking a DEEPER LOOK

The concept of Inversion is often interpreted in two different ways, both are valuable to consider.

The first is the idea of considering the opposite. In particular, envision the negative things that could happen in life. The Stoic philosophers like Marcus Aurelius, Seneca, and Epictetus regularly conducted an exercise known as a premeditatio malorum, which translates to a “premeditation of evils.”

The second is the idea of working with the end in mind. German mathematician Carl Gustav Jacob Jacobi was famous for some work on elliptic functions that eludes me. Jacobi often solved difficult problems by following a simple strategy: “man muss immer umkehren” (or loosely translated, “invert, always invert.”).

Both approaches look at the end result uniquely. Considering an opposite asks you to hold your ideal result loosely, and to consider the opposite of your desired result. Working with the end in mind assumes you are keeping the same goal but approaching the solution from a different direction, by backing into it.

Very few problems can be solved directly. The most wicked, intractable problems must be dealt with indirectly. As such, the Inversion model is one of the most powerful mental models in our toolkit as human beings.

If you are always inverting a problem, like the way you play with a Rubik’s cube, you experience them from multiple perspectives. Multiple vantage points challenges your certainty. It can shake your beliefs.


Let’s take a look at some examples.

Let’s start with the positive-negative notion. When I coach clients, I get many people at major points of transition in their lives and careers. Some are facing big promotions, others are considering leaving their jobs for a second chapter.

Often I’ll ask: what is it you want? Seems like a simple enough question, but it’s really hard to answer. Specifically, what do you really want to happen?

Many people have a very hard time imagining the life, career, or outcome we want because we’ve been conditioned for such long periods of our life (at home, in school, at work) to think a certain way or to embrace a certain idea of success.

However, when asked to consider what would guarantee our unhappiness…and few are at a lack of words.

Let’s move on to the positive-negative notion. I teach an EMBA class called Managing Innovation. Most people take the class to learn how to improve and manage innovation in their organizations.

The course is guided by the central question: What can be done to foster innovation? The answers are pretty standard: engage small teams, enable autonomy, consider the tension of deliberate and emergent strategies, etc. And, by the way, implementing any one of those things in a culture that doesn’t naturally gravitate toward those qualities is really hard. 

But if we invert the problem to: How do we avoid becoming traditional or unoriginal? we consider all the things we can do to discourage innovation: reduce feedback loops, increase top-down decision making, enable homogeneous thinking, foster resistance to risk. Generally speaking, we would want to avoid these things, right?

And, it sounds so easy, doesn’t it? If we were to follow our own council we would have to take our own advice: “Just stop doing these things and do less of these other things instead.” Behavior change of any kind is no small thing.

Moving indirectly gains more ground than directly. 

Thinking forward/backward or negative/positive about a problem results in some action, you can also think of adding vs. subtracting.

Despite our best intentions, thinking forward increases the odds that you’ll cause harm (through unintended consequences). For example, drugs designed eradicate one disease might also have adverse effects, become harmful if overused, or cause antibiotic resistance in bacteria.

Thinking backward, call it subtractive avoidance or inversion, you are less likely to cause harm. Inverting the problem won’t always solve it, but it will help you avoid trouble and thinking through some of the undesirable and unintended consequences. You can think of it as the avoiding negativity filter. It’s not sexy but it’s a very easy way to improve.

So what does this mean in practice?

Thinking about what you don’t want isn’t necessarily inspiring, but it does bring clarity and can aid decision making to a problem or question that brings nothing but overwhelm. Many of the smartest people in history have done this naturally.

Inversion helps improve understanding of the problem on which you are focused. By using this method, you are forcing yourself toward doing the work of having an opinion that considers multiple perspectives.

The key takeaway: Spend less time trying seeking the right answer and more time avoiding the wrong answer. Avoiding loss is an easier starting point than seeking gain.