"The initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programming, I continue to believe that its most important use remains to be exploited: as a simple, precise, executable notation for the teaching of a wide range of subjects."

"I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations."

"We owe a great debt to Kenneth Iverson for showing us that there are programs that are neither word-at-a-time nor dependent on lambda expressions, and for introducing us to the use of new functional forms."

"With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation."

"The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation."

"Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation."

"Everyone knows that debugging is twice as hard as writing a program in the first place. So if you're as clever as you can be when you write it, how will you ever debug it?"

"Associative arrays are very very useful things and if you are only going to have one data structure that's the one to have. Because you could build everything else with it if you want."

"Controlling complexity is the essence of computer programming."

"Mechanical rules are never a substitute for clarity of thought."

"C is a razor-sharp tool, with which one can create an elegant and efficient program or a bloody mess."

"Advice to students: Leap in and try things. If you succeed, you can have enormous influence. If you fail, you have still learned something, and your next attempt is sure to be better for it. Advice to graduates: Do something you really enjoy doing. If it isn’t fun to get up in the morning and do your job or your school program, you’re in the wrong field."

"Do what you think is interesting, do something that you think is fun and worthwhile, because otherwise you won't do it well anyway."

"The most effective debugging tool is still careful thought, coupled with judiciously placed print statements."