Alan Iverson’s Turing Award lecture; delivered in 1979, published in 1980.
Some nice quotes:
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
— Alfred North Whitehead
Q. What deficiencies does Iverson identify with mathematical notation?
A. It’s not universal: interpretation depends on the topic, author, context.
Q. What three advantages does Iverson see in programming languages over mathematical notation as a tool of thought?
A. They’re universal (i.e. general-purpose), executable, and unambiguous.
Q. Thesis?
A. Notation increases our mental capacity; there’s an opportunity to combine the advantages of mathematical notation with the advantages of programming languages.
Q. What is a suggestive notation?
A. A notation is suggestive if the forms of the expressions arising in one set of problems suggest related expressions which find application in other problems.