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.

— "A Personal View of APL",

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.

— "Kenneth E. Iverson", autobiographical sketch from an unfinished work (ca. 2004), on his experience at Harvard with "a Masters program in Automatic Data Processing in 1955; in effect, the first computer science program."

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**.

— Ch. 10, §D (Math for the Layman (1999))

The difficulty, as in all this work, is to find a **notation** which is both concise and intelligible to at least two people of whom one may be the author.

— with Abdus Salam. (October 1951). "The Renormalization of Meson Theories".

I counted to ten slowly, using binary **notation**.

— Chapter 8 (The Door Into Summer (1957))

In all engineering disciplines nowadays, software engineering excluded, there exists an established engineering process to develop a system, which is accompanied by a number of suited modeling description techniques. Software engineering, being a rather new field, has not as yet established any clear methodical guidance or a fully standardized modeling **notation**.

— Bernhard Rumpe (2002). "Executable Modeling with UML. A vision or a Nightmare."

The development of Indian trigonometry , based on sine as against chord of the Greeks , a necessity for astronomical calculations with his own concise **notation** which expresses the full sine table in just one couplet for easy remembrance. One of the two methods suggested by him for the sine table is based on the property that the second order sine differences were proportional to sines themselves.

— In, P.245 (Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures)

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.

— Kenneth E. Iverson, "A Personal View of APL",

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,

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**.

— Ch. 10, §D (Math for the Layman (1999))