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. — Kenneth E. Iverson Copy Share Image
If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from… — Kenneth E. Iverson Copy Share Image
The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation… — Kenneth E. Iverson Copy Share Image
It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. [...] Indeed,… — Kenneth E. Iverson Copy Share Image
The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical]… — Kenneth E. Iverson Copy Share Image
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,… — Kenneth E. Iverson Copy Share Image
Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant… — Kenneth E. Iverson Copy Share Image
Overemphasis of efficiency leads to an unfortunate circularity in design: for reasons of efficiency early programming languages reflected the characteristics of the early computers,… — Kenneth E. Iverson Copy Share Image
The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the amount… — Kenneth E. Iverson Copy Share Image
The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide… — Kenneth E. Iverson Copy Share Image
Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows… — Kenneth E. Iverson Copy Share Image
I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I… — Kenneth E. Iverson Copy Share Image
The initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programming,… — Kenneth E. Iverson Copy Share Image
![“It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. [...] Indeed, the very suggestiveness of a notation may make it seem harder to learn because of the many properties it suggests for exploration.” quote by Kenneth E. Iverson](https://sms4smile.com/quotes/img-quotes/3f1/kenneth-e-iverson-37528_describing_it-is-important-to-distinguish-the-diffi_460789.jpg)
![“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.” quote by Kenneth E. Iverson](https://sms4smile.com/quotes/img-quotes/d25/kenneth-e-iverson-37528_ambiguity_the-precision-provided-or-enforced-by-pr_471194.jpg)
![“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…” quote by Kenneth E. Iverson](https://sms4smile.com/quotes/img-quotes/1ab/kenneth-e-iverson-37528_application_although-mathematical-notation-undoubted_1904632.jpg)
