Carolina QuotesRalph P. Boas, Jr.
North Carolina · connected1912–1992
American mathematician (1912–1992)
- Worked at Duke University
mathematician, university teacher
In the libraries
Read Ralph P. Boas, Jr.
Recorded without a firm citation
Kept here, labelled, rather than mixed in above.
The predecessors of Newton and Leibnitz knew perfectly well how to determine tangents and areas, but they had to approach each problem from first principles. The great contribution of Newton and Leibnitz was precisely to make the procedures for finding tangents, areas, etc. into a calculus, that is, a systematic way of calculating—a collection of algorithms, to use the currently fashionable word.
Suppose you want to teach the "cat" concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats, saying "kitty" each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. They should come one at a time; too many at once overload the circuits.