Re: [HM] the importance of notation
Leo Andrew McCreary-Lusk (llusk@ccmail.gc.cc.fl.us)
Tue, 11 May 99 09:19:01 -0600
Friends,
The thread of which mathematical symbols or notations we feel is most
important in the advancement of mathematics is indeed a delightful -
and less strained - topic we can all enjoy and contribute to. I sight
just a few remarks attributed to our noteworthy predecessors.
Augustus de Morgan, who was a student of the history of mathematics
himself, is quoted as saying, ". . . Mathematical notation, like
language, has grown up without much looking to, at the dictates of
convenience and with the sanction of the majority." (Cajori - History
of Mathematical Notation, Vol II)
J.W.L. Glaisher ("Logarithms and Computation" - 1915) rallys to the
importance of the role notation has played in mathematical development
and points to the history of notation as a topic worthy of scholarly
study: "Nothing in the history of mathematics is to me so surprising
or impressive as the power it has gained by its notation or language.
No one could have imagined that such 'trumpery tricks of abbreviation'
as writing + and - for 'added to' and 'diminished by,' or x^2, x^3, .
. . for xx, xxx, . . . , etc., could have led to the creation of a
language so powerful that it has actually itself become an instrument
of research which can point the way to future progress."
In Alfred North Whitehead's "An Introduction to Mathematics" he writes
in a matter-of-fact manner on the power of symbols: "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."
I can't pick the notation I feel is most important - it is like asking
me to chose between chocolate and vanilla ice cream. I like both - I
appreciate all. I have enjoyed the contributions sent in by my
colleagues. Please continue. Your thoughts are interesting and
valuable.
Leo Andrew McCreary-Lusk