Re: [HM] the importance of notation
James A Landau (JJJRLandau@aol.com)
Mon, 10 May 1999 08:54:56 EDT
In a message dated 99-05-10 06:41:35 EDT, manatcas@maltanet.net (Emmanuel
Attard Cassar) wrote:
> Which were, in your opinion, the notations that have permitted the greatest
> advances in mathematics?
One candidate is the use of exponents. It is said that if Archimedes had had
a decimal notation, he would have invented calculus. This I doubt. However,
Archimedes did find the indefinite integrals of at least a few simple
polynomial expressions. If he had had our notation for exponents, I suspect
he would have been able to generalize from this to the Fundamental Theorem of
Calculus, or at least a form of the Fundamental Theorem for polynomials.
This reminds me of a nightmare one of my calculus teachers told us: suppose
that infinitesimals and the epsilon-delta technique had never been invented.
Can you imagine having to do all the problems in this class using Archimedes's
Method of Exhaustion?
James A Landau