Re: [HM] the importance of notation

John Conway (conway@math.Princeton.edu)
Mon, 10 May 1999 18:13:57 -0400 (EDT)

On Mon, 10 May 1999, James A Landau wrote:

> 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.

But Archimedes DID invent the calculus - or at least, the integral calculus!

> Can you imagine having to do all the problems in this class using Archimedes's
> Method of Exhaustion?

Yes, since Archimedes' method of exhaustion really IS just the
epsilon-delta method for the integral calculus, except that since he uses
inequalities he has to repeat the argument for every particular case.

John Conway