[Haskell-cafe] mathematical notation and functional programming

Fritz Ruehr fruehr at willamette.edu
Fri Jan 28 15:10:07 EST 2005

Well, I don't know about modern works which might appeal to knowledge 
of FP languages, but there is a well-known, 2-volume work by Cajori:

     Cajori, F., A History of Mathematical Notations, The Open Court 
Publishing Company, Chicago, 1929 (Available from Dover).

I know it through Ken Iverson (may he rest in peace), the creator of 
APL. (Dr. Iverson's own notations were not to everyone's taste, but I 
think they were a bigger influence on Backus and the recent wave of FP 
than is generally acknowledged.)

APL *did* have "implicit maps and zipWiths" in the sense that scalar 
functions would be automatically extended to vectors (and similarly for 
higher dimensions). I think my PhD advisor, Satish Thatte, did some 
work on extending this sort of "notational abuse" to Hindley-Milner 
systems, but I don't have the citations at hand.

OK then, googling on Cajori yields this quote from a math history site:

   "He almost single-handedly created the history of mathematics as an 
academic subject in the United States
    and, particularly with his book on the history of mathematical 
notation, he is still one of the most quoted
    historians of mathematics today."

More googling on "mathematical notation" reveals that there *are* 
people concerned about these issues, Steven Wolfram being an 
easily-recognized example (he refers to Cajori's work).

   --  Fritz

On Jan 27, 2005, at 12:14 PM, Henning Thielemann wrote:

> I wonder if
> mathematical notation is subject of a mathematical branch and whether
> there are papers about this topic, e.g. how one can improve common
> mathematical notation with the knowledge of functional languages.

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