Also, Walter Noll of Carnegie Mellon Univ. wrote a book, "Finite-Dimensional Spaces" in 1987 which basically presented undergraduate math in a notationally and conceptually unified manner. Some of the notation and terminology was strange, but consistent. Mike Matsko ----- Original Message ----- From: Fritz Ruehr Date: Friday, January 28, 2005 3:10 pm Subject: Re: [Haskell-cafe] mathematical notation and functional programming

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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