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I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied diet, with plenty of content from things other than alphabets alone. Math notation is an important part of the menu I have in mind, and I'm writing now to ask for recommendations as to articles suited to general college-student readers.

I know the rich Cajori book History of Mathematical Notations (which dates from the Hoover Presidency) and Jeff Smith's website http://jeff560.tripod.com/mathsym.html. Both are filled with detail, and detail is good. But I'd also like to find some more general, focused, and readable essays about the intellectual history of this field. Do kindly share your favorites with me.

What I'm looking for is not abstract semiotics but concrete ideas — and perhaps disputes over ideas, which are often helpful for understanding what was important to people in a different time and state of mind than ours.


Addendum: Since there has been little movement since the original post, let me add a bit more about what I know. I have a bibliography of twenty-two items at the end of John Sören Pettersson's "Numerical Notation," Section 69 of Peter T. Daniels and William Bright's The World's Writing Systems, (New York: Oxford University Press, 1996), pp. 795–806. It is very concise, and it lacks the idea-orientation I am hoping to find.

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I'm not posting this as an answer because I don't have a good reference for you, but you could do a pretty interesting talk on the history of the equals sign. It was invented by Robert Recorde in 1557. (I wrote a blog article about this.) One curious thing about the history is that for a long time the = only caught on in England. Descartes introduced ∝ instead, and Descartes' symbol was dominant in continental Europe until the mid-17th century. –  MJD Aug 23 '12 at 12:03
    
I'm pretty sure there should be examples for you during Leibniz's and Newton's development of what we now call "calculus". It should also be especially rich with differing viewpoints on what is important. –  rschwieb Aug 23 '12 at 12:31
    
Charles Babbage also commented on the importance of notation, including exponential: writing $x^3$ instead of $xxx$ led to non-integral exponent $x^a$, and Leibniz' 'd' notation for derivatives versus the overdot. In fact he helped reform notation at the Analytical Society at Trinity College. See "Mathematical Work of" and the collected works. –  alancalvitti Aug 23 '12 at 13:30
    
@MJD, the link 'a scan of the relevant pages to Wikipedia' from your article on Recorde returned 404. –  alancalvitti Aug 23 '12 at 13:33
    
@alancalvitti Thanks very much for the report. The page is now here, and I am in process of correcting the link on the blog. –  MJD Aug 23 '12 at 13:39

2 Answers 2

One particularly intriguing piece of history of the sign for equality is Leibniz's use of the sign "$_{\ulcorner\!\urcorner}$" for equality, rather than the "=" we are familiar with. On the other hand, Leibniz emphasized repeatedly that his was a generalized relation of equality "up to" an infinitesimal, so that one could have $a +dx \;{}_{\ulcorner\!\urcorner} \;a$ for nonzero real $a$. This piece of notation is mentioned in an article by McClenon, R. B.: A Contribution of Leibniz to the History of Complex Numbers. American Mathematical Monthly 30 (1923), no. 7, 369-374 online here. For a related discussion of Leibniz, see the recent article here.

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A recent book by Joe Mazur called Enlightening symbols may be the answer to your dreams.

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