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When I look in old mathematical textbooks from the seventies and before, mathematics is always upright. Their use of italic letters in other contexts, however, shows that this is not because of technical limits. On the other hand, all textbooks I have seen with italic math look very TeX-like. So I was wondering if this is a coincidence? could italic math be an invention by Knuth introduced in TeX?

Does someone know the history of italic math?

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I think Knuth was trying to mimic a very specific style used by Addison Wesley for the first volumes of his TAOCP books (before TeX). –  Stephan Lehmke Jun 24 at 17:20
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Warning opinionated brief history ahead; Old publishers used a very pragmatic foundary process but they have made it in a very stylish way which in turn became very hip (very much like the technical drawings from 60s). Then as technology advanced, people were less impressed and looked for handwriting-like stuff just like the great mathematicians' notes. It's very much like buying the guitar of your favorite guitar player. Every generation redefines what a legendary guitar is. –  percusse Jun 24 at 17:43

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No, it was a standard convention. See, e.g., http://www.ams.org/journals/tran/1936-040-03/S0002-9947-1936-1501880-4/S0002-9947-1936-1501880-4.pdf (year 1936).

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French mathematics are traditionally typeset in italic for lower case letters, while uppercase and greek letters (both uppercase and lowercase) are upright. –  Bernard Jun 24 at 17:53
    
My 1927 copy of "Ordinary Differential Equations" by E.L. Ince, published by Longmans, Green & Co also used italic math. It does look very LaTeX -like, though I note they use widely separated horizontal dots on a line by itself, where today we would use \vdots. Another difference I note is that there is no \mathrel spacing in \displaystyle or \textstyle, but there appears to be such spacing in \scriptstyle (just the opposite of modern typesetting). Finally, greek uppercase letters are also italicized. p.s. footnote symbols are not superscripted, but inline. They are also centered –  Steven B. Segletes Jun 24 at 19:01
    
AFAIR I've even seen this style in math books that are a few 100 years old –  daleif Jun 24 at 19:51

I've never noticed any math books with an upright font for variables. I think italics have been very standard for a very long time, at least in American books. Here are three old American books that use italics:

Also:

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For a notable exception to the general rule of math books using italic math fonts, see the book "Concrete Mathematics" (ca 1990) by Graham, knuth, and Patashnik. The math font used for that book is Euler, designed by Zapf. Definitely not italic... –  Mico Jun 24 at 21:54
    
Looking at those books one can clearly see where Computer Modern came from :) –  Manuel Jun 24 at 22:11
    
Your 1807 Hutton reference, while using italics for lower-case variables, seems to use small-caps for upper case variables. See, for example, the figures on p.62 and references to them in the text. –  Steven B. Segletes Jun 25 at 12:50

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