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The celebrated gothic R and I glyphs are present in the Don Knuth's computer modern symbols family. Is there any "story" concerning the glyphs, e.g. why they where abandoned in the realisation of the euler "cousin", and, maybe, on which typeface Knuth took inspiration to design them? Personally, I would be very interested in discover how the whole alphabet (uppercase and lowercase) could appear, since so far I cannot figure out it nor any "font detector" helped me along this research.enter image description here

Martino
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    Without knowing anything about the true story, I might just guess that "R" and "I" were being set aside for Real and Imaginary number usage. – Steven B. Segletes Mar 28 '24 at 18:38
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    @StevenB.Segletes -- It is definitely Knuth's preference to use fraktur R and I for real and imaginary numbers; other mathematicians prefer "Re" and "Im". But the shapes that Knuth used in his Metafont fonts were not adopted into Euler because the shapes don't fit with the design of Euler. Hermann Zapf was an exceedingly competent and noted font designer, and the design of Euler is consistent. I don't know what Knuth's model was, but I suspect that looking at old issues of the AMS Transactions or Acta Mathematica will turn up similar shapes. – barbara beeton Mar 28 '24 at 18:50
  • Barbara's answer at https://tex.stackexchange.com/questions/192692/why-does-amsmath-use-fraktur-for-real-and-imaginary-parts is perhaps related. – Steven B. Segletes Mar 28 '24 at 19:17
  • For many examples showing the wide range of Fraktur, see https://tex.stackexchange.com/questions/320403/how-do-i-typeset-a-fraktur-x-that-looks-like-r/320407#320407 – Steven B. Segletes Mar 29 '24 at 21:30

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Why do you think the glyphs were abandoned? Knuth's Computer Modern has no Fraktur font but Zapf's Euler has one. That is, the complete alphabet in upper- and lowercase is available. And AMS placed the uppercase Fraktur R and I into font eusm10 using the slots known from cmsy10.

Knuth might have designed only these two Fraktur letters as he didn't need more. So he had a lot of freedom as there is no complete alphabet. To get Zapf's complete alphabet look at eufm10, for example.

It's impossible to say which typefaces inspired Knuth; or better, only he might be able to say that. We know that he looked at a lot of math books, the complete set of the Transactions of the AMS, articles by type designers from different centuries, alphabets by artists like Dürer, and many other sources.

When you look at the Luthersche Fraktur (1708) or the Breitkopf-Fraktur (1750), just to name two fonts, you will find the two-part I and elements of the decoration of the R. That is, the letters might be influenced by old Fraktur fonts.

Udo Wermuth
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I've ever written a material about mathematical alphabets which contains some history, while unfortunately is in Chinese. Let me rewrite the history about the Euler Fraktur letters by Zapf here in English.

"With Donald Knuth’s assistance and encouragement, Hermann Zapf, one of the premier font designers of this century, was commissioned to create designs for Fraktur ...". (See page 3 of User’s Guide to AMSFonts Version 2.2d). From a font instruction (see page 23), we could find that Zapf design the Euler Fraktur letters in 1980-1983.

Zapf reshaped many letters in the amsfonts package which was updated in 2009 (see here).

M. Logic
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