Diversity in math fonts

We will examine the issues raised when modifying (LA)TEX fonts within math environments, and attempt to suggest effective means of accessing a larger variety of font options, while avoiding typographic nonsense. “Don’t mix faces haphazardly when specialized sorts are required” — Robert Bringhurst [9] 1 Stating the problem The advent of LATEX2ε has resulted in a type of ‘standardizing’ of font selection schemes (NFSS, in other words). The advantages are many, but the main one for me is this: unlike other software that’s more expensive and of poorer quality, changing fonts is as easy as changing your socks. In fact, the ‘heroic’ days of plain are just a memory, where changing from the default \textfont0 meant generating a new format, not to mention various encodings . . . The temptation to play is therefore very great, especially if you want to break with the monotony of countless preprints and other (LA)TEX documents. I won’t say much about anything other than PostScript fonts, mainly because I can only test my hypotheses on them. Sebastian Rahtz’ psfonts now allows anyone equipped with a PostScript printer to choose their text fonts for use with LATEX: Times, Bookman, New Century Schoolbook, Palatino. You can ftp to ctan sites to pick up everything you need to use a wide variety of commercial fonts. Alan Jeffrey’s fontinst program makes it easier to create the interface needed to use PostScript fonts with LATEX. The choices are almost limitless, with some 20,000 fonts to choose from for your document. Unfortunately, if your document has equations, this diversity is pretty much an illusion. There are actually very few math fonts, and of these, only a few are designed to work with TEX. To my 1 Note that ‘LATEX’ can be understood as having two relatively independent meanings: it’s a program to typeset scientific texts, and it’s also a standard in the electronic exchange of documents. This article is concerned with the former: producing documents which are to be printed and thereby benefit from typographic programs adapted to the purpose. 2 This count, based on Unique IDs, is relatively outdated, as recent fonts IDs would imply that we’ve reached a count approaching 90,000! knowledge, here are the font collections that provide a significant set of mathematical glyphs: The native TEX fonts: these are, of course, cmmi/ cmsy/cmex, with the addition of the AMS symbol fonts (msam/msbm); Some non-native TEX fonts: initially developped in MetaFont format to complement the Concrete text fonts by Knuth, are the Euler fonts, which aren’t coded in quite the same way as the standard TEX fonts, and do not really provide a replacement, as so many extra symbols are missing. There is an option available on CTAN, euler.sty by F. Jensen and F. Mittelbach, which makes installing the Euler fonts easier. However, the Eulers weren’t designed to be combined with any particular text fonts— the best you can say is that they ‘work’ with Bitstream Charter or, of course, Concrete. Karl Berry has recently used Euler with Palatino, a valid combination since both font families were designed by Hermann Zapf. U. Vieth designed a math font based on Knuth’s Concrete fonts. It is also missing many variants and glyphs, but enjoying an NFSS support package; MathTime: this family is a full alternative to the CM collection, but is missing some glyphs from the AMS collection; Lucida New Math: this family is as comprehensive as possible; PostScript Symbol font: almost as widespread as Courier, it yields upright Greek letters, and includes a number of basic math symbols; Mathematical Pi: usually used by (photo)typesetting software, this is a collection of six fonts whose glyph set is rather extensive; and some more: let us also notice that many scientific software programs use proprietary fonts to display equations on-screen or print them on paper. Not to mention the specific proprietary fonts used by some publishers. In current (LA)TEX, a math font family needs to have at least three members: math italic (cmmi is the default), symbols (cmsy), and extensions for building different-sized symbols (cmex). Taking design consistency and glyph set exhaustivity into account, of the fonts listed above, we are effectively left with with three font families, alternatives which are both complete and unified (well, one less so than the others): 3 Among them, Mathematica provides a font set with a rather rich set of glyphs. U. Vieth has made TEX virtual fonts for them, along the lines of mathptm; see below. 122 TUGboat, Volume 19 (1998), No. 2 Conjecture 1.— Let x, y, z, be integers; for α ∈ N, denote by Ωα ⊂ N the set of prime integers p (called p-primes in the sequel) such that the following equation (known as Frimas’ last equation) x + y = z admits infinitely many solutions divisible by α. We conjecture: • Ωα = ∅ (Ωα is not empty), • more precisely, cardΩα > w where w is the well-known Whylles' constant. Evidence for the conjecture.— Denoted by A, M, O, the famous inferior constants of Whylles, the three following formulae are very instructive: x = 2πz ⇐⇒ cardΩα | M and φ(t) = 1 √ 2π ∫ t