I don’t apologise for revisiting one of my pet topics. This was partly inspired by reading Simon Garfield’s book Just my type over the holidays.
About the only generally accepted principle in typography is
People read most efficiently what they are used to.
Now the majority of written mathematics today is typeset in LaTeX, with Computer Modern fonts. On the other hand, the rest of the world rather likes uncontrolled experimentation in the choice of fonts: Garfield points out that the advent of font design programs puts this in everybody’s reach. The general principle may suggest that mathematicians should stick to their current way of working, but is there a case for more variety?
In fact, it doesn’t greatly matter what you do, since when you publish the paper, the journal will put it into their own house style. This can result in some horror stories. One from my own experience involved a publisher who, between getting my proof corrections and issuing the journal containing the paper, changed all the fonts. Not only was my work on producing good line and page breaks completely wasted, but the new fonts did not include blackboard bold, and the publisher had not even noticed – the paper appeared with blank spaces where blackboard bold letters should have been. I complained, and the paper was reprinted correctly in the next issue of the journal.
But bad things happen routinely too. A major academic publisher sets the abstract, section headings, and body text in three different fonts. That is possibly OK; the problem arises because mathematical formulae are also set in three different fonts.
One thing that is vital for mathematics is that the same object should be represented by the same character, and we use typography to distinguish different characters. When I was a student, I spent some time reading Richard Brauer’s papers. For him, is a group; its order is , and a typical element of the group is . Hard enough (with my limited exposure to Fraktur) as it was; imagine if the different Gs had proliferated because of the journal’s style!
But there are some situations in which we have control. I see three of these: producing course material for teaching; making beamer slides; and book publishing (if either you publish the book yourself, or you are lucky enough to have a publisher who trusts you to do the book design within their constraints, as I was with my book Permutation Groups).
I see no need to argue that we should continue to use LaTeX, or at least some flavour of TeX; its understanding of the rules of mathematical typesetting is far superior to any more recent software product. Now changing fonts in LaTeX is not especially difficult; any font can be used, as long as its metrics have been made available in TeX format. What is more difficult is ensuring balance between the text fonts and the mathematical fonts. All too often, you see a very different text font used with the standard Computer Modern math fonts.
Donald Knuth designed Computer Modern (the name “modern” indicates that the fonts are based on the “modern” designs associated with Bodoni and Didot in the eighteenth century) so that the text and math fonts would be well matched but well suited to purpose. The math italic font is slightly different from the text italic font for this reason. He later designed Computer Concrete (for the book Concrete Mathematics with Ron Graham and Oren Patashnik) to work with the AMS Euler math fonts. Other examples are somewhat limited, but include Times Roman and Palatino, each of which is called by loading a single package (mathptmx and mathpazo respectively).
The beamer package for slides uses sans serif fonts as the default; the designer made a positive decision to do so. But it is possible to change to other fonts. I have used this package to produce a few examples, shown here.
I don’t know how to display a PDF file within a WordPress page. (Turning it into a graphics file loses too much quality for my purpose here). So you will have to click on these examples separately. I have typeset a small shaggy dog story containing some mathematics in Beamer default sans serif, in Computer Modern, in Computer Concrete, in Palatino, and in Times Roman.
[Added later: now also in Vera Sans, see comments.]
Personally, I use Times Roman for teaching material and Palatino for beamer slides. (The argument for sans serif beamer slides is that they tend to be quite low resolution and the detail of serifs is lost; I partly agree, but feel that Palatino is more robust than Computer Modern.)
What do you think?