Communication of Mathematics with TEX

IntroductionUntil about the early 1960s, most published mathematics was typeset professionally by skilled compositors working on Monotype machines. As this form ofhot-metal composition became less readily available, on account of both cost and the fact that skilled compositors were retiring and not being replaced, typewriters began to be used to prepare less prestigious publications. Phototypesetting (cold type) began to appear gradually, although it was more expensive than typewriter-based composition, and generally not as attractive in appearance as professionally prepared Monotype copy.By the mid-1970s, Monotype composition was essentially dead. Donald Knuth, a professor of computer science at Stanford University, was writing a projected seven-volume survey entitled The Art of Computer Programming (TAOCP). Volume 3 was published in 1973, composed with Monotype. By then, computer science had advanced to the point where a revised edition of volume 2 was in order but Monotype composition was no longer possible. The galleys returned to Knuth by his publisher were photocomposed. Knuth was distressed: the results looked so awful that it discouraged him from wanting to write any more. But an opportunity presented itself in the form of the emerging digital output devices-images of letters could be constructed of zeros and ones.1 This was something that he, as a computer scientist, understood. Thus began the development of TeXThe problemMathematics as a discipline depends on its own arcane language for communication. Prior to the ubiquitous availability of personal computers, the options for communicating mathematical knowledge were limited to faceto-face contact, preferably with a writing surface handy, although conventions developed to enable intelligible telephone discussion, personal letters (at least bits of which required handwritten notation), or formal publication. The last mode required a highly skilled compositor, working either with traditional hand-set type or with a hot-metal typecaster, or a combination of the two.The gold standard for typeset mathematics in the midtwentieth century was the Monotype typecaster [PhR, PhH]. The audience was relatively small, and the work exacting. Since mathematical notation is essentially multi-level (see Figure 1), the Linotype, the linear-type workhorse for newspapers and most book publishing, was not up to the task. Only a few suppliers would take on such work, and mathematical composition was always considered penalty copy''.2For the first half of the twentieth century, a mathematical work for publication began as a manuscript, either handwritten or partially typewritten (the text) with mathematical symbols inserted with pen and ink. A typescript was typically prepared by a secretary: senior faculty had their own personal assistant, junior members relied on departmental staff. Often the secretary primarily responsible for manuscript preparation had a typewriter with special capabilities, greatly reducing the need for manual insertions.Various mechanical advancements improved the visual quality of manuscripts, and documents intended for limited audiences or quick distribution, such as lecture notes or proceedings of meetings, were often published from such copy. The Varityper and IBM Selectric Composer, two enhanced typewriters with interchangeable type heads (and type styles emulating traditional printing typefaces), in the hands of a skilled typist, were capable of producing quite readable output, with character sets for typical mathematical notation and variant type sizes needed for accurate representation of sub- and superscripts. What they generally lacked was an easy mechanism for justifying lines, an easily recognizable characteristic of typeset copy; justification was possible, but it always required a second pass, which was usually not fully automatic. Nonetheless, as prices increased for hot-metal composition, even some traditional journals began to use this method of preparing copy for the printer. …