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I was wondering how did mathematical and scientific books got typeset before TeX? I see lots of papers from the 50's and 60's (on IEEE for example) running more than 20 pages long, with tons of complex equations and references. Yet they still look very neat and accurate (to some extent). How did it work back then?

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    Well, the types were set at that times at the printing company ;-) – user31729 May 10 '15 at 6:14
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    With typesetting machines (Linotype or Monotype) and mathematics, to a certain extent, set by hand. – egreg May 10 '15 at 9:03
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    If you're interested in how math material used to be typeset, before the advent of TeX, I recommend you read David Wishart's 2003 article, "The Typesetting of Mathematics," in: Type & Typography: Highlights from Matrix, the review for printers and bibliophiles, Mark Beatty Publisher. Excerpts from this piece may be found in section 1.6, "Setting maths", of "A few notes on book design", which is part of the memoir class. Type texdoc memguide at a command prompt to get this document. – Mico May 10 '15 at 11:15
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    I think that Mico meant 'texdoc memdesign' rather than 'texdoc memguide'. – Peter Wilson May 10 '15 at 18:13
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    Related to a post in History of Science and Maths:Writing Mathematical Symbols in 20th century – Gonenc May 10 '15 at 20:49
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actually, there was setting of math with computers before tex. very specialized, and usually quite expensive. in what follows, "symbol" is used to mean either a letter of some alphabet, a digit, or some other shape.

there are several phases in the history of math composition:

  • hand-set type -- anything before the late 1800s.

  • monotype -- several patents from 1885-1890 covered this system and its basic operation for ordinary text. the wikipedia article covers this pretty well. what it doesn't mention is the "4-line system" that was required for math. this is described in daniel rhatigan's m.a. thesis. this is the system used to compose the first editions of the first two volumes of knuth's "the art of computer programming", and it was the switch away from monotype that is the reason that tex exists today.

  • "typewriter" composition. actually, this is an oversimplification. the "direct type" methods were of two distinct kinds. both were best used on machines with a carbon rather than an inked ribbon.

    • traditional one-symbol-per-key typewriters. an "ordinary" typewriter has keys linked to type bars containing usually two symbols, with a "shift" key to change from lower to uppercase. any symbol not on one of these type bars had to be added by another method, either by hand or by the use of a widget called a "typit", a plastic device with a raised symbol at one end that could be stuck into a guide mounted on the typewriter where a key would impact the ribbon, and any key could be struck to impact the typit and transfer the image of that symbol to the ribbon and paper. typits were used on machines with either proportional or fixed spacing.

    • a machine with interchangeable "fonts". i know of two kinds used for direct manual input.

      the "varityper", had a revolving drum onto which two semicylindrical fonts could be mounted, allowing both latin and greek (for example) to be available at the same time. switching one font for another was reasonably fast, and the use of proportional spacing resulted in an appearance that was more refined than possible with a monospace typewriter, but not nearly the quality of real composition.

      the ibm selectric and "clones" used a "golf ball" mechanism. these type units were easy to switch, although only one "font" (containing the same number of symbols as keys on the keyboard, times however many shift keys were provided) could be in use at one time.

  • photocomposition was the next advance. i know of one direct-input photocomposer used for math -- the photon 200. a keyboard with several automobile-like shift levers controlled the input. images of symbols were transparent shapes on a glass disk otherwise coated with black, like a photographic negative. for "pi" symbols not on the disk, there was a "whirligig" with eight arms, onto each of which could be mounted a photographic negative of one symbol; jobs had to be carefully edited beforehand to make sure that no more than the eight available pi symbols would be needed, since changing the pi set in the middle of a job could run the risk of exposing the output medium, which would mean starting over. there was sufficient computer power in this machine to calculate line length and apply justification (in text), but for the most part, such decisions for math were manual, and required a highly skilled operator.

    for more automated photocomposition, input was keyed into some recording medium -- punched cards, paper tape, ocr forms, floppy disk, ... -- and input to the typesetting machine for output to photographic paper. since photographic paper was messy and expensive, there were sometimes preliminary proof runs in which the input code was printed out on greenbar; not ideal, and accurate really only for text, but often less expensive than other alternatives. (and patching paper tape was definitely an "interesting" undertaking.)

    output devices varied in how images were transferred to the photographic medium.

    • the photon 713 had a cylindrical drum into which were mounted 35mm film strips, each with about the equivalent of what would fit on a selectric golf ball. there were 16 of these fonts, so the available collection included roman, italic, bold, greek, and a reasonably comprehensive collection of math symbols. the drum rotated at high speed, and the images were set by a carefully timed strobe while the disk assembly was advanced across the width of the paper by an absolutely gorgeous worm gear.

    • crt output was another possibility. these devices were originally devised for use by newspapers, where speed was essential, and cost secondary. the imaging process usually involved moving a crt beam along a predetermined path, turning it on and off as appropriate. the symbols in fonts were designed by hand, which involved defining the paths for the beam. only certain directions were possible -- vertical, horizontal, and at 45 degrees, but one of these was not permitted (i've forgotten which), so it was necessary to make sure that a symbol could be completed in a single, continuous path, avoiding the proscribed direction.

  • there were a few small companies that developed math composition software before tex. one was science typographers, whose program was used in-house at ams for about 20 years; a discussion of the impact of tex on the suppliers of commercial math composition software appeared in tugboat in 1983. (on rereading what i wrote then, i find that i haven't changed my mind about what makes tex a good choice for composition in general, and the most compelling argument against it has dissipated with advances in hardware technology.)

  • one other essentially non-commercial typesetting system deserves mention -- troff -- which, with its companion eqn was created at bell labs and available on unix systems from the early 1970s, but which originally produced typeset output only on the cat typesetter, and was freely available only to unix sites.

this review has gone on long enough. if anything significant is missing, or any errors are noted, please let me know, and i'll try to remedy the situation.

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    I wish I could upvote this answer more, even if only for the link to the TUGboat article, which is instructively sobering for anyone who has been on one side or another of an argument about disruptive new technology. Also, it reminds us that TeX was new once. Also because it reminds us how quickly TeX stopped being new (I remember first hearing about it in 1987, as a thoroughly established Thing). Also because it shows how damn weird the TeX logo looks when it's spaced incorrectly. – Norman Gray May 10 '15 at 16:25
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    Do you have a document which was typeset usin STI? I'd like to see its output. – Sigur May 10 '15 at 18:08
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    Don't forget interchangeable daisy-wheels. I once had a typewriter which printed a line at a time to achieve full justification and could stop mid-line to allow the wheel to be changed. It could even cope with some multi-line stuff by defining/remembering horizontal position. – Andrew Leach May 11 '15 at 7:35
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    What a wonderful answer, Thanks a lot Barbara, especially for TUGboat link! – Bichoy May 12 '15 at 3:02
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    @Sigur -- the ams proceedings were set using the sti system from (don't remember exactly, but sometime in the 1960s) until the early 1980s. all the content more than 5 years old is available in pdf form scanned from the original pages. this link is for the first issue of 1980 – barbara beeton May 12 '15 at 14:42
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They were printed on linotype or monotype machines, which literally casted type. I had a close escape from the IBM golfball for my thesis:

enter image description here

As PhD students at the time we had to type our work on an IBM typewriter. This meant that when you got to equations you had to change the typewriter head, that looked like a golf ball, so don't complain about font changing commands in LaTeX. One advantage with this arrangement was that one became economical with words and more careful with spelling and writing.

Luckily TeX and LaTeX appeared and I moved onto using LaTeX when the LaserJet 1 appeared.

From YouTube Commercial for IBM's Selectric Typewriter 1960's

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    Today was the first time I have seen this ball. On a YouTube video I could see how fast the ball turns. Amazing! – Sigur May 10 '15 at 10:06
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    These typewriters were amazing and they had this beautiful whizzing noise. IBM also had these as terminals for mainframes and minicomputers. Edit my post please and add the link to the youtube video for others. – Yiannis Lazarides May 10 '15 at 11:53
  • actually, very little math was set on linotype; monotype was much more capable, especially when setting fractions, sub-/superscripts, anything that required symbols "off the baseline". – barbara beeton May 10 '15 at 12:21
  • @barbarabeeton Thanks for the comment, I was always confused with the two. – Yiannis Lazarides May 10 '15 at 13:07
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Many old books were typeset using typewriter with some symbols written by hand.

For example, Milnor's book Lectures on the h-cobordism theorem from 1965. Here is a preview of some part:

enter image description here

Also, changing the font they could type Greek letters.

enter image description here

  • or not so old documents like my thesis:-) – David Carlisle May 10 '15 at 9:33
  • @DavidCarlisle, just for curiosity: is it online? – Sigur May 10 '15 at 9:38
  • No, as I indicate, it was written with an IBM golfball typewriter, with large brackets done by hand (1985:-) – David Carlisle May 10 '15 at 9:41
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    @DavidCarlisle, so you didn't asked your students to scan it to you?! :) – Sigur May 10 '15 at 9:43
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    @Random832, I have no idea. Maybe it is related to the company. – Sigur May 12 '15 at 14:42
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In Germany, immediately before the arrival of LaTeX, a WYSIWYG program called SIGNUM (by Application System Heidelberg) on the Atari was quite popular for writing math and sciences. The program only died out when the supply of Atari computers ended---it had its fans despite being inferior to TeX in almost any aspect.

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    Signum is still available from ASH, if Google Translate is to be trusted (my reading German is not great). Admittedly you may have a hard time finding a working 680x0 Atari system to run it on, but there are plenty of emulators (e.g. the free Hatari and PacifiST). – dodgethesteamroller May 11 '15 at 21:39
  • Approximately at the same time, there was also ChiWriter - I've once submitted a paper prepared with its help. – Alexander Konovalov May 26 '15 at 14:07
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You can buy a secondhand hardcover copy of the classic

The printing of mathematics;: Aids for authors and editors and rules for compositors and readers at the University Press, Oxford

at

http://www.amazon.com/The-printing-mathematics-compositors-University/dp/B0007JHCTQ

Here's the only Amazon review, from 2005.

For a long time, this was the most thorough description in English of math typesetting. Rather than giving long lists of rules, it is an engagingly written essay. However, its concerns are not those of today's typesetter. In every section, the authors stress the need to consider the economics of each choice. That no longer matters, since with computer typesetting, layout can be chosen purely on aesthetic grounds. Read it for historical interest, but for practical guidance get the Chicago Manual of Style or Mathematics into Type.

In response to @Johannes_B : I recommend this as a fun read if you can locate a copy. There would be no point in advertising an out of print hard to find book.

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    Can you extend your answer? Right now, this seems like pure advertisement. – Johannes_B May 10 '15 at 14:29
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    this is one of the books listed by knuth in his published gibbs lecture, 'mathematical typography", as being a significant influence on the design of tex. another book along the same lines is by karel wick, "rules for typesetting mathematics". (bibliography of the article is listed on the linked page; pdf of artlcle also linked from that page.) – barbara beeton May 10 '15 at 16:08
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    Maybe not of interest to most, since it's in Swedish, but for those who can read it I must recommend the wonderful "Almqvist & Wiksells sättningsregler" by W. N. Lansburgh (1961) as well, being a manual for typesetters in science, with half of the book being used for typesetting of mathematics. – pst May 10 '15 at 17:59
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This is somewhere inbetween nostalgia and an answer. If you look at many papers and pre-prints from the University of Chicago into the late 70's, they usually thank Fred Flowers for typing the manuscript. There was a very expensive special purpose IBM machine for mathematical typing in the department. It was Fred's full time job to type mathematics on it.

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    are any of these viewable on line, and can you provide a link? (i'd like to pursue this.) – barbara beeton May 12 '15 at 21:08
  • I'll look and see if I have any of my old pre-prints. In the meantime, googling "fred flowers" chicago typing turned this up- – aginensky May 13 '15 at 0:01
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    books.google.com/… – aginensky May 13 '15 at 0:01
  • i found several references like the one you linked, but no links to actual preprints. if you find one, i'd be delighted if you could scan a representative page and add the image to your answer as an example. i think the machine you may be referring to is the "selectric composer"; the output is quite recognizable. – barbara beeton May 13 '15 at 12:37
  • I've looked and it seems that I was forced to get rid of all my old lecture notes when I moved. It is possible that a friendly note to the math dept at UC may turn up photocopies or a link to where they can be found in the UC library system. – aginensky May 15 '15 at 2:54

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