7
$\begingroup$

In some ways, mathematics has been written in a fairly consistent manner. For those fluent in German, apparently, Gauss's Disquisitiones Arithmeticae is apparently very readable. A large part is that the style Gauss introduced in this work basically set the standard for subsequent mathematics textbooks. However, there are many other older papers that are basically incomprehensible to modern day readers, largely because the conventions, notations, and even subject matter are now arcane to a modern audience.

My question is whether the influence of technology in terms of mathematical writing has been studied. I can think of several pieces of technology that must have surely influenced things: the first is the typewriter, making it more convenient to produce manuscripts. I suspect that this may have had little influence, because even well into the 20th century and even 21st century, some older mathematicians still had the habit of hand-writing their manuscripts and getting a secretary/graduate student to type it up for them. The next major technological advance I can think of is the personal computer, and especially the advent of $\LaTeX$.

Although a small number of older folks cling to the old ways, the introduction of these technologies must have had a measurable impact at a large scale. Has this been studied?

Improve this question
$\endgroup$
7
  • 13
    $\begingroup$ Wasn’t Gauss's Disquisitiones Arithmeticae written in Latin? $\endgroup$ Commented Jul 8 at 18:41
  • 2
    $\begingroup$ Related (but more anecdotal) on Academia.SE: Do people write research papers differently nowadays? $\endgroup$ Commented Jul 8 at 18:49
  • 1
    $\begingroup$ Just some nice timeline events: TeX arrived in 1978; there was a Documenter's WorkBench, the troff/nroff series, with the eqn preprocessor arriving in 1974. Those eventually made typewriters obsolete. Typewriters are listed on Wiki as arriving in 1874, though it took a bit more time to roll that out; LaTeX also took some time to percolate through maths & physics. This means that there was about a century of typewriter supremacy; you should read some typewritten manuscripts and seen how deleterious it was to maths. Very unreadable. $\endgroup$ Commented Jul 8 at 18:54
  • 3
    $\begingroup$ To give an even more blatant and older example: The invention of the equals sign and subsequent establishment of symbolic math did wonders to the readability and (I would argue) the progress of mathematics. If you ever tried communicating any complex mathematics in prose, you know that this doesn’t work well. I have no literature to back this up though. $\endgroup$ Commented Jul 9 at 7:45
  • 2
    $\begingroup$ @naturallyInconsistent wasn't the practive with typewriters to just leave spaces for handdrawn formulas where needed? $\endgroup$ Commented Jul 9 at 13:53

2 Answers 2

Reset to default
9
$\begingroup$

Mechanical typewriters, then electric typewriters, then those with interchangeable ball heads, and finally, $\LaTeX$ definitely changed the layouts. You can see in old texts, and I have read quite a few, how they were typed, e.g., by manually adding specific characters. It makes a big difference whether you have to insert $\alpha$ manually, change the ball head for a single character, or simply type \alpha. But those developments are a matter of convenience. Technical progress is always an improvement in convenience.

The more interesting developments are, in my opinion, a) the changes in lingua franca from Latin to French and German, and nowadays to English, and b) the style in which mathematics is written. There is a clear cut into a pre-Bourbaki and a post-Bourbaki era. It mainly changed from prose to a very technical structure of definition - example - lemma - proposition - theorem. van der Waerden and Artin wrote completely different than Serge Lang.

I remember that I once found a manuscript of Galois, and although I was already familiar with his theory, I didn't understand a word. There are also various styles of writing. At Fermat's time, mathematicians corresponded mainly by letters, and sometimes even posed problems of which they already knew the answer. Kronecker was famous for his harsh criticisms, Schrödinger talked a lot in his articles, and if you look up the original papers of Noether or Einstein, you wouldn't recognize them as the breakthroughs they were. The modern treatment of their theories is quite different.

I think the subject has many different layers, of which technology is just one.

Improve this answer
$\endgroup$
3
$\begingroup$

The writing style depends more on the author, rather than technology. A modern mathematician can read Archimedes or Kepler, with great pleasure, in a good translation to any modern language. I agree that Galois' papers made a very difficult reading. Same applies to many 19 century and early 20 century authors.

There was a lot of progress in technology since Archimedes and Kepler, which facilitates writing, but on my opinion this did not have much direct influence on the writing style. People just started to write more, as publishing becomes easier.

One problem is with pictures. Making and reproducing pictures in mathematical manuscripts was always very difficult and labor consuming. For this reason, we do not have original pictures from any ancient Greek authors. Nowadays, with computers, this became somewhat easier, but the problem is still very far from being solved.

The greatest change of the writing style in 20th century happened under the influence of Bourbaki who started publishing their treatise in the 1940s. But this had nothing to do with technology. They used ordinary typewriters, with formulas inserted by hand, as everyone else at that time.

Improve this answer
$\endgroup$

Your Answer

Draft saved
Draft discarded

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.