2
$\begingroup$

The Elements are often regarded as the cornerstone of the axiomatic approach to mathematics. However, mathematical textbooks have served as the foundational pillars upon which writing style, language, notation and the structural development of mathematics have been solidified over the centuries. Could someone provide further insight into the pivotal role that the Elements played in shaping these aspects? Are there significant predecessors, or was it the initial serious attempt to establish the framework for the communication and instruction of mathematics? If possible, I would also like to understand what factors contributed to their widespread acceptance in the tradition of writing math.

$\endgroup$
2
  • 1
    $\begingroup$ Do you mean Euclid's Elements? it is not clear at first read. $\endgroup$
    – Mauricio
    Commented Aug 30, 2023 at 16:10
  • $\begingroup$ Oh, I'm sorry. I thought the question content plus the [euclid] tag would make it clear enough. $\endgroup$ Commented Aug 30, 2023 at 17:13

1 Answer 1

4
$\begingroup$

Euclid was not the first book of this type, among his predecessors the ancient sources mention Hippocrates of Chios, Theudius of Magnesia, Leon and Hermotimus of Colofon. See this Wikipedia article for references. However none of these previous books survives. We only know those names from some surviving ancient histories of mathematics. (This frequently happens that someone writes a book which is judged by contemporaries superior to the work of his predecessors, and they stop using the previous books, and do not care about copying them). Unfortunately only a very small portion of ancient literature survived to our days.

Then, for almost two millennia, Euclid's Elements was the standard of mathematical exposition, it was used in teaching, as a reference and as a standard of the style of mathematical writing. This includes, for example Newton's Principia, where he tries to imitate Euclid's exposition. Even non-mathematicians like Spinoza tried to imitate Euclid's style. Only in 18th century (after the invention of Calculus) this started to change.

$\endgroup$
4
  • 1
    $\begingroup$ I still have on my shelves a copy of Books I-IV of the Elements which my father used at school in the period between the world wars in the last century. He was just an ordinary pupil not a maths whiz. $\endgroup$
    – mdewey
    Commented Aug 30, 2023 at 13:53
  • $\begingroup$ I'm curious about your comment about the style shift in the 18th century. What caused this shift away from the Euclidean style? $\endgroup$
    – Andrew R.
    Commented Aug 30, 2023 at 15:44
  • 1
    $\begingroup$ @Andrew R.: For the case of teaching Euclid in British schools, early issues of Mathematical Gazette have several informative articles. Do a search-in-page here for "teaching" (look for articles about the teaching of geometry or about proposed reforms), and then look up the articles themselves -- all are freely available at various places online (specifically: google-books, internet archive, JSTOR). This MSE answer will be helpful in understanding the context behind some of the reforms. $\endgroup$ Commented Aug 30, 2023 at 16:47
  • 3
    $\begingroup$ @Andrew R. As I hinted in my answer, the reason was the spread of Calculus. Calculus was not rigorously justified (to Euclid's standard) until the second half of 19th century, so one just could not write about it in Euclid's style. $\endgroup$ Commented Aug 30, 2023 at 17:01

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.