Math Historians -- What terms did the ancient Greeks use for math?

by deftnous

Generally, I am curious if there are any interesting translations of ancient Greek (or other cultures) math terms (i.e. their literal meanings and how they differ from modern ones today).

Specifically, I was curious if they had a special name for numbers of interest like the square root of 2. But I'd also be interested in their general terms for square-roots, integers, ratios, irrational numbers, etc.

H5oD

[This comments on the question. This is not an answer to this question]

As mathematician I have to interject that this is honestly a rather boring question: A bit like "The English language calls it pineapple while (iirc at least most of Europe) says [Ananas] (in some form or colour). Are there more languages using something different than [Ananas]?".

The general problem your question has (from my perspective as mathematician) is that mathematics works with concepts. Because of that it doesn't matter at all how you call a concept X as long as it still is (per definition) concept X. It only adds confusion. This ends with today most recent concepts just being called by their original (in general English) name which often only changes if/when some different field makes use of the concept (or it enters the domain of more common knowledge).

What might be more interesting for you (due to 'names' being of no importance) is how the concepts themselves were defined at that time and how they changes over time.

The best book if you want to have a look at this would be Euklid's Elements. While the content of the book is not always 'easy' it is still possible to work through it without additional knowledge. Also the concepts are very clear and well explained (albeit that also depends a bit on the translation) and since the topic is geometry it is not something abstract.

Changes are generally if a concept has been expanded upon i.e. while today there are the concepts of (straight) line [which is infinite], ray [which has 1 endpoint] and line segment [which has 2 endpoints] in Euclid's Elements there is only the concept of the third (It limits itself to what you can draw, basically).

That not much has changed [in terms of the introduced concepts being changed; there has been plenty of expansion and new concepts] can be seen since there is a whole block of geometry which is today called "Euclidean geometry".