Is euclidean geometry the basis of maths?

Question

Euclid wrote ‘The Elements’ to be a basis for all mathematics, but in modern settings, it’s mostly seen to be just about geometry. Apparently, this was because geometry was a concrete/visual way of interpreting mathematics before you could go into the more abstract stuff like algebra or even arithmetics. So, seeing this, is Euclidean geometry a good foundation to learn maths in order of increasing difficulty or is this view just completely wrong?

Answer 1

Euclid wrote books on arithmetic and number theory, too.

However, before "Greek Mathematics" (Euclid) came "Babylonian Mathematics." The Babylonians made plenty of relevant discoveries. However there was no unifying structure. When the Babylonians discovered something useful, or interesting, they stamped it into a tablet. And each fact was as separate fact. It is similar to the way that elementary school, and sometimes high-school, math is taught. What is your problem? We have a formula for that. Look up the formula.

Euclid's big contribution was to say that everything known to mathematics can be generated from a small list of axioms. This still drives the way that mathematicians think about the subject.

Answer 2

What the famous British mathematician G.H.Hardy wrote about ancient Greek mathematics is fully applicable, in particular, to Euclid's Elements:

“The Greeks were the first mathematicians who are still ‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand: as Littlewood said to me once, they are not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another college’. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.”

(G.H.Hardy, A Mathematician's Apology, 1940)

Hardy thus assures us that Euclid's Elements will remain a good and permanent foundation. The Elements (which, by the way, include not only geometry but also some elementary number theory and algebra) will remain an indispensable part of good mathematical education and, moreover, an important part of our overall cultural heritage. For example, Abraham Lincoln felt very influenced by three books: the King James Bible, the works of William Shakespeare, and Euclid’s Elements.