[FOM] mathematics as formal

[Wayne Aitken]

On 3/5/08 6:24 AM, "Michael J Barany" <mjb245 at cornell.edu> wrote:
 
> The second half of the nineteenth century was dominated by attempts to try out
> different axiom systems and to experiment with different formal structures.

Can you give examples? I am under the impression that the axiomatic
approach to mathematical structures came later. For example, Dedekind
studied algebraic extensions of Q and their rings of integers in the late
19th century, but his subject matter was very concrete. Later, in the
1920s or so, Noether developed an axiomatic theory of "Dedekind domains".
There are other examples of concrete mathematical objects from the
19th century that were approached axiomatically in the early 20th century
(culminating in the Bourbaki notion of structure in mid 20th century).