Is wikipedia's attribution of the four mathematical subfields correct?

Question

This is a bit of a philosophical question.

Wikipedia gives a very intuitive (in my view) description of the four main fields of mathematics, according to what they are "about".

it says

• number theory is about "quantity"

• algebra is about "structure"

• geometry and topology are about "space" (I suppose this is meant in the traditional sense as in physics, not the modern mathematical sense, in which almost any set can be a space even if there is no conception of closeness)
• analysis is about "change"

However, to what extent is this categorization really correct? number theory really is about quantity it seems, and algebra is about structure, but isn't analysis also about structure? it seems analysis is mainly about limits, not necessarily about change, and restrictions on a set on the basis of limits surely also create structure just as algebra does? Also, is analysis ever not about space?

(ps. I currently have only an elementary understanding of pure mathematics)

Answer 1

You did not mention the key words broadly speaking in your citation from wikipedia, leading to a biased interpretation. The actual reference is the section Fields of mathematics of this article, reproduced below

Fields of mathematics

See also: Areas of mathematics and Glossary of areas of mathematics

Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty. While some areas might seem unrelated, the Langlands program has found connections between areas previously thought unconnected, such as Galois groups, Riemann surfaces and number theory.

If you want a real description of mathematics, just follow the link Areas of mathematics.