When an area in math is presented to students, it usually starts by presenting or defining the objects it will be working with along with properties and axioms, which makes me wonder if there is necessarily a connection or relation between them, since I sometimes see calculus problems being solved using linear algebra or even topology and the concepts they manage seem related but not quite. So I just wanted to know if it is just a coincidence that you can sometimes "merge" two areas to work one problem or if there is some reason behind this. To clarify: I know practically nothing about set theory nor ZF set theory and it will probably be related to that.
2026-03-27 16:53:59.1774630439
Are all areas in math related in some way?
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Yes: all areas of math were invented by humans.
This is really a philosophical question, which cannot admit precise mathematical answers. But I'm quite serious about my pithy response above. To explain more: when mathematicians create mathematics, they do not do it by coming up with random axioms and searching randomly for theorems. They instead create mathematics to solve certain kinds of problems and understand certain kinds of patterns and phenomena. This process started with trying to solve real-world human problems and later to develop tools for science, and it has since expanded into more and more abstract realms, as understanding more mathematics leads to new natural questions to ask and new (abstract) patterns and phenomena to try to understand.
But the point is that the development of mathematics is guided by human interests and human concerns (and is centered around common themes of measurement, space, structure, etc. as mentioned in Mauro's comment), and new mathematics is usually born by analogy and abstraction from existing mathematics. So it should not be at all surprising that there are lots connections between distinct branches of mathematics.