# Is mathematics only used with quantitative data?

Can mathematics only be applied when there are numbers involved? I know there are mathematics branches like mathematical logic that doesn't deal with numbers, but do those areas have applications outside of mathematics?

Can mathematics only be applied when there are numbers involved? I know there are mathematics branches like mathematical logic that doesn't deal with numbers, but do those areas have applications outside of mathematics?

It depends on what you mean. There are many fields which do not work with numbers directly, like geometry and topology. And these fields have important application in physics.

The colored patterns using shapes is a basic math topic, but it applies to physics to read color coded resistances.

It seems to me that in "higher" math, the higher the math is, the less you deal with numbers. Even in areas such as differential equations, where the objects you're dealing with are defined in a way that makes reference to numbers, you may almost never deal with them (not counting an occasional e or 2pi). Instead you talk about functions and work with symbols.

I think it's a fundamental mistake to think that math is primarily about numbers.

^ It depends on the field and what you mean by "dealing with numbers." If you mean computations, then sure. If you mean literally "seeing" numbers, you'll be getting quite used to them in particular applied math fields (numerical analysis, analysis, PDEs, ODEs, etc.). You usually don't deal with numbers until you actually get down to the computations. In the theory of these fields, it's still mostly abstractions (elements, sets, mappings, etc.).

But in other fields as mentioned, you almost never use numbers to deal with anything. Rather you're almost never working in the set of reals again. You simply work with mappings and properties of new definitions, seeing what comes from it (geometry/topology, algebras, logic, etc.).