In some of my classes (e.g. graph theory, mechanics), the professors encourage the students to visualize solutions to problems; I do well in these classes. In other classes (e.g. linear algebra), we are encouraged instead to reason about abstract concepts; I usually do worse in these classes (relative to the same set of peers). My professors have corroborated my suspicion that the usefulness of visualization depends on the type of problem being solved.


Overall, it seems that I do well with visualization, but have a harder time reasoning about symbolic formulas or abstract entities.


Have people here found that certain areas of mathematics better lend themselves to specific types of mathematical reasoning? I am especially interested in identifying more subjects in math & science that emphasize visual reasoning since I very much enjoy these subjects.



What subfields of mathematics better lend themselves to visualization?
The classes that lend themselves to visualization certainly include graph theory
and mechanics, and I expect you would do well in classical geometry too. In
other cases, it may depend on which book you use. For example, I am sure
you would enjoy the approach to complex analysis in Tristan Needham's book
*Visual Complex Analysis* (Oxford University Press 1997), whereas you may
find other complex analysis books less friendly.


By all means use your strength in visualization to get a foothold in various
areas of math (this should also be possible in linear algebra), but try to develop other strengths too -- you will need them eventually.


