Good at abstractions bad with numbers

Question

Ever since I had an interest in math I was aware that what I'm good at and what really pulled me was the abstract thinking. My intuition for even the simplest number related concepts (modulo arithmetic, simple combinatorics) is realy weak yet from what I learned so far I really like (and am good at) is topology and abstract aspects of analysis and geometry.

I really like math and so my question is whether my limitations in "number intuition" is a real obstacle or is there a chance for people like me to overcome their weaknesses and shine with their strengths?

Answer 1

I'll let you into a "dirty secret":

MANY (and perhaps most) mathematicians rely heavily on calculators and computers to do any necessary arithmetic or extensive computation.

I think those who are good with numbers but "bad" at abstraction have far more to worry about if they plan to pursue serious mathematics.

As we cross the threshold from the more concrete to the more abstract in mathematics, we inevitably do less in terms of concrete calculations than what we once spent an extraordinary amount of time on, and so it is not at all uncommon to get rusty with some of those skills: time and practice will sharpen those skills, or, when needed, there's the calculator to help out.

Answer 2

You have to consider that mathematics is in fact a really, really broad field, composed of radically different areas, both in the instruments you have at disposition, and in the ways of reasoning. It is not unusual for a mathematician to be really good in, say, algebra/topology/category theory and to be kinda bad at analysis, number theory or statistics.

What I mean with this is that you don't have to worry if you lack of intuition in some areas, it is not uncommon. You should try not to neglect those areas where you are the weakest, but other that that you will come to a point where you will be able to really concentrate on what you like the most.