When someone says “I’m good at Math”, what are things that you would expect them to be good at?

Dr. Alexander Peach Assistant Professor, Durham University Dept. of PhysicsUpvoted by Tom McFarlane , M.S. Mathematics, University of Washington (1994) and Jeremy Collins , M.A. Mathematics, Trinity College, CambridgeMay 17

It depends on their background, but the following is based on my own experience:

Layperson: I can do mental arithmetic quickly and accurately (an avid darts-player, for example), probably good at numerical, logic-based puzzles such as sudoku, for example.

Scientist: (non-physicist/mathematician): I can do algebra, stats and mental arithmetic.

Physicist: I’m very comfortable doing the kinds of very high-level maths that most of my colleagues don’t care to: differential calculus, differential geometry, linear algebra, tensor calculus, group/representation theory.

Mathematician: It’d take you years to even understand the names of the particular areas of abstract mathematics that I’m used to working with.