They need elementary math for many reasons.
- Figure out precisely what you want to say. (Think e.g. the difference between the mean and median, what does “it’s 90% nutrition” mean.)
- Doing simple modeling. (I’m not an advocate of complicated economics style modelling such as general equilibrium, most uses of differential equations, and so on.)
- Gain awareness of important phenomena and understand how to deal with them. An example would be range restriction.
- Be able to see through hot air such as factor analysis, mixed effects generalized linear models, latent class models, time series econometrics, all that fancy stuff. The social science literature is littered with statistical shit.
- That said, one should understand basic statistics, most importantly linear regression. Linear regression works surprisingly well, but be aware of tables with many covariates. For understanding, smaller tables are probably better, as interpreting linear regressions with many covariates is next to impossible, even if the statistical model assumptions are perfectly met.
That said, mastering the simple math requires experience with mathematics, which you gain from taking basic math courses such as
- Elementary algebra
- Linear algebra
- Real analysis
- Groups, rings, and fields
But higher math is probably a waste of talent, and probably not worth studying at all.
- Set theory
- Algebraic geometry
- Functional analysis
- Prestigeous statistics such as semi-parametrics.
- Complexity theory. (I can understand it if you disagree here, but complexity theory has no real applications and probably isn’t very transferable.)