These three things require wildly different levels of ability: incorrectly using a t-test (e.g. using it in the wrong circumstances), correctly using a t-test,

These three things require wildly different levels of ability: incorrectly using a t-test (e.g. using it in the wrong circumstances), correctly using a t-test, inventing the t-test. I think Wilson is saying that whilst scientists need to be able to use mathematical tools effectively, they don't need to be able to come up with them. (Though statistics is probably much easier to use in this way than, say, calculus. Mathematica is very good at differentiation, but I think in many situations where you need to know how to differentiate, rather than just the result?)