In many areas of mathematics, there are problems that admit a natural formulation in any dimension. It often happens that such a problem is easier to solve in dimension $n>k$ as compared to dimension $k$. Sometimes, the problem is solved in all but finitely many dimensions.
The examples are, e. g., Poincaré conjecture, or Milnor's solution to the "Can one hear the shape of a drum" problem.
So, the question is, what is the earliest known example of this situation?
One that I can think of is Maxwell's derivation of velocity distribution in a gas, which wouldn't work in dimension 1. But since it's not so clear what the associated mathematical problem is, let's not take it as a cut-off for possible suggestions.