[bluGill]

The difference is if both are sound the math will cover all cases. Your tests can be sound but miss a special case and thus be wrong. In that sense the math proof is better because it will catch all special cases.

Note that tests will often catch cases where the math is not sound. Because you are putting an expected result it is more likely that you have a sound reason for that expected result even if you cannot express is mathematically. I recommend you use both: in the real world they cover different areas of the problem.