As someone with degrees in both law and mathematics I was struck by the similarities in the subjects when I learn law. Everyone was surprised when I told them that... except for my cousin, a mathematician. It didn't surprise him at all.

Law (analytically - practically it is about problem solving, strategy, tactics, understanding your client's problems, clear presentation of ideas, etc. like any other business) is all about logic, reasoning, thinking clearly, separating precedent and antecedent, the logical flow of ideas, etc.

In practice, legal reasoning is more inductive than deductive (not entirely), which means if has a different flavour in practice. It is still just as much about logic.

But don't get distracted by things like the standard of proof etc. That has much more to do with the fact that you are making decisions based on unreliable and imperfect information, as opposed to reasoning about entirely abstract ideas like a mathematician.