Some habits of thoughts in mathematics which are useful outside mathematics are:
Quantitative thinking - Often it is very important to understand quantitative aspects of an issue.
Logical thinking - Mathematics is a very clear platform for precise logical thinking.
Computational thinking - Often we need to make some computations, to write some formulas and manipulate them, in order to address an issue
probabilistic thinking - The ability to think about luck, chance, risks and decisions in probabilistic terms and to draw insights from probability theory is important in many areas