Eric Bell, a Scottish mathematician, once said that “Mathematics is the Queen and the Servant of the Sciences.” I think this is a great way to think of the scope and power of mathematical thinking. To me, mathematics underlies the sciences, and that statement is only becoming more true as time passes. (You cannot be a modern day biologist or forensic scientist without understanding something of probability).  But, as a tried and true mathematician, I understand that the tools of the trade involve a real appreciation for logic and abstraction.