A question from Yahoo! Answers:

A Mathematician and A Physicist?

What is the basic difference between a mathematician and a physicist considering they both deal with numbers?

Let’s start with physicists. Physicists come in two flavors; theoretical physicists study material world mathematically, sometimes making predictions that certain things must happen in a certain way; experimental physicists actually build experimental installations to test the theoretical physicists’ predictions. So it is theoretical physicists who look like mathematicians sometimes.

The difference between theoretical physicists and mathematicians is that mathematicians do not need their brainwork to describe anything in the physical world (their only concern is internal consistency of their proofs), while theoretical physicists seek ways to describe the physical world mathematically and make testable predictions based on their mathematical reasoning (during the 20th century, for example, a whole slew of elementary particles were predicted by theoreticians before being discovered by experimenters).