The difference between mathematics and statistics? I am learning how to construct proofs. I always wondered why stats is considered "different" to math? I know that it is an open-ended question.  
 A: I've always thought that statistics is part of mathematics.
A: There are two primary aspects of statistics. The first is the development of statistical theory and statistical tests. While not all properties of these statistical tests are always rigorously proven, this first aspect still fundamentally remains in the realm of mathematics.
The second aspect is the choice of which statistical tests are appropriate for achieving certain objectives. This is truly a science and cannot come from purely mathematical thinking. Methods are often employed because they empirically give good results, or because they align with certain intuition that the user intends to follow. Real-life systems are given mathematical models before statistics can be applied, models that are often not clear-cut.
A: If you feel mathematics and statistics are different, you should check out Mathematical Statistics. I think you'll be in for a pleasant surprise.
Interestingly, wikipedia defines Mathematical Statistics as the 'application of mathematics to statistics'. So I guess your question isn't completely unwarranted (as some of the down-voters may be implying).
It's worth noting that a 'statistic' itself is a function of a realized random variate to the real number line. Because of this, I suppose you can have a 'statistic' in the rawest sense of the term. But it's the mathematical study of these 'statistics' that allow you to use them effectively.
It's no surprise that the study of these objects lends to the name of the field itself.
