Why is there so little overlap between calculus and statistics? I was an applied math major and took several calculus-based courses, including differential equations and real analysis, as well as an introductory course sequence in probability and statistics. Both calculus and statistics are extremely useful and broadly applicable to the natural and social sciences, but it seems like their tools and methods are completely different. Are the "statistical" and "calculus-based" approaches to solving problems fundamentally different, or is there actually significant overlap between these fields that is not evident to someone who only learned about these fields at the undergraduate and introductory levels?
It seems like one of the major goals of a calculus-based approach to understanding a system is to come up with a differential equation to model the data. And it seems like the statistical approach seeks to obtain causal and inferential relationships between variables. So it seems as if one of the primary goals of both fields is to come up with quantitative relationships between variables being observed in a system. So why are their methods and tools so different?
Also, certain sciences use calculus more than statistics (like physics) whereas others use statistics more than calculus (biology), and others use both extensively (economics). What about a scientific discipline makes  either analytical or statistical methods more useful?
 A: It depends on the quantities that you measure or calculate. Most of the measurements are discrete and are processed using statistical methods. This is field independent. Then, when you model the underlying process, one usually has continuous variables (for example some time evolution). Those are described by calculus.
In the undergraduate physics, most of the time one looks at the models. The experiments were done long time ago. Everyone knows that the gravity next to the surface of the Earth is described by a downward constant acceleration. Then you use calculus to describe projectile motion.
In biology, there is much less detailed knowledge about some underlying mechanism. To try to tease out the correlations, one will therefore use some statistical methods first. Once you have a model, you write the differential equations, solve them to predict other outcomes. But this is also true in the current physics research.
A: As far as I know, all mathematics fields are deeply connected to each other.
For example, Riemann hypothesis can be "reduced" to a "simple" arithmetic problem:
M(n)=O(sqrt(n))
where M(n) is the arithmetic mean of mu(1), mu(2), ... , mu(n), O is just big-O and sqrt(n) is a square root of n.
Here's a discussion in Russian:
Habr.com
And here's the original article.
