1) In geography, it is used in weather prediction, impact of atmospheric change on aquatic and non-aquatic life.
2) In history, it is used to find out the time period from which various artifacts, scriptures belong.
3) Study of economics is heavily based on it. It helps in calculating various index like inflation, crop production etc.
4) In science, it is used in every application like in motion, gravitation, work, energy, electricity, magnetism etc. Whether its Maths, Math, Matt or Mutt the discipline of 'Mathematics is a highly disciplined one' for highly disciplined people. Those who cannot subject themselves to the discipline, cannot dedicate time, cannot assiduously cultivate her like one madly in love with a girl, fall by the wayside. As 21st century progresses there will be two kinds of people - mathematically abled and Mathematically disabled or disadvantaged. The latter takes orders from the former.
It is a misnomer to call Arithmetic as Mathematics. Arithmetic is a part of Mathematics, like porch is a part of a house.
Broadly, historically it conprises of two sides - Geometry and Algebraic subjects. A mathematician is like that prince serching for the Ox-headed Minotar in his Cretean maze with the thread in his hand symbolising Mathematics.
There is no branch of knowledge that doesn't summon Mathematics to its service. In Physiology vascular (blood) flow requires fluid dynamics principles. How a particular plant species unfurls its leaves is modeled as Fibonacci numbers.
Similar architecture and its analyses whether natural or man-made is made by man by using Golden proportion or ratio. It is interesting - a rectangle of this ratio (of length versus breadth)is