In basic terms maths, or to give it its full name mathematics, is the study of numbers and the effects that their patterns and systems can have. Maths, as a science, can work as a stand-alone study or can be applied to a variety of scientific orientated disciplines and involves looking at numbers to solve problems or to come to specific conclusions.
On a day to day basis we all use maths in some form. We may count change in a shop or use a calculator to plan our household budgets. The study of maths that we all go through at school is usually divided into various disciplines. Students may, for example, study algebra, geometry and arithmetic at various times during their studies. Other options here include mathematical set theory and logic.
A mathematician, on the other hand, will use numbers to help them make deductions, prove abstractions, count and measure. The aim here is to use maths to work towards proving that something is true or feasible. Maths plays an integral part in various research fields including other sciences, technology, astronomy, engineering, medicine and economics.
In general terms there are two primary types of maths. Applied maths is used to foster research and developments in other fields and sectors. So, for example, maths may be used as part of a space research project with the aim of contributing to a greater whole. On the other hand pure maths is studied on its own merits and is not necessarily designed for use with other disciplines. Success in pure maths, however, can have a knock on effect that can then be applied to other disciplines over time.