Beginning of Essay
Mathematics is of key importance to most aspects of modern life. Due to the great diversity and nature of mathematics it is a subject that is hard to define. Over the years great mathematicians have given there own definitions of mathematics. In general we can def ....

Middle of Essay
.... set of postulates and axioms. The theorem is considered valid if it is consistent with itself and the mathematical system that it is a part and does not create any contradictions within the system. If something is mathimatically true it just means that it is valid. Mathematics can be divided into two main areas, Pure mathematics and Applied mathematics. Applied mathematicians concern themselves with maths that can be applied to the real world like engineering. To consider a theorem true it must work in the outside world. Pure mathematicians are concerned with abstract ideas and the logical process that is taken to prove these ideas. Absolute certai ....