Is Mathematics Invented or Dis
Is Mathematics Invented or DisMathematics 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 define it as " a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape and space and there interrelationships using a specialized notation." Maths has often been described as the language of science because it is often used by scientists to express new theories. Unlike science though, maths is based on a set of axioms and postulates and not on experimentation or observation. Axioms and postulates are statements that are assumed to be true without being proven. For example "the whole is greater than the part." An axiom is a statement common to all sciences whereas a postulate is a statement peculiar to the particular science being studied. Other statements or theorems must be logically implied by the 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 certainty of results in pure maths comes from developing theorems from axioms by logical analysis.
There is disagreement between mathematicians over the relationship between maths and reality and whether mathematical objects are real. There are three different groups that have oposing ideas on the subject. One, the Platonist, says that mathematical objects are real and exist independent of our knowledge of them. So mathematicians discover mathematical theories and formulas. Formalists on the other hand argue that there are no mathematical objects and that mathematicians just create them. Constructivists disagree with both and say that genuine mathematics is only what can be obtained by a finite construction. The set of real numbers or any other infinite set cannot be obtained.
According to formalism mathematics consists of axiom postulates and formulas, but they are not about anything. When the formulas or theories are applied to the physical world then they acquire meaning and can either be true or false. But by itself as a purely mathematical formula it has no real meaning or truth value. To a formalist there is no real number system, except as we choose to create it by creating the appropriate axioms to...
To view the complete essay, you be registered.