Is Mathematics Invented or Discovered

A detailed Summary of Is Mathematics Invented or Discovered

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 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

Whether mathematics is invented or discovered is an impossible question to answer because it is impossible to prove or disprove and it will probably remain so no matter how far our mathematical knowledge advances in the future. There will always be maths that can be applied to the physical world and maths that seems to be just made up by someone. Though there is evidence to support both the Formalists and the Platonists neither can be absolutely sure the other is wrong. Maybe both are right. Does it really matter? Whether maths is real or just a product of our imaginations it will continue to be developed and applied to different areas of our lives and maybe one day we will come close to answering this question.

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.

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