The history of the Math

The Math is an ancient science and humanity is dealing with it for ages (so long that he could not say exactly how long). The Greeks in the V century BC bring proof of the main (and only) acceptable method to reach new knowledge. By that time it was used mainly measurement approach. The Greeks developed math not because of its application, and for its sake. The knowing of math was a sign of high culture and social status.

 In the early ages the math has developed mainly in the philosophical schools (equivalent to modern universities) of the famous philosophers of that time (mathematics) - Pythagoras, Plato, Aristotle, Euclid and others. After separation of the philosophy of math comes from the line of reasoning as the main culprit of what is considered Aristotle. The Aristotelian logic is known now as syllogistic logic. It has been doing work in the conduct of scientific disputes, but was woefully inadequate for proving mathematical theorems. Aristotle classifies the claims of several groups and says what judgments (between statements from different groups) are correct. Contribution to mathematics is Euclid, who introduced more general logic that works and mathematicians.

 At the end of the 19th century the math was divided into several parts - algebra, analysis, geometry, etc. Mathematicians began to question what really is the thing these shares. Cantor has undertaken this difficult task and thus laid the foundation of set theory. Unfortunately, the initial version of the theory was wrong - Cantor himself discovered a contradiction in cardinal numbers (reflecting infinity). Philosopher Russell also discovered just contradiction. Russell's theory by offering numerous to be considered at levels as elements from one level can participate in many of the upper level. The math automatically 'builds' on set theory without the need of reformulation of definitions / theorems, etc. Development of mathematics continues to Hilbert, who has several problems of the mathematical community. One of them is the construction of complete and unequivocal mathematical theory. A theory is complete if every claim can be proved by it that is either true or false. Unequivocal means that one cannot claim to prove that it is both true and false (that we saw in Russell's paradox). Consistency of the theory can be demonstrated by creating a pattern in its other theory, which has been shown that it is non-contradictory. In the end, it all boils down to the theory of natural numbers (arithmetic - addition, multiplication) so its consistency is demonstrated all can relax. Logic has developed quite early 20th century just to try to prove the consistency (and possibly completeness) of arithmetic.

  The mathematicians soon calmed down and resigned to the fact that they cannot prove the consistency of maths. Over time, the question arises whether the machine to prove the facts of a given system and verify their faithfulness or unfaithfulness. After clarification of the concept of an algorithm is proved that assertion of maths cannot be ascertained whether it is right or wrong, but for geometrical proposition possible. The math has developed dynamically through proven geniuses, so now we can learn from their discoveries, and why not to proceed them.