What is math?

It is generally believed that the founder of the formal approach to mathematical basic research is the German mathematician David . Hilbert ( divID Hilbert , 1862–1943 ). What is the formal processing method of mathematics? In this view, what is mathematics?

Hilbert's formal approach has two basic principles:

All mathematical symbols in mathematics are completely regarded as meaningless content, even if the symbols, formulas or any meaningful or possible explanations of the proofs are not heeded, but only regarded as purely formal objects, studying their structural properties;

Second, the adoption of the principle of limited treatment, that is, in the limited mechanical steps can be verified within the form of a series of formulas in the system whether there is a "proof."

Hilbert's motive is: the application of mathematical formal processing method in such a formal system of definition, can avoid involving infinite inference, which excludes the infinite inference method of Cantor set theory brought about by the paradox. The idea is to apply a reliable method only, because to prove that mathematics or part of its non-contradictory approach is universally acknowledged to be credible, the whole of mathematics has a solid foundation.

According to Hilbert's point of view, the object of a mathematical study is a string, a string of symbolic strings without any meaning. The concrete content of mathematics is not, it becomes the computer program in the execution itself. In this view, the authenticity of the mathematical proposition depends on the computer operation in the finite steps can be finally determined.

Note: The above views are only a genre in the basic research of modern mathematics, can not cover everything, also does not represent my point of view.

Shimen 6 Month - Day

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

What is math?