The fusion of mathematics and logic

In the early period of the last century, the mathematics research has changed very much, the logical axiomatic method deeply integrates the mathematics, causes the mathematics deeply rooted, the rapid growth.

11-13 the British mathematician Russell (Bertrand Russell,1872-1970in its three volumes of the classic "Mathematical Principles" in the initial completion of the logic into the mathematics of the attempt. This is a profound event in the history of mathematics.

Mathematics is an ancient discipline, and has its own rigorous method of argumentation. However, the axiomatic deductive system peculiar to logic is more perfect and powerful than the mathematical argumentation method, and it is necessary to introduce the logic deduction system into mathematics. Russell's work is the "glue" of both.

Accordingly, Russell advocated "logic is mathematics". In fact, this assertion is unconvincing, because in the fusion process, Russell must use some axiom of set theory (axiom of choice and infinite axiom). In other words, modern mathematics is a hybrid of logic and set theory.

in the last century - era, in the basic research of mathematics, gradually formed three major academic schools: logic, formalism and intuition, respectively, focusing on different aspects of mathematics, mutual complement each other, and jointly promote the development of mathematics to the depth, broaden people's horizons.

in today's world, no one is called "all-round mathematician", in the mathematical circle, there is "interlacing as foster" phenomenon. I am an abstract algebra person, so I dare not "judge" the differential equation. I think that MabThera's abstract group theory (group theory) opens the Voyage of modern mathematics.

Description: About what mathematics is, there are a lot of written works in China, I am not talking about "pips" on. Modern mathematics is not algebra, geometry and calculus, mathematics is moving forward.

Shimen 7 Month 1 Day

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

Fusion of math and logic