Computer Due To The Philosophy Of Mathematics To Reflect On

Computer has become the most powerful tool to change the way of life and thought since 1940' s, and put forward many new philosophical problems deserving to think before us. This discourse will study the mathematical philosophy problem lead by the use of computer in mathematics.The new applications of computer in mathematics present a series of newly emerging things to the public: After 1950₆0' s mathematical logician proves that deductive proof being particular of mathematics may implement by computer, so machine proof becomes reality. For more than one hundred years, four-color conjecture meditated by many people is proved with the aid of computer. Chaos and solition in non-linear science are found by numerical experiment of computer. After 1970' s, fractal geometry which is about nature is created by Benoit B. Mandelbrot(l924 ⁾, computer plays a very important role for its strong graphicfunction. ......Obviously, computer is changing the traditional way of studying mathematics, andcauses controversy of mathematical philosophy problem.: Is fractal geometry mathematics? Iscomputer proof of four-color conjecture mathematical proof? What is mathematical proof? ......Us essence is about mathematical nature.I review the history of evolution of calculation tool, and relate the extend of the function of computer: from numerical calculation to theorem proof and to mathematical experiment, then together with the computer proof of four-color conjecture and the establishing of fractal geometry, 1 draw forth the controversy. Following, 1 set forth the significance of transforming mathematical research way. Because the essence of controversy is on mathematical nature, I inspect all kinds of view in the history of mathematical philosophy, and put forward the dialectical unity of experience and deduction in mathematical nature.This discourse includes four chapters.The first review the evolution of calculation tools, especially the emerging of electronic computer that is regarded as the tool of numerical calculation and theorem proof and mathematical experiment. Because 1 want to present the material of reforming traditional studying way of mathematics: a piece of paper and a pen and a few of reference books.The second inspect the two typical cases: computer proof of four-color conjecture and establishing of fractal geometry. It majors in providing the controversy: Is computer reliable? iscomputer proof proof? Is fractal geometry mathematics? ...... According to these controversies,I point out that the essence is about mathematical outlook, that is to say, what is the nature of mathematics?In the third, I approve the significance of reforming mathematical studying way: not only-opens a new field of mathematical mechanization, but also expands the field of mathematical studying, and so accelerating the development of mathematics. At the same time, I analyse the dialectical relation between algorithm and axiomatic method, which is hided in computer.In the fourth, by inspecting all kinds of views about mathematical nature in the history and quoting the exposition of some famous mathematicians, I affirm the duality of mathematical nature at first, then state the dialectical relation between them, at last expound the view that mathematical nature is the unity of experience and deduction.