فلسفة الرياضيات برؤية تكاملية الاتصال و الانفصال

الملخص EN

The research aims to investigate the continuity and discontinuityconcepts which accompanied the science and philosophy of mathematic.

Then the research focused on the new philosophical view for mathematics which appropriate with the great transformations for establishment the discipline of numbers, especially irrational and imaginary numbers.

After the preface to the research, the research's sections came as follow: Section ( 1 ): "Dialectics of geometry and arithmetic", in line with the philosophical debate between continuity and discontinuity, the central theme to explain this problem.

Section(2 ): "Kingdom of numbers", to follow up the construction of the discipline of arithmetical numbers, to analysis the philosophical problem faced it, and to reach the line of real numbers which caused the problems of irrational and imaginary numbers.

Section(3 ): "Problem of irrational numbers", which by its solution, the debate of interference between continuity and discontinuity reached to its end, and paved the way for solving the puzzle of imaginary numbers.

Section ( 4 ): "Paradox of the imaginary number", to know what we mean by the imaginary number and the depth of its problematic.

Section( 5 ): "Solving the puzzle of imaginary numbers", which was accompanied by a new philosophical vision of the complementary between arithmetic and geometry.

Section( 6 ): "Simulation of the nature to the imaginary numbers" to reach that the natural existence is possibly written according to a symbolization of the compound numbers which emerge from the imaginary numbers