Mathematical dating proof
Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest.For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge.In addressing, say, "Does the interval between prime numbers form a pattern?" as a theoretical question, mathematicians are interested only in finding a pattern or proving that there is none, but not in what use such knowledge might have.Mathematicians, like other scientists, are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory.Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest elaborateness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.
The discoveries of theoretical mathematicians frequently turn outsometimes decades laterto have unanticipated practical value.
To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.
This chapter focuses on mathematics as part of the scientific endeavor and then on mathematics as a process, or way of thinking.
Theoretical mathematics, unlike the other sciences, is not constrained by the real world, but in the long run it contributes to a better understanding of that world.
Because of its abstractness, mathematics is universal in a sense that other fields of human thought are not.This is so for several reasons, including the following: Using mathematics to express ideas or to solve problems involves at least three phases: (1) representing some aspects of things abstractly, (2) manipulating the abstractions by rules of logic to find new relationships between them, and (3) seeing whether the new relationships say something useful about the original things.