Proofs in Mathematics: Past, Present and Future
Noureddine Daili
*
Department of Mathematics, University F. Abbas, Setif 1, 19000 Setif, Algeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper we give an answer to the question what is a mathematical proof? We give a historical chronology of the proof then the different type of proofs. At a first glance the answer seems obvious: a proof is a series of logical steps based on some axioms and deduction rules which reaches a desired conclusion. Every step in a proof can be checked for correctness by examining it to ensure that it is logically sound. To speak of the mathematical proof, it is necessary to set up a whole body of knowledge on the theories and the systems hypothetico-deductive. Hence, a mathematical proof is a reasoning which allows, from certain axioms, to establish that an assertion is true. The proof uses logic but usually includes elements of natural language while avoiding the introduction of ambiguities as much as possible. In general, it occupies a central place in any activity of a human being who runs behind the truth. In particular, proof in mathematics occupies a special place since it represents a fundamental tool which especially characterizes this discipline. Any research on its teaching poses the problem of transmission of its construction, just like any mathematical concept.
Keywords: ABO blood group, Mathematics, Association of Tuberculosis, history of mathematics, ABO gene frequencies., proofs
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