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数学猜想实际上是一种数学想象,是人的思维在探索数学规律、本质时的一种策略。它是建立在已有的事实经验基础上,运用非逻辑手段而得到的一种假定,是一种合理推理。数学方法理论的倡导者,波利亚曾说过,在数学领域中,猜想是合理的,是值得尊重的,是负责任的态度。数学猜想能缩短解决问题的时间;能获得数学发现的机会;能锻炼数学思维。历史上许多重要的数学发现都是经过合理猜想这一非逻辑手段而得到的,例如,
Mathematical conjecture is actually a kind of mathematical imagination, which is a tactic of human thinking in exploring the laws and essences of mathematics. It is based on the existing factual experience, the use of non-logical means to get a hypothesis, is a reasonable reasoning. As Advocate of Mathematical Methodology, Polia once said that conjecture is reasonable, respectable, and responsible in the field of mathematics. Mathematical conjecture can shorten the time to solve the problem; to get the chance of mathematical discovery; to exercise mathematical thinking. Many important mathematical discoveries in history have been made through the non-logical means of reasonable conjecture. For example,