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If you wish to learn swimming,you have to go into the water,and if you wish to become a problem solver,you have to solve problems.（如果你想学会游泳,你必须下水；如果想成为解题能手,你必须解题.） ——波利亚 The only way to learn mathematics is to do mathematics.(学习数学的惟一方法是做数学.) ——哈尔莫斯 Some teachers demand that students solve mathematics problems only by the method taught in class,This process can thwart initiative,compound frustration,and promote avoidance.(有的教师要求学生只用课堂上教的方法解数学题.这种做法会阻碍独创能力的发展,导致失败,并造成回避困难的心理.) ——波雅妮 When students are forced to develop their own approaches to unsolved problems,they benefit much more than from exposure to the mathematics alone.（当一个学生被迫大展身手去对付未解决的问题时,比仅仅学习数学知识,其受益要多得多.） ——斯潘尼尔 数学心脏费护持 The problem is the heart of mathematics． (问题是数学的心脏.) ——哈尔莫斯 He who seeks for methods without having a difinite problem in mind seeks for the most part in vain． (心中没有一定的问题而要寻找方法的人,多半都是徒劳无获的.) —— 希尔伯特 The problem solver may do creative work even if he does not succeed in solving his own problem； his effort may lead him to means applicable to other problems,Then the problem solver may be creative indirectly be leaving a good unsolved problem which eventually leads others to discovering fertile means． (即使在解某一道题时,解题者未获成功,他也可能做了有独创性的工作；他的努力可能使他得到适用于解决其他问题的工具.此外,他可能留下一个很好的未解决问题,这个问题最终能使其他人发现更有成效的解题手段.这样,他间接地作出了独创性的贡献.) ——波利亚 One of the virtues of a good problem is that it generates other good problems． (一道好题的价值之一在于它能产生其他一些好题.) ——波利亚 Each problem that I solved became a rule which served afterwards to solve other problems． (我解决过的每一个问题都成为日后用以解决其他问题的法则.) ——笛卡尔
If you wish to learn swimming,you have to go into the water,and if you wish to become a problem solver,you have to solve problems.（如果你想学会游泳,你必须下水；如果想成为解题能手,你必须解题.） ——波利亚 The only way to learn mathematics is to do mathematics.(学习数学的惟一方法是做数学.) ——哈尔莫斯 Some teachers demand that students solve mathematics problems only by the method taught in class,This process can thwart initiative,compound frustration,and promote avoidance.(有的教师要求学生只用课堂上教的方法解数学题.这种做法会阻碍独创能力的发展,导致失败,并造成回避困难的心理.) ——波雅妮 When students are forced to develop their own approaches to unsolved problems,they benefit much more than from exposure to the mathematics alone.（当一个学生被迫大展身手去对付未解决的问题时,比仅仅学习数学知识,其受益要多得多.） ——斯潘尼尔 数学心脏费护持 The problem is the heart of mathematics． (问题是数学的心脏.) ——哈尔莫斯 He who seeks for methods without having a difinite problem in mind seeks for the most part in vain． (心中没有一定的问题而要寻找方法的人,多半都是徒劳无获的.) —— 希尔伯特 The problem solver may do creative work even if he does not succeed in solving his own problem； his effort may lead him to means applicable to other problems,Then the problem solver may be creative indirectly be leaving a good unsolved problem which eventually leads others to discovering fertile means． (即使在解某一道题时,解题者未获成功,他也可能做了有独创性的工作；他的努力可能使他得到适用于解决其他问题的工具.此外,他可能留下一个很好的未解决问题,这个问题最终能使其他人发现更有成效的解题手段.这样,他间接地作出了独创性的贡献.) ——波利亚 One of the virtues of a good problem is that it generates other good problems． (一道好题的价值之一在于它能产生其他一些好题.) ——波利亚 Each problem that I solved became a rule which served afterwards to solve other problems． (我解决过的每一个问题都成为日后用以解决其他问题的法则.) ——笛卡尔