我发现了

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今天,我想向全世界宣布,我发现了一个美妙的数学公式!有了它,各种函数之间的关系都一目了然;有了它,什么哥德巴赫猜想,黎曼猜想都不在话下;有了它,大数的计算以及函数阶的估计便可精确到任何程度!

还好,我只是在我的个人博客里叨叨,不会有太多的人知道。我不想受到太多干扰,因为我还要写书,还有学生要教。

其实我没有做什么。只不过是把已有的一些公式,以某种方式组合到一起而矣;然而,当看到它是如此美妙时,我又不禁怀疑自己的俗眼是否配看它。

为了它,我苦苦探索了三十年!哪怕是在艰难打工的日子里,或是遭遇无数次挫折的时候,我从来没有放弃它;因为我坚信,它在那里,只是人们还不知道它。

为什么要这长时间才能揭开它的面纱?因为我们受到的教育就是如此这是我刚刚学到的一句话。昨天,我读到一道题的解答:25支球队进行淘汰赛;问要比赛多少场,才能产生冠军队?解答说:冠军队只有一个,当然要淘汰24支球队,所以要比24场。如此简捷!我可不是这么做的,也根本想不到这样做。当然,该书也给出了大多数人(包括我)的解法:

25支球队,第一轮比12场,1队轮空;第二轮,13支球队比6场,1队轮空;第三轮,7支球队比3场,1队轮空;第四轮,4支球队比2场;第五轮,2支球队比1场,冠军产生。一共比赛 12 + 6 + 3 + 2 + 1 = 24 场。

该书也问,为什么我们想不到第一种解法?因为我们受到的教育就是如此。没有人教我们全部的数学知识,也没有人教我们如何思考。我在前面的某篇博文中还曾抱怨这事,没想到,该书作者十几年前就知道了。当然没有人能知道全部的知识/全部的方法,因为新的知识和方法永远在不断地产生;但是,作为老师,我们能不能让学生知道已有的全部知识和方法?我们不必教会每个学生,但有学生想知道时,我们有什么权力剥夺他们的求知欲望?为什么不能教给他/她全部?原因只有一个:老师自己不知道。

因此,我想写书。我要尽量把全部的数学知识和方法展示给学生,更重要的,教会他们如何思考:这远比发现一个公式,或解决一个猜想来得重要。

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