以前是学数学的,觉得这个东西不实际,在现实生活中可有可无的,试想下,古代人不学,不也是生活得很好吗。再说了,现在那些学文的人不学数学,不也正常生活么,我们这些学理的,不搞文的,也是生活的过去呀。但就我本身的情况来说,我还是喜欢文学的,试想,假如连文科的东西都不学的话,那觉得自己这个人就应该什么的,反正就是感觉很糟的。
且不谈数学在生活中的用处吧,就简要谈谈在其他学科中的用处了,没听别人说过么,一个优秀的数学家至少能抵得上一个王牌师呢。
先说说在物理上的故事,近代的量子力学就得益于统计力学。没有量子力学,就没有后来的核弹,核能,电子计算机,通信科学。可见数学的功用了。讲量子力学就不得不讲狄拉克和海森堡了。狄拉克数学很好,他提出了著名的狄拉克方程,预言了antiparticle的存在,是量子力学的奠基人之一,诺贝尔获得奖者。更有趣的就是量子力学的另一位创始人海森堡,也是位诺贝尔奖获得者,他的数学不是很擅长,而且他小时候就不是喜欢数学的,结果他写的文章,由开始oneman paper 到three manpaper【1】,为什么呢,他的数学不好,一个很好物理上想法他能知道,可是就苦于不能用很好数学表达出来,据说当时的就是要靠矩阵这个东西,可是他就不知道用矩阵来表示,所以就变成了threeman paper,呵呵,后来他后期发现了数学的重要,完成了量子力学的“互补性理论”。
再说说在经济学的,华人经济学家张五常,想必人们都很熟悉了,他的佃农理论以及合约和企业方面独创的意见等,可是他的不能好好利用数学,他本人说过,搞完佃农理论以后,他不再读书,要是这些理论用数学模型来统一起来,诺贝尔奖早就是有他的份了,他的二道贩子用了他的理论,加以完备的数学模型描述,名声甚至超过了这个原创者,张五常也说过他的一篇文章里有个注脚数学公式【2】写的非常奇怪,不是专业的,当然也与他的个性有关系,28岁以后,就声言不再读书了。另一位大名鼎鼎诺贝尔奖获得者经济学家纳什,他就是数学出身的,可以说,他本身就是一个数学家,博弈论的提出者,在经济学上做出巨大的贡献。
可见,真的要是学好数学,用好数学的话,数学还真有经纶济世的之功用,不可小觑,尤其在计算机方面的功用要说大就有多大了,毫不夸张。可我们这些小老百姓用它来做甚呢?数学能使人思维敏捷,能使人逻辑严密,这就是数学的最实际的功用了,看来只要不掉进书袋子里,就是有用处的呀,真得要好好体会下培根的《论读书》上的话了。
注释:【1】大概的意思是杨振宁在凤凰卫视世纪大讲堂上的演讲
【2】张五常自己在博客中叙述过的大概意思
附录参考:论读书
Of study --Bacon.Francis
STUDIES serve for delight, for ornament, and for ability.Their chief use for delight, is in privateness and retiring; forornament, is in discourse; and for ability, is in the judgment, anddisposition of business. For expert men can exe-cute, and perhapsjudge of particulars, one by one; but the general counsels, and theplots and marshalling of affairs, come best, from those that arelearned. To spend too much time in studies is sloth; to use themtoo much for ornament, is affectation; to make judgment wholly bytheir rules, is the humor of a scholar. They perfect nature, andare perfected by experience: for natural abilities are like naturalplants, that need proyning, by study; and studies themselves, dogive forth directions too much at large, except they be bounded inby experience. Crafty men contemn studies, simple men admire them,and wise men use them; for they teach not their own use; but thatis a wisdom without them, and above them, won by observation. Readnot to contradict and confute; nor to believe and take for granted;nor to find talk and discourse; but to weigh and consider. Somebooks are to be tasted, others to be swallowed, and some few to bechewed and digested; that is, some books are to be read only inparts; others to be read, but not curiously; and some few to beread wholly, and with diligence and attention. Some books also maybe read by deputy, and extracts made of them bothers; but thatwould be only in the less important arguments, and the meaner sortof books, else distilled books are like common distilled waters,flashy things.
Reading make a full man; conference a ready man; and writingan exact man. And therefore, if a man write little, he had needhave a great memory; if he confer little, he had need have apresent wit: and if he read little, he had need have much cunning,to seem to know, that he doth not. Histories make men wise; poetswitty; the mathematics subtitle; natural philosophy deep; moralgrave; logic and rhetoric able to contend. Abeunt studia in mores.Nay, there is no stand or impediment in the wit, but may be wroughtout by fit studies; like as diseases of the body, may haveappropriate exercises. Bowling is good for the stone and reins;shooting for the lungs and breast; gentle walking for the stomach;riding for the head; and the like. So if a man/'s wit be wandering,let him study the mathematics; for in demonstrations, if his wit becalled away never so little, he must begin again. If his wit be notapt to distinguish or find differences, let him study theSchoolmen; for they are cymini sectors. If he be not apt to beatover matters, and to call up one thing to prove and illustrateanother, let him study the lawyers/' cases. So every defect of themind, may have a special receipt.
论读书 --王佐良译
读书足以怡情,足以博彩,足以长才。其怡情也,最见于独处幽居之时;其傅彩也,最见于高谈阔论之中;其长才也,最见于处世判事之际。练达之士虽能分别处理细事或一一判别枝节,然纵观统筹、全局策划,则舍好学深思者莫属。读书费时过多易惰,文采藻饰太盛则矫,全凭条文断事乃学究故态。读书补天然之不足,经验又补读书之不足,盖天生才干犹如自然花草,读书然后知如何修剪移接;而书中所示,如不以经验范之,则又大而无当。有一技之长者鄙读书,无知者羡读书,唯明智之士用读书,然书并不以用处告人,用书之智不在书中,而在书外,全凭观察得之。读书时不可存心诘难作者,不可尽信书上所言,亦不可只为寻章摘句,而应推敲细思。书有可浅尝者,有可吞食者,少数则须咀嚼消化。换言之,有只须读其部分者,有只须大体涉猎者,少数则须全读,读时须全神贯注,孜孜不倦。书亦可请人代读,取其所作摘要,但只限题材较次或价值不高者,否则书经提炼犹如水经蒸馏、淡而无味矣。
读书使人充实,讨论使人机智,笔记使人准确。因此不常作笔记者须记忆特强,不常讨论者须天生聪颖,不常读书者须欺世有术,始能无知而显有知。读史使人明智,读诗使人灵秀,数学使人周密,科学使人深刻,伦理学使人庄重,逻辑修辞之学使人善辩:凡有所学,皆成性格。人之才智但有滞碍,无不可读适当之书使之顺畅,一如身体百病,皆可借相宜之运动除之。滚球利睾肾,射箭利胸肺,慢步利肠胃,骑术利头脑,诸如此类。如智力不集中,可令读数学,盖演题须全神贯注,稍有分散即须重演;如不能辨异,可令读经院哲学,盖是辈皆吹毛求疵之人;如不善求同,不善以一物阐证另一物,可令读律师之案卷。如此头脑中凡有缺陷,皆有特药可医。