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印度天才梦见3900个公式 成最伟大数学家

时间:2016-07-10 12:26:20 作者:admin 来源:转载 查看:4153

你有没有试过跟别人说

你要成为世界上最伟大的科学家?

一般我这样说了以后

对方会说:

你做梦去吧。

万万梦想到

真的有人靠做梦成为了数学家

梦里有个女神会来托梦送公式!

我服了

今天的主人公

在一般人眼中是命运多舛

英年早逝的可怜小年轻

而在数学家眼中

是千年一遇

不可多得的数学大师

他是被称为印度之子的——

拉马努金


拉马努金出生在印度

一个穷困潦倒的家庭

电影里那种衣衫褴褛

踩着破草鞋的可怜小孩

就是它的真实写照

穷人的孩子早当家

就是因为穷苦的家境

让他从小就认真刻苦学习

帮家里分担家务

是个懂事的孩子

12岁时,高年级的同学

借给他一本数学家朗内写的《三角学》

他在很短的时间里

就完全读懂了整本书

做出了书中所有的问题

还推导出了欧拉公式:eix=cosx+isinx

就算老师讲的是个毛线学霸也能把它织成毛衣...

就算在读教科书

也能发现新定理...

然而在他14岁时

不同寻常的事情又发生了——

那个同学又给了他一本

英国数学家卡尔写的

《纯粹数学与应用数学概要》

他打开这本书

发现里面有5000多个

复杂的数学公式躺在那里

只写出了结果

而没有给出证明过程

印度学霸梦见3900个公式,一夜成最伟大数学家

就在这时他发现

很多公式自己扫一眼

脑海中就能浮现出证明过程

要知道

这个时候的他

距离第一次接触数学只有4年而已

学校只教过最简单的数学运算

后来他以优异的成绩

考入了当地的一所大学

他对数学的热情变得更加强烈

每天废寝忘食,只研究数学

就在这时

神奇的事情又发生了——

他每天晚上睡觉的时候

都会梦到自己所信宗教的女神——

娜玛卡尔女神

印度学霸梦见3900个公式,一夜成最伟大数学家

拉马努金醒来以后,脑子里充满了各种各样的公式,那以后,女神每天都出现在他的梦里,给他灵感。所以,拉马努金每天清晨都要赶快拿出笔记本,把冒出 来的公式记在本上,由于笔记本的费用对他来说很高昂,所以每次女神给他恩惠的时候,他只把最终得出的,最简化的公式抄到本上。从几年下来,他得到了3900个复杂的公式!

这些公式的样子是长这样的——

印度学霸梦见3900个公式,一夜成最伟大数学家

印度学霸梦见3900个公式,一夜成最伟大数学家

印度学霸梦见3900个公式,一夜成最伟大数学家

那么他的模式

是一个什么样的模式呢?

相当于爱因斯坦什么都没干

一觉醒来就得出了

E=MC平方的质能方程

相当于牛顿在苹果树下睡了个午觉

醒来就写下了三大运动定律

而3900个这样的公式

简直比我最精华的东西还要精华很多...

由于当时印度的数学水平很落后

周围的老师们都不理解他

甚至嘲笑他的公式是一堆垃圾

1913年,

他把自己成果中的一小部分

写成一封信

分别寄给了3位英国数学家

其中一位回了信

他就是当时英国最有才华的数学家——

哈代

印度学霸梦见3900个公式,一夜成最伟大数学家

哈代到底有多厉害呢?

在哈代出现以前

欧洲大陆的数学家

一直和英国的数学家存在矛盾

彼此不相往来

而在数学领域闭关锁门的代价是

英国数学落后其他国家很远

就在这时

哈代出现了

他凭借一己之力

创立了数学领域中的哈代学派

把整个欧洲数学研究的区域重心

从欧洲大陆移动到了英国

许多有世仇的外国数学家

全都不计前嫌地前往英国

拜访这位绝世的大师

就在哈代学术生涯最顶峰的那个时期

他收到了一封印度的来信

就是我们的主人公

拉马努金的来信

信中列出了100多个复杂的公式

是这样子的——

印度学霸梦见3900个公式,一夜成最伟大数学家

哈代认真看了一遍

立即跟同僚说:

“这上面的每一个公式

都超出了最高级数学考试的标准”

哈代后来对这100多个公式

进行了细致的研究

发现即使是他这样的天才

也完全无法发明如此复杂的公式

有些公式甚至让他难以理解

印度学霸梦见3900个公式,一夜成最伟大数学家

哈代立刻寄钱

让拉马努金来到英国剑桥大学深造

经过更深的接触以后

哈代发现了更令他惊讶的事情——

拉马努金几乎没受过任何像样的数学教育

许多常识性的数学定理

他从未听过

许多非常基本的数学分支

他从未接触过

在剑桥的日子里

拉马努金把他之前岁月里

写满公式的笔记本让哈代过目

从头到尾看完后

哈代差点跪在地上...

笔记本里记录着整个欧洲数学史上

几乎所有的重要的数学公式

而这只占了三分之一

剩下三分之二

是他完全没有见过

大开眼界的全新公式

印度学霸梦见3900个公式,一夜成最伟大数学家

哈代感慨道:

他一个人战胜了整个欧洲数学界

他评价拉马努金

是超越整个世纪

1000年也遇不到的数学奇才

可以与欧拉、高斯

这种等级的天才相比拟

智商超群的数学家哈代

在他面前就像乳臭未干的孩子

只能俯首称臣

他们在一起的5年里

写出了29篇重要的论文

为数学界做出了巨大的贡献

哈代将这段经历描述为

“我一生中最浪漫的事”

印度学霸梦见3900个公式,一夜成最伟大数学家

图:英国数学家哈代

拉马努金由于信教

不能吃任何肉

每天只能吃水果和蔬菜

然而1914年

第一次世界大战爆发了

英国的蔬果进口源被切断

没有食物的拉马努金

经常过着忍饥挨饿的生活

久而久之

他患上了严重的肺结核

1920年,

他的病严重恶化

哈代带着病危的他搭出租车去医院

出租车的车牌号是1729

哈代觉得这个数字毫无规律

想有不好的征兆

而拉马努金迅速说道:

“不,1729是个很有规律的数

它既是1的立方与12的立方之和

也是9的立方与10的立方之和”

求哈代当时的心理感受...

然而这次对话成为了两人最后的故事

拉马努金在不久后去世

临终前

他最后一次梦到了他的女神

并且用手写下了最后一个数学公式

印度学霸梦见3900个公式,一夜成最伟大数学家

这个公式让同时代所有的数学大师

都大惑不解

只能猜测它描述了一种神秘的函数

即使是70年后的1990年代

科学家们也只能揭示它属于那个数学分支

2012年,这个神秘的公式

终于被破解

科学家们说这个公式

对黑洞行为的研究具有帮助

然而在100年前,

拉马努金写下这个公式的时候

人类甚至还不知道什么是黑洞!

印度学霸梦见3900个公式,一夜成最伟大数学家

1976年,有人在剑桥大学图书馆

发现了拉马努金的第4本笔记

记载了600多个令人匪夷所思的数学公式

后来,随着人类科技的进步

科学家们发现

他那些令人费解的公式

对现代人工智能

粒子物理、统计力学、计算机科学、密码技术和空间技术等不同领域

起着相当重要的作用

他的数学公式

引领了人类科学进步100年...

看完这个故事

我似乎懂得了一些道理

一般人梦里都梦到思念的亲人来托梦

学霸梦到的却是女神来托公式

不说了,我要去认真睡觉了

印度女神我来了!(以上来源于酷玩实验室)


(以下来源于百度百科)

天才与贫困

1887年12月22日,拉马努金出生于印度泰米尔纳德邦埃罗德县的一个没落的婆罗门家庭。父亲是一家布店的小职员,每月只有20卢比的工资,一家7口人就靠这点微薄的收入维持生活。小时候他大部分的时间是在祖母家里度过的。从小他就喜欢思考问题,曾问老师在天空闪耀的星座的距离,以及地球赤道的长 度。在12岁时开始对数学发生兴趣,曾问高班同学:“什么是数学的最高真理?”当时同学告诉他“毕达哥拉斯定理”(即中国人称“勾股定理”)可以作为代 表,这引起了他对几何学的兴趣。差不多在这个时候,他对等差级数和等比级数的性质自己做了研究。他那时的同学后来回忆说:“我们,包括老师,很少可以理解 他,并对他‘敬而远之’”。

他15岁时,朋友借给他英国数学家卡尔(G. Carr)写的《纯粹数学与应用数学概要》一书。该书收录了代数、微积分、三角学和解析几何的五千多个方程,但书中没有给出详细的证明。这正好符合拉马努 金的胃口,他把每一个方程式当成一个研究题,尝试对其进行独特的证明而且还对其中一些进行推广。这花去了他大约5年的时间,留下了几百页的数学笔记。他证 明了其中的一些方程,而以后他研究的基础却受益于这本书。

拉马努金在贡伯戈纳姆读高中,毕业时各项成绩突出,被校长形容为“用满分也不足以说明他如此出色”。但进入当地著名的贡伯戈纳姆学院后,他把全部精 力投入数学研究,导致其他科目不及格;他不仅失去了奖学金,而且被学校开除。1905年,18岁的他为此离家出走3个月。一年后,拉马努金被马德拉斯的帕 凯亚帕学院录取,但这个数学成绩优异的学生,还是难以逃脱被开除的命运,他的5门文科课程两次不及格。此后拉马努金开始做家教维持生计,同时从图书馆借来 数学书,然后把自己的研究结论写在笔记本里。

根据印度的习俗,他家人在1909年为他安排了婚事,妻子是一个9岁的女孩,在当时的印度这是相当常见的。有了家而且是长子,必须帮助家里解决一些 生活费用,他不得不极力寻找工作,后来朋友艾亚尔(S. Aiyar)推荐他去找马德拉斯港务信托处官员拉奥(R. Rao)。拉奥是一个有钱的人,也是一个数学爱好者,他很赏识拉马努金的数学才能。他认为拉马努金只适合搞数学而不适合做其他工作,因此宁愿每个月给他一 些钱,让他挂名不上班,在家专心从事数学研究。

1911年,拉马努金的第一篇论文“关于伯努利数的一些性质”发表在《印度数学会会刊》上,从此他开始了与数学界同行的正式交流。拉马努金在他的第二篇论文里发表了一系列共14条关于圆周率π的计算公式;神奇的是,其中一条公式每计算一项就可以得到8位的十进制精度。

巧遇伯乐

由于印度当时的数学水平不高,国内几乎没有人能看懂拉马努金的研究成果。于是,艾亚尔极力主张他把研究成果寄给英国数学家,最初的两个数学家都未回 音。1913年1月16日,他再次鼓起勇气写信给第三个数学家——剑桥大学教授哈代(G. Hardy);信是这样开头的,“尊敬的先生,谨自我介绍如下:我是马德拉斯港务信托处的一个职员……我未能按常规念完大学的正规课程,但我在开辟自己的 路……本地的数学家说我的结果是‘惊人的’……如果您认为这些内容是有价值的话,请您发表它们……”他还给哈代寄去了一大堆自己研究得出的数学公式和命 题;由于没有证明的过程,有些连哈代也不大明白。哈代在咨询了另一个英国数学家、他的合作伙伴李特尔伍德(J. Littlewood)之后,认定拉马努金是一个难得的数学天才。拉马努金多少有些运气,哈代的慧眼识金,使得拉马努金能够在1914年进入剑桥大学。这 则动人故事如今已成为数学史乃至科学史上的传奇故事之一,同时作为两个人学术生涯的转折点——拉马努金因哈代而崭露头角,哈代因拉马努金而增光溢彩。

按哈代的说法,拉马努金总是和蔼可亲,性情很好。但可以肯定,拉马努金初到剑桥对哈代超出数学范围的谈话几乎不懂。他听哈代说话时似乎总带着耐心的 微笑,面容友善、真诚,但即使是谈论数学,由于他们受教育程度不同,用词及表述也就有差异。拉马努金是自学的,他对现代学术意义上的严谨一无所知,在某种 程度上他不知道什么叫证明,于是哈代就向他演示如何写出严谨的数学证明。有一次哈代喝醉酒以后曾经写道,如果拉马努金能受到更好的教育,将少一点拉马努金 的特性。当他清醒以后,他说那些话是胡说,应该说如果拉马努金受到了更好的教育,他将会比现在更出色。

拉马努金是个有神论者,哈代则是个无神论者,但他们却能为数学而进行合作研究;在5年里,他们共同发表了28篇重要论文。哈代曾将这段经历描述为“我一生中最浪漫的事件”。因为在数学上的卓越成就,拉马努金31岁就当选为英国皇家学会的外籍会员(亚洲第一人)以及剑桥大学三一学院的院士(印度第一 人),走到了他的荣誉最高峰。

由于拉马努金是个虔诚的婆罗门教徒,绝对奉行素食主义,在英国生活那段时间,他自己煮食物,常常因研究而忘记吃饭,加上冬天寒冷的天气,他的身体越 来越衰弱,1917年常感到身上有无名的疼痛。后来才发现他患上了当时难以医治的肺结核病。有一天哈代去医院看他时,抱怨所乘的出租车牌号1729是个不 吉利的数字;而拉马努金的第一反应则是,这是个有趣的数字,因为这个整数可以写成12的立方与1的立方之和,也可以写成10的立方与9的立方之和。后来李 特尔伍德回应这宗轶闻说:“每个整数都是拉马努金的朋友。”

拉马努金思乡心切,却因为一战爆发而无法回国。这一度令他变得抑郁,甚至试图卧轨自杀。1919年4月,他终于回到印度,但回家之后的生活并不愉 快,且病情日渐加重。1920年4月26日,他病逝于马德拉斯,年仅32岁。他身后留下了一份使人着魔的、深奥的数学遗产,其中包含了大量没有证明的公式 和命题。许多数学家都致力于这方面的研究,一直到1997年,才总算是完成了其中的一部分,并整理成5大卷出版。

神秘的直觉

拉马努金的数学贡献为现代数学家从事数学研究提供了很好的史料,对现代数学的发展也产生了难以估量的影响。他在堆垒数论特别是整数分拆方面做出了重 要贡献,在椭圆函数、超几何函数、发散级数等领域也有不少成果。他有着很强的直觉洞察力(可称之为“数感”),虽未受过严格数学训练,却能独立发现了近3900个数学公式和命题。他经常宣称在梦中娜玛卡尔女神给其启示,早晨醒来就能写下不少数学公式和命题。他所预见的数学命题,日后有许多得到了证实。如 比利时数学家德利涅(V. Deligne)于1973年证明了拉马努金1916年提出的一个猜想,并因此获得了1978年的菲尔兹奖。

除了在纯粹数学方面做出卓越的成就以外,拉马努金的理论还得到了广泛的应用。他发现的好几个定理在包括粒子物理、统计力学、计算机科学、密码技术和 空间技术等不同领域起着相当重要的作用,甚至晶体和塑料的研制也受到他创立的整数分拆理论的启发,而他在黎曼ζ函数方面的研究成果,现在已经与齿轮技术的 进步挂上了钩,还被用于测温学及冶金高炉的优化。他生命中的最后一项成果——模仿θ函数有力地推动了用孤立波理论来研究癌细胞的恶化和扩散以及海啸的运 动;最近有专家认为,这一函数很可能被用来解释宇宙黑洞的部分奥秘,而令人吃惊的是,当拉马努金首次提出这种函数的时候,人们还不知道黑洞是什么。

拉马努金的亦师亦友哈代曾感慨道:“我们学习数学,拉马努金则发现并创造了数学。”他更喜欢公开声称的是,自己在数学上最大的成就是“发现了拉马努 金”。他在自己设计的一种关于天生数学才能的非正式的评分表中,给自己评了25分,给另一个杰出的数学家李特尔伍德评了30分,给他同时代最伟大的数学家 希尔伯特(D. Hilbert)评了80分,而给拉马努金评了100分。他甚至把拉马努金的天才比作至少与数学巨人欧拉(L. Euler)和雅可比(C. Jacobi)相当。

印度之子

为了激励年轻人刻苦学习和奋发向上,马德拉斯大学于1950年建立了一个用拉马努金的名字来命名的高等数学研究所,并在研究所门前为他矗立一个大理 石半身像;后来该所培养了不少优秀数学人才。印度人在纪念拉马努金时,把他和圣雄甘地(M. Gandhi)、诗人泰戈尔(R. Tagore)等人一道,称作“印度之子”。在1962年拉马努金诞辰75周年之际,印度发行了一套纪念他的邮票。1975年印度成立了“拉马努金学 会”,1986年开始出版会刊。到1987年即拉马努金诞辰100周年之际,印度已拍摄了3部有关他生平的电影。1987年在拉马努金的故乡马德拉斯,当 容纳他最后一年心血的遗著《失散的笔记本》出版时,印度前总理甘地(R. Gandhi)亲自赶去祝贺并参加了首发式。

美国佛罗里达大学于1997年创办了《拉马努金期刊》,专门发表“受到他影响的数学领域”的研究论文;该校还成立了一个国际性的拉马努金数学会。千 禧年时,《时代》周刊选出了100位20世纪最具影响力的人物,其中就有拉马努金,并称赞他是一千年来印度最伟大的数学家。现在国际上有两项以拉马努金命 名的数学大奖,专门颁发给“与他有相同研究方向”的杰出青年数学家;已获奖的华人数学家有洛杉矶加州大学教授陶哲轩、北京大学教授史宇光、北京清华大学访 问学者张伟和斯坦福大学教师恽之玮。

为纪念拉马努金对数学的贡献,印度总理辛格(M. Singh)于2012年2月26日宣布其诞辰为“印度数学日”(每年12月22日)及2012年为“印度数学年”。在拉马努金诞辰125周年之际,印度 举办了一系列纪念他的活动。美英等国的一些著名科学家在报上发表纪念文章,向拉马努金表示崇高的敬意。《美国数学会志》在2012年12月号和2013年1月号上连续刊发纪念拉马努金的系列文章,高度评价了他对数学作出的巨大贡献。有趣的是,谷歌网站为纪念拉马努金诞辰125周年专门绘了一张描述他少年学 习情景的涂鸦。

值得一提的是,由于拉马努金的传奇色彩,世界上有多种关于他的传记版本。其中麻省理工学院科学写作教授卡尼格尔(R. Kanigel)1991年所著的《知无涯者:拉马努金传》(2008年被中国数学家、武汉大学前校长齐民友等翻译成中文)最为成功,在美国成为畅销书, 并曾获1992年“美国书评界传记奖”。美国数学科普大师加德纳(M. Gardner)对该书的评语是:“至今出版过的关于当代数学家的传记中,这是最好的、文献最丰富的作品之一……你一定会发现,对本世纪最杰出、谜一般的 智者之一的光辉的研究会吸引住你。

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