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“数学家埃尔米特5次高考不及格、尖锐批评考试与课本“疑是恶搞

已有 6999 次阅读 2014-6-2 17:47 |个人分类:数学与统计园地|系统分类:观点评述| 恶搞, 数学家埃尔米特

             ——疑是恶搞的第一个大陆版本《考试折磨不了真雄杰——-记厄尔米特》(2004年出笼)


  “数学家埃尔米特5次高考不及格、尖锐批评考试与课本”的故事近年广泛流传于各种报刊,且正在流传之中。

    经《中国青年报》为首的多家媒体进行了宣传,谎言的重复已超过千遍,并已走进了不少中小学课堂。

    经过我的一段梳理,我大体得出结论,这可能是出于中国的一场恶搞,但骗过了、并且继续欺骗着无数的、善良的从事教育、关心教育、接受教育的人们,且有持续疯传之势。几乎完全相同的内容在大陆、台湾的不同报刊、不同网站以许多不同的作者署名出现。

    就我目前的考证,即使不是全部虚构,里面也充斥着谎言。

    详情可看本人博文:“数学家埃尔米特5次数学高考不及格、不会考试”传言似明显失实”。之所以另开一帖,是想加快辟谣的速度。http://blog.sciencenet.cn/home.php?mod=space&uid=350729&do=blog&id=799530

    因为这则消息以科普的名义在公众媒体与中小学广泛传播。如果恶搞属实,那么,它除了歪曲埃尔米特的个人形象外,明显地丑化了大中小教材与考试的正常形象,影响比较恶劣。

    美国宾州大学数学副教授Eugene C. Boman在他的主页http://php.scripts.psu.edu/faculty/e/c/ecb5/提供了一个数学史链接,指向由英国安德鲁大学维护的数学史数据库(The MacTutor History of Mathematics archive,http://www-groups.dcs.st-and.ac.uk/~history/index.html。该数据库有大量的数学家传记,似乎有一定的权威性。关于埃尔米特的介绍详见附件5。


   真相逐渐浮上水面:http://www.uh.edu/engines/epi2376.htm


    据我多方搜索,截止目前,这则中文消息的最早出处是2004年5月(《中国青年报》以王波署名公开发表与传闻非常类似的内容为2010年7月,http://news.sciencenet.cn/htmlnews/2010/7/234242.shtm。王波是否为2004年消息的原创者我尚不清楚):

http://www.newsmth.net/nForum/#!article/Science/45123

信人: wdek (我是民科民哲文德奎), 信区: Science
标  题: [转载]考试折磨不了真雄杰——-记厄尔米特
发信站: BBS 水木清华站 (Fri May 28 10:39:28 2004), 站内
 
发信人: astroguy (tired to argue), 信区: Astronomy
标  题: [转载]考试折磨不了真雄杰——-记厄尔米特
发信站: BBS 水木清华站 (Thu May 27 17:44:59 2004), 站内
 
发信人: geodesic(billard ball), 信区: Mathematics. 本篇人气: 142
标  题:  考试折磨不了真雄杰——-记厄尔米特
发信站: 南京大学小百合站 (Thu May 27 10:10:05 2004)
 
前记:原创来自清华,几经转载,作者名字已丢失了。本文略有增益,不敢掠美,特此说明。

期末考试马上来临,讲个故事给孩儿们打打气。    
爱因斯坦不是考试的料,地球人都知道;这里还有一个更绝的。  

1 这无疑是一个天才,一个奇特的天才。他一方面能够以非凡的洞察力给出五次方程式的通解,一方面在数学的考场上似乎永远也考不及格。    

这是厄而米特(Charles Hermite),十九世纪最伟大的代数几何学家。  

大学入学考试重考了五次,每次失败的原因都是一样的——-数学考不好。他的大学读到几乎毕不了业,原因也还是一样——-数学这一科拖了后腿。大学毕业后考不上任何研究所,因为考不好的科目还是——数学。  

数学是他一生的至爱,但是数学考试是他一生的恶梦。不过这无法改变他的伟大:课本上“厄尔米特矩阵”是他先提出来的,这对于海森堡(Heisenberg)1925 年创建的量子力学关系重大;而厄而米特多项式和厄而米特函数在求解薛定谔(Schrodinger)波动方程也特别有用。这都是他在研究数论问题时搞出来的,谁也不会想到许多年后会在物理上得到如此意想不到的应用。这大概只能又归之于数学在自然科学上那种“不可思议的有效性”(unreasonnable effectiveness)了。  

人类一千多年来解不出“五次方程式的通解”,是他先解出来的。大家知道,阿贝尔(Abel)在此前很多年就已经证明,一般的五次方程不能用只包含四则运算和根式运算的函数求解。厄而米特却惊人地证明五次方程可以用椭圆函数来求解。

自然对数的“超越数性质”,全世界,他是第一个证明出来的人。  

他的一生证明“一个不会考试的人,仍然能有胜出的人生”,并且更奇妙的是不会考试成为他一生的祝福。怎么会这样呢?嗯……也许能在本文中找到答案喔!  

2 厄尔米特1822年12月24日出生在洛林的小村庄Dieuge,他的父祖辈都参与了法国大革命,祖父被大革命后的极端政治团体巴黎公社(Commune)逮捕,后来死于狱中;有些亲人死在断头台上;他的父亲是杰出的冶矿工程师,因为被公社通缉,逃到法国边界的洛林小村庄,在一家铁矿场中隐姓埋名做矿工。铁矿场的主人叫雷利曼(Lallemand),一个标准强悍的洛林人,有一个比他更强悍的女儿玛德琳(Madeleine)。在那个保守的时代,玛德琳就以“敢在户外穿长裤不穿裙子”而著名,凶悍地管理矿工。但是一遇到这位巴黎来的工程师,她就软化了,明知对方是死刑通缉犯还是嫁给他,而且为他生了七个孩子。埃尔米特在七个孩子中排名第五,生下来右脚就残障,需扶拐杖行走。他身上一半流著父亲优秀聪明、理想奋斗的血液,一半流著母亲敢作敢为、敢爱敢恨的洛林强悍血统,谱成不凡生涯的第一个升记号。  

厄尔米特从小就是个问题学生,上课时老爱找老师辩论,尤其是一些基本的问题。他尤其痛恨考试;后来写道:“学问像大海,考试像鱼钩,老师老要把鱼挂在鱼钩上,教鱼怎么能在大海中学会自由、平衡的游泳?”厄尔米特花许多时间去看数学大师,如牛顿、高斯的原著,他认为在那里才能找到“数学的美,是回到基本点的辩论,那里才能饮到数学兴奋的源头。”他在年老时,回顾少年时的轻狂,写道:“传统的数学教育,要学生按部就班地,一步一步地学习,训练学生把数学应用到工程或商业上,因此,不重启发学生的开创性。但是数学有它本身抽象逻辑的美,例如在解决多次方程式里,根的存在本身就是一种美感。数学存在的价值,不只是为了生活上的应用,也不应沦为供工程、商业应用的工具。数学的突破仍需要不断地去突破现有格局。

厄尔米特的表现让父母忧心,父母但求他能把书念好,再多的钱也愿意付出,就把他送到巴黎的路易大帝中学(Louis-le-Grand)。因其超卓的数学天份,他无法把自己塞入数学教育的窠臼,但是为了顺父母的意,又必须每天面对那些细微繁琐的计算,以致痛苦得不得了。这位孝顺的天才,似乎注定终生的自我折磨。巴黎综合工科技术学院入学考试每年举行两次,他从十八岁开始参加,考到第五次才以吊车尾的成绩通过。其间他几乎要放弃时,遇到一位数学老师李察(Richard)。李察老师对埃尔米特说:”我相信你是自拉格朗日(Lagrange)以来的第二位数学天才。”但是埃尔米特光有天份不够,李察老师说:“你需要有上帝的恩典,与完成学业的坚持,才不会被你认为垃圾的传统教育牺牲掉。”因此他一次又一次地落榜,却仍继续坚持应试。厄尔米特进技术学院念了一年以后,法国教育当局忽然下一道命令:“肢障者不得进入工科学系”,埃尔米特只好转到文学系。文学系里的数学已经容易很多了,结果他的数学还是不及格。      

有趣的是,他同时在法国的数学研究期刊《纯数学与应用数学杂志》发表《五次方方程式解的思索》,震惊了数学界。在人类历史上,第三世纪的希腊数学家就发现一次方程与二次方程的解法,之后,多少一流数学家埋首苦思四次方程以上到n次方的解法,始终不得其解。没想到三百年后,一个文学系的学生,一个数学常考不及格的学生,竟然提出正确的解法。厄尔米特知道自己已经“对数学的开创性研究中毒很深,热爱得无法自拔”,幸得好朋友勃特伦(Bertrand)赶忙帮他补习学校要考的数学。对这一个具有开创性的天才,僵化的数学教育带来无边的苦难;惟有友谊的了解与鼓励能够支持他走下去,并使他在二十四岁时,能以及格边缘的成绩自大学毕业。由于不会应付考试,无法继续升学,他只好找所学校做个批改学生作业的助教。这份助教工作,做了几乎二十五年,尽管他这二十五年中发表了代数论、分数理论、函数论、方程论……已经名满天下,数学程度远超过当时所有大学的教授,但是不会考试,没有高等学位的埃尔米特,只能继续批改学生作业。      

厄尔米特在四十九岁时,巴黎大学才请他去担任教授。此后的二十五年,几乎整个法国的大数学家都出自他的门下,其中有我们熟知的毕卡(Picard),波雷尔(Borel),还有上世纪的最后一个全才,我们的动力系统之父---庞卡莱(Poincare)。

对于他的教学风格,从庞卡莱说得一段话里可领略一二:“和厄而米特先生谈话,他从未求助于具体形象,但你能立刻体会到,对于他来说,最抽象的观念就像活的一样。”他不喜欢几何。但非常喜欢数论和分析,尤其擅长椭圆函数,在那里,数论和分析有许多奇妙的结合。五次方程的通解问题,厄尔米特矩阵,都是从这里生长出来的。

我们无从得知他在课堂上的授课方式,但是有一件事情是可以确定的──没有考试。

3 不会考试给厄尔米特他带来许多麻烦:工作不顺利、多次重考、他人的轻视、自卑等;但是不会考试也给他带来许多祝福:认识妻子、好友、信仰,与整个生命的成熟。后来美国加州理工学院数学系的教授贝尔(Bell),在他对历史上数学伟人的回顾上,用一段话描述埃尔米特:“在历史上的数学家愈是天才,愈是好讥诮,讲话愈多嘲讽。只有一个人例外,就是厄尔米特,他有真正完美的人格。”      

厄尔米特死于1901年1月4日。他对数学有自己独特的哲学,有点像毕达哥拉斯学派的味道。晚年他写道:“三角几何是永恒、是不朽的。自然界里没有任何一个东西是绝对的三角形,但是在人的脑中却存在著完美、绝对的三角形,去衡量外面的形形状状。没有人知道为什么三角的总和就是180°,没有人知道为什么三角的最长斜边对应最大角。这些三角几何的基本特性,不是人去发明出来或想像出来的,而是人在懵懂无知的时候,这些三角特性就存在,并且无论时空如何改变,这些特性也不会改变。我只不过是一个无意中发现这些特性的人。三角几何的存在,证明有一永久不改变的世界存在。”

附注:特挑出厄尔米特这段名言,大家肯定喜欢:

“学问像大海,考试像鱼钩,老师老要把鱼挂在鱼钩上,教鱼儿怎么能在大海中学会自由、平衡的游泳?”


    hillside:有点奇怪的是,这则消息声称原创出于清华大学,然而,“水木清华”仅能搜索到此则冠以“转载”的文章,“原创”谦虚得没了踪影。以上黑体字部分系我所加,基本上属于子虚乌有。我大体可以判定,"我们无从得知他在课堂上的授课方式,但是有一件事情是可以确定的──没有考试。"完全是胡诌.埃尔米特的上课风格在他的杰出弟子庞加莱与阿达玛的简短回忆中说得非常清楚,而"没有考试"之歪理邪说从来就没有踪影.转载者的"本文略有增益"式故弄玄虚将水搅得更浑.


附2:旧版博士论坛帖子合集.htm ( http://old.math.org.cn)

http://old.math.org.cn/%E6%97%A7%E5%8D%9A%E5%A3%AB%E6%95%B0%E5%AD%A6%E8%AE%BA%E5%9D%9B%E5%B8%96%E5%AD%90%E9%A2%98%E7%9B%AE2004%E5%B9%B4-2009%E5%B9%B4.pdf

1646 论坛的兴旺与败落!

1648 求教几种方法的翻译和区别

1649 正反问题和内外问题

1651 自学概率论,请教几个问题。

1655 六一快乐!(hillside:据相关材料,时为2005年)

1660 A First Course in Information Theory  

1661 [博导] Raymond W. Yeung 香港中文大学 信息论  

1663 南开大学陈省身获首届邵逸夫奖-数学科学奖  

1664 考试折磨不了真雄杰——-记厄尔米特


http://old.math.org.cn/%E6%97%A7%E7%89%88%E5%8D%9A%E5%A3%AB%E8%AE%BA%E5%9D%9B%E5%B8%96%E5%AD%90%E5%90%88%E9%9B%86(1108-2500).htm

1664强烈同意
心声啊 laugh.gif 

1664只能证明一点:
考试是考察人的应用已有知识的能力,而有时候我们更需要创造新知识的能力!

1664cool.gif 很有同感啊!走在学校里听见一个人对另一个人说“你这么喜欢数学,为什么还考得很糟糕”的时候,是我最想揍人的时候。

1664有点道是无情却有情的意味 ,给人无心插柳柳成阴的感觉。
他是不是故意的?我真想看看他当年一张张考试卷子,说不定是老师有眼无珠呢?!
不管是不是,他的故事值得数学教育界和数学家们研究和探讨。


附3:台湾静宜大学网站的消息,但无发表日期

http://elearning.emath.pu.edu.tw/mkuo/2001%BC%C6%BE%C7%A5v/%BE%FA%A9%A1%BC%C6%BE%C7%AEa%C2%B2%A4%B6.files/iii/19/france.htm


埃爾米特Hermite1822~1901

1.年代1822~1901

2.數學家姓名:

3.出生地: 法國

4. 數學事蹟: 他是十九世紀最偉大的代數幾何學家,但是他大學入學考試重考了五次,每次失敗的原因都是數學考不好。他的大學讀到幾乎畢不了業,每次考不好都是為了數學那一科。他大學畢業後考不上任何研究所,

因為考不好的科目還是── 數學。數學是他一生的至愛,但是數學考試是他一生的惡夢。不過這無法改變他的偉大:課本上「共軛矩陣」是他先提出來的,人類一千多年來解不出「五次方程式的通解」,是他先解出來的。自然對數的「超越數性質」,全世界,他是第一個證明出來的人。他的一生證明「一個不會考試的人,仍然能有勝出的人生」,並且更奇妙的是不會考試成為他一生的祝福。怎麼會這樣呢?嗯……也許能在本文中找到答案喔!翻開歐洲的地圖,在法國的東北角嵌著一塊小小的版圖,名叫洛林Lorraine)。

這個地方自古以來就是兵家必爭之地,因為北扼萊茵河口,南由馬恩河(Marne River)可以直搗巴黎;瀕臨的阿登高地(Ardennes)是軍事制高點;地層中蘊藏歐洲最大的鐵礦。早在神聖羅馬帝國時代,洛林草場上就染滿騎士的鮮血;1871年德國的鐵血雄兵蹂躪法國後,要求法國割讓的土地就是洛林。

革命家的血統

經過百年來戰爭的洗禮,洛林留下來的是一批苦幹、達觀的法國人,足能面 對環境的苦難。埃爾米特(Charles Hermite)1822年12月24日出生在洛林的小村 莊Dieuge,他的父祖輩都參與了法國大革命,祖父被大革命後的極端政治團 體巴黎公社(Commune)逮捕,後來死於獄中;有些親人死在斷頭台上;他的父親是傑出的冶礦工程師,因為被公社通緝,逃到法國邊界的洛林小村莊,在一家鐵礦場中隱姓埋名做礦工。

鐵礦場的主人叫雷利曼(Lallemand),一個標準強悍的洛林人,有一個比他更強悍的女兒瑪德琳(Madeleine)。在那個保守的時代,瑪德琳就以「敢在戶外 穿長褲不穿裙子」而著名,兇悍地管理礦工。但是一遇到這位巴黎來的工程師,她就軟化了,明知對方是死刑通緝犯還是嫁給他,而且為他生了七個孩子。埃爾米特在七個孩子中排名第五,生下來右腳就殘障,需扶枴杖行走。他身上一半流著父親優秀聰明、理想奮鬥的血液,一半流著母親敢作敢為、敢愛敢恨的洛林強悍血統,譜成不凡生涯的第一個升記號。

從大師認識數學之美

埃爾米特從小就是個問題學生,上課時老愛找老師辯論,尤其是一些基本的問題。他尤其痛恨考試;後來寫道:「學問像大海,考試像魚鉤,老師老要把魚掛 在魚鉤上,教魚怎麼能在大海中學會自由、平衡的游泳?」 老師看他考不好,就用木條打他的腳,他恨死了;後來寫道:「達到教育的 目的是用頭腦,又不是用腳,打腳有什麼用?打腳可以使人頭腦更聰明嗎?」 他的數學考得特別差,主要原因是他的數學特別好;他講的話更讓數學老師 抓狂,他說:「數學課本是一灘臭水,是一堆垃圾。數學成績好的人,都是 一些二流頭腦的人,因為他們只懂搬垃圾。」他自命為一流的科學狂人。不 過他講的也沒錯,歷史上最偉大的數學家大多是文學、外交、工程、軍事等, 與數學不相干科系出身的。 埃爾米特花許多時間去看數學大師,如牛頓、高斯的原著,他認為在那裡才 能找到「數學的美,是回到基本點的辯論,那裡才能飲到數學興奮的源頭。」 他在年老時,回顧少年時的輕狂,寫道:「傳統的數學教育,要學生按部就 班地,一步一步地學習,訓練學生把數學應用到工程或商業上,因此,不重 啟發學生的開創性。但是數學有它本身抽象邏輯的美,例如在解決多次方方 程式裡,根的存在本身就是一種美感。數學存在的價值,不只是為了生活上 的應用,也不應淪為供工程、商業應用的工具。數學的突破仍需要不斷地去

突破現有格局。」

孝順的天才

埃爾米特的表現讓父母憂心,父母但求他能把書唸好,再多的錢也願意付出,就把他送到巴黎的「路易大帝中學」(Louis-le-Grand)。因著超卓的數學天份, 他無法把自己塞入數學教育的窠臼,但是為了順父母的意,又必須每天面對 那些細微繁瑣的計算,以致痛苦得不得了。這位孝順的天才,似乎註定終生 的自我折磨。 巴黎綜合工科技術學院(Polytechnique)入學考每年舉行兩次,他從十八歲開始 參加,考到第五次才以吊車尾的成績通過。其間他幾乎要放棄時,遇到一位 數學老師李察(Richard)。李察老師對埃爾米特說:「我相信你是自拉格朗日 (Lagrange)以來的第二位數學天才。」 拉格朗日被稱為數學界的貝多芬,他所作的求根近似解被譽為「數學之詩」。 但是埃爾米特光有天份不夠,李察老師說:「你需要有上帝的恩典,與完成 學業的堅持,才不會被你認為垃圾的傳統教育犧牲掉。」因此他一次又一次 地落榜,卻仍繼續堅持應試。

騎在蝸牛背上的人

埃爾米特進技術學院唸了一年以後,法國教育當局忽然下一道命令:「肢障 者不得進入工科學系」,埃爾米特只好轉到文學系。 文學系裡的數學已經容易很多了,結果他的數學還是不及格。有趣的是,他 同時在法國的數學研究期刊「純數學與應用數學雜誌」發表「五次方方程式 解的思索」,震驚了數學界。

在人類歷史上,第三世紀的希臘數學家就發現一次方程與二次方程的解法,之後,多少一流數學家埋首苦思四次方程以上到n次方的解法,始終不得其 解。沒想到三百年後,一個文學系的學生,一個數學常考不及格的學生,竟 然提出正確的解法。埃爾米特知道自己已經「對數學的開創性研究中毒很深,熱愛得無法自拔」,幸得好朋友勃特倫(Bertrand)趕忙幫他補習學校要考的數學。對這一個具有開 創性的天才,僵化的數學教育帶來無邊的苦難;惟有友誼的瞭解與鼓勵能夠 支持他走下去,並使他在二十四歲時,能以及格邊緣的成績自大學畢業。 由於不會應付考試,無法繼續升學,他只好找所學校做個批改學生作業的助 教。這份助教工作,做了幾乎二十五年,僅管他這二十五年中發表了代數連 分數理論、函數論、方程論……已經名滿天下,數學程度遠超過當時所有大 學的教授,但是不會考試,沒有高等學位的埃爾米特,只能繼續批改學生作 業。社會現實對他就是這麼殘忍、愚昧。

不考試的老師

能夠使埃爾米特不憤世嫉俗、坦然前行的動力是什麼? 有三個重要的因素,一是妻子的瞭解與同心。埃爾米特的妻子,是他大學好 友勃特倫的妹妹,她無怨無悔地跟隨這個不會考試的天才丈夫,一年一年地走下去。二是有人真正地讚賞他,不因他外表的殘廢與沒有耀人的學位而輕視他。欣 賞他的人後來也都在數學界享有盛名──包括研究無窮級數收斂、發散與微 分方程式而著名的柯西(Cauchy),發表橢圓函數、行列式理論而著名的雅科 比(Jacobi),「純數學與應用數學雜誌」的主編劉維爾(Liouville)。這些都是行 家,而來自真正行家的惺惺相惜,比考試高分的一點虛偽榮耀,更能支助一 個失敗者走較遠的路。三是埃爾米特的信仰。埃爾米特在四十三歲時染患一場大病,柯西來看他, 並且把福音傳給他。信仰給他另一種價值與滿足。 埃爾米特在四十九歲時,巴黎大學才請他去擔任教授。此後的二十五年,幾乎整個法國的大數學家都出自他的門下。我們無從得知他 在課堂上的授課方式,但是有一件事情是可以確定的──沒有考試。

三角幾何裡認識另一個世界

不會考試給他帶來許多麻煩:工作不順利、多次重考、他人的輕視、自卑… …。但是給他帶來許多祝福:認識妻子、好友、信仰,與整個生命的成熟。 後來美國加州理工學院數學系的教授貝爾(Bell),在他對歷史上數學偉人的 回顧上,用一段話描述埃爾米特: 「在歷史上的數學家愈是天才,愈是好譏誚,講話愈多嘲諷。只有一個人 例外,就是埃爾米特,他有真正完美的人格。」 埃爾米特死於1901年1月4日。晚年寫道: 「三角幾何是永恆、是不朽的。自然界裡沒有任何一個東西是絕對的三角形, 但是在人的腦中卻存在著完美、絕對的三角形,去衡量外面的形形狀狀。 沒有人知道為什麼三角的總和就是180°,沒有人知道為什麼三角的最長斜 邊對應最大角。這些三角幾何的基本特性,不是人去發明出來或想像出來的, 而是人在懵懂無知的時候,這些三角特性就存在,並且無論時空如何改變, 這些特性也不會改變。我只不過是一個無意中發現這些特性的人。 三角幾何的存在,證明有一永久不改變的世界存在。」

5著作:

6資料來源: Bell E. T. 1937, "The Man, Not The Method -Hermite", Men of Mathematics, pp. 448~465. Simon & Schuster, INC. USA.

資料蒐集:黃義成


附3:来自台湾一教育类网站的基本相同的消息。内容与静海大学雷同,但标注了作者,发表时间不详。

http://content.edu.tw/primary/math/ch_dc/math/mathman.htm

                                      (科學檔案) 數學成績最爛的數學大師──埃爾米特

                                                                         張文亮

他是十九世紀最偉大的代數幾何學家,但是他大學入學考試重考了五次,每次失敗的原因都是數學考不好。他的大學讀到幾乎畢不了業每次考不好都是為了數學那一科。他大學畢業後考不上任何研究所,因為考不好的科目還是──數學。數學是他一生的至愛,但是數學考試是他一生的惡夢。

......不會考試給他帶來許多麻煩:工作不順利、多次重考、他人的輕視、自卑……。但是給他帶來許多祝福:認識妻子、好友、信仰,與整個生命的成熟。......

資料來源:

Bell E. T. 1937, "The Man, Not The Method -Hermite", Men of Mathematics, pp.

448~465. Simon & Schuster, INC. USA.  


hillside:上述张文亮署名文章被http://jcb.ahcbxy.cn/page.php?fp=newsdetail&id=1729全文转载,与台湾版一样,仍为繁体字。值得注意的是,该文提供了一篇参考文献,值得追索。故事的源头是否在台湾?


附4:上海大学数学系编写的电子书《线性代数中的数学家》,该书摘录了传闻消息的部分内容

http://math.shu.edu.cn/jpkc/la/download/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E4%B8%AD%E7%9A%84%E6%95%B0%E5%AD%A6%E5%AE%B6/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E4%B8%AD%E7%9A%84%E6%95%B0%E5%AD%A6%E5%AE%B6.pdf


附5:http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hermite.html

Charles Hermite

Born: 24 December 1822 in Dieuze, Lorraine, France


Died: 14 January 1901 in Paris, France

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Charles Hermite's father was Ferdinand Hermite and his mother was Madeleine Lallemand. Ferdinand Hermite was a trained engineer and he worked in this capacity in a salt mine near Dieuse. After he married Madeleine he joined in the draper's trade in which her family were involved. However he was an artistic man who always wanted to pursue art as a career. He had his wife look after the draper's business and he took up art. Charles was the sixth of his parents seven children and when he was about seven years old his parents left Dieuse and went to live in Nancy to where the business had moved.

Education was not a high priority for Charles's parents but despite not taking too much personal interest in their children's education, nevertheless they did provide them with good schooling. Charles was something of a worry to his parents for he had a defect in his right foot which meant that he moved around only with difficulty. It was clear that this would present him with problems in finding a career. However he had a happy disposition and bore his disability with a cheerful smile.

Charles attended the Collège de Nancy, then went to Paris where he attended the Collège Henri. In 1840-41 he studied at the Collège Louis-le-Grand where some fifteen years earlier Galois had studied. In fact he was taught mathematics there by Louis Richard who had taught Galois. In some ways Hermite was similar to Galois for he preferred to read papers by Euler, Gauss and Lagrange rather than work for his formal examinations.

If Hermite neglected the studies that he should have concentrated on, he was showing remarkable research ability publishing two papers while at Louis-le-Grand. Also like Galois he was attracted by the problem of solving algebraic equations and one of the two papers attempted to show that the quintic cannot be solved in radicals. That he was unfamiliar with Galois's contributions, despite being at the same school, is not at all surprising since the mathematical community were completely unaware of them at this time. However he might reasonably have known of the contributions of Ruffini and Abel to this question, but apparently he did not.

Again like Galois, Hermite wanted to study at the école Polytechnique and he took a year preparing for the examinations. He was tutored by Catalan in 1841-42 and certainly Hermite fared better than Galois had done for he passed. However it was not a glorious pass for he only attained sixty-eighth place in the ordered list. After one year at the école Polytechnique Hermite was refused the right to continue his studies because of his disability. Clearly this was an unfair decision and some important people were prepared to take up his case and fight for him to have the right to continue as a student at the école Polytechnique. The decision was reversed so that he could continue his studies but strict conditions were imposed. Hermite did not find these conditions acceptable and decided that he would not graduate from the école Polytechnique.

Hermite made friends with important mathematicians at this time and frequently visited Joseph Bertrand. On a personal note this was highly significant for he would marry Joseph Bertrand's sister. More significantly from a mathematical point of view he began corresponding with Jacobi and, despite not shining in his formal education, he was already producing research which was ranking as a leading world-class mathematician. The letters he exchanged with Jacobishow that Hermite had discovered some differential equations satisfied by theta-functions and he was using Fourier series to study them. He had found general solutions to the equations in terms of theta-functions. Hermite may have still been an undergraduate but it is likely that his ideas from around 1843 helped Liouville to his important 1844 results which include the result now known as Liouville's theorem.

After spending five years working towards his degree he took and passed the examinations for the baccalauréat and licence which he was awarded in 1847. In the following year he was appointed to the école Polytechnique, the institution which had tried to prevent him continuing his studies some four years earlier; he was appointed répétiteur and admissions examiner.

Hermite made important contributions to number theory and algebra, orthogonal polynomials, and elliptic functions. He discovered his most significant mathematical results over the ten years following his appointment to the école Polytechnique. In 1848 he proved that doubly periodic functions can be represented as quotients of periodic entire functions. In 1849 Hermite submitted a memoir to the Académie des Sciences which applied Cauchy's residue techniques to doubly periodic functions. Sturm and Cauchy gave a good report on this memoir in 1851 but a priority dispute with Liouville seems to have prevented its publication.

Another topic on which Hermite worked and made important contributions was the theory of quadratic forms. This led him to study invariant theory and he found a reciprocity law relating to binary forms. With his understanding of quadratic forms and invariant theory he created a theory of transformations in 1855. His results on this topic provided connections between number theory, theta functions, and the transformations of abelian functions.

On 14 July 1856 Hermite was elected to the Académie des Sciences. However, despite this achievement, 1856 was a bad year for Hermite for he contracted smallpox. It was Cauchy who, with his strong religious conviction, helped Hermite through the crisis. This had a profound effect on Hermite who, underCauchy's influence, turned to the Roman Catholic religion. Cauchy was also a very staunch royalist and Hermite was influenced by him to also become a royalist. We made comparisons with Galois earlier on in this article, but with royalist views, Hermite was now completely opposed to the views which the staunch republican Galois had held.

The next mathematical result by Hermite which we must mention is one for which he is rightly famous. Although an algebraic equation of the fifth degree cannot be solved in radicals, a result which was proved by Ruffini and Abel, Hermite showed in 1858 that an algebraic equation of the fifth degree could be solved using elliptic functions. He applied these results to number theory, in particular to class number relations of quadratic forms.

In 1862 Hermite was appointed maître de conférence at the école Polytechnique, a position which had been specially created for him. In the following year he became an examiner there. The year 1869 saw him become a professor when he succeeded Duhamel as professor of analysis both at the école Polytechnique and at the Sorbonne. Hermite resigned his chair at the école Polytechnique in 1876 but continued to hold the chair at the Sorbonne until he retired in 1897. In the 1890s Hermite became much less interested in the new results found by the mathematicians of the next generation.

The 1870s saw Hermite return to problems which had interested him earlier in his career such as problems concerning approximation and interpolation. In 1873 Hermite published the first proof that e is a transcendental number. This is another result for which he is rightly famous. Using method's similar to those of Hermite, Lindemann established in 1882 that π was also transcendental. Many historians of science regret that Hermite, despite doing most of the hard work, failed to use it to prove the result on which would have brought him fame outside the world of mathematics. Hermite is now best known for a number of mathematical entities that bear his name: Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitianmatrices.

For Hermite certain areas of mathematics were much more interesting than other areas. Hadamard, who unlike his teacher Hermite worked in all areas of mathematics, spoke of Hermite's dislike for geometry:-

[Hermite] had a kind of positive hatred of geometry and once curiously reproached me with having made a geometrical memoir.

Hermite's great love was for analysis and, not surprisingly, he had a great respect for Weierstrass. When Mittag-Leffler arrived in Paris to study with him, Hermite greeted him warmly but said:-

You have made a mistake, sir, you should follow Weierstrass's course in Berlin. He is the master of us all.

Poincaré is almost certainly the best known of Hermite's students. He once suggested that Hermite's mind did not proceed in logical fashion. He wrote:-

But to call Hermite a logician! Nothing can appear to me more contrary to the truth. Methods always seemed to be born in his mind in some mysterious way.

Hadamard like Poincaré was very interested in the way that mathematics was discovered. He also had this to say about the way that Hermite made his discoveries:-

Hermite used to observe [that biology] may be a most useful study even for mathematicians, as hidden and eventually fruitful analogies may appear between processes in both kinds of studies.

Hadamard had great respect for Hermite as a teacher. He said:-

I do not think that those who never listened to him can realise how magnificent Hermite's teaching was, overflowing with enthusiasm for science, which seemed to come to life in his voice and whose beauty he never failed to communicate to us, since he felt it so much himself to the very depth of his being.

[Hermite] was making a deep impression on us, not only with his methods and those of Weierstrass, but also with his enthusiasm and love of science; in our brief but fruitful conversations, Hermite loved to direct to me remarks such as: "He who strays from the paths traced by providence crashes." These were the words of a profoundly religious man, but an atheist like me understood them very well, especially when he added at other times: "In mathematics, our role is more of servant than of master." It goes without saying that gradually, as years and my scientific work unfolded, I came to understand more and more deeply the aptness and scope of his words.

Cross, reviewing [10] where 125 letters from Hermite to Mittag-Leffler are reproduced, writes:-

So there stands revealed one of the most engaging and influential men in Parisian and French mathematics in the second half of the 19th century, one might even say the central character for the period in which he published, 1842-1901. What radiates from the text is [Hermite's] humility, his Catholicism, his concern for his (very extended) family, his willingness to fight for colleagues whose merit he discerns, and his devotion to family, merit, and principle rather than simple influence.

In terms of his family life Hermite had married Louise Bertrand, Joseph Bertrand's sister. One of their two daughters married émile Picard. Struik writes:-

Hermite lived a retired life, with his family. His working hours were devoted to mathematical research and teaching. His outlook on mathematics was realistic in the Platonic sense: a mathematician, like a naturalist, discovers an outside world, in his case a world of ideas. Hermite, therefore, disliked Cantor's world, in which a new mathematical world was created.





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