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“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

已有 14479 次阅读 2014-6-1 15:51 |个人分类:数学与统计园地|系统分类:观点评述| 数学家埃尔米特, 数学高考5次不及格, 不会考试, 考试里手

                                            ——埃尔米特并非考试白痴,仅是表现平平


                            ——国内普遍用作励志宣传的“埃尔米特数学高考5次不及格”完全不成立

                            ——充斥国内报刊的埃尔米特批评“考试”与“课本”的言论似出于有意捏造

                            ——“5次”之讹疑源于误解passed the examinations for the baccalauréat

                            ——高考一考即中,但数学光芒四射而仅列名校总排名68,显得不够威风

                            ——埃尔米特讨厌几何繁琐教学,对代数情有独钟,并非不会考试

                            ——埃尔米特是一位伟大的教师与数学伯乐,手下名徒庞加莱、阿达玛

                            ——埃尔米特尽管腿有先天残疾,本科甫一毕业,即获名牌母校聘用

                           

   本文重在指出所谓法国数学名家埃尔米特数学高考5次不及格,不会数学考试这类传闻的矛盾之处,基本断定国内普遍用作励志宣传的“埃尔米特数学高考5次不及格”不成立。我认为,网络所传埃尔米特“任教授后取消考试”也不见得靠谱,所谓埃尔米特对于考试的多句恶评可能也是始作俑者的向壁虚构,不过暂时还没有发现有效证据进行证伪。

   因时间关系,本文结构显得比较松散、杂乱,条理性存在欠缺。不过,写作风格是严谨的,志在追求真实。

   中文网页中,经我的分析,难得的信史介绍当属于上海财经大学浙江学院网页的http://ggjcjxb.shufe-zj.edu.cn/index.aspx?lanmuid=117&sublanmuid=278&id=1829。至于国外网页,英国圣安德鲁大学数学与计算科学学院数学家历史传记库(http://www-gap.dcs.st-and.ac.uk/history/Biographies/Hermite.html)有较高的可信度。

   下面针对流传于中文各类媒体、充斥中小学科普期刊有年的埃尔米特不会考试的故事进行择要质疑。

1.他差点再次栽在巴黎综合工科学校的数学考试上。这已经是埃米尔特第5次参加考试了。

   有材料称,埃米尔特仅用一年时间准备就考取了巴黎综合工科学校。一年之内有可能参加同一学校的5次入学考试吗?昔日法国高考的年出场率不会如此之高,即使是自主招生,并非今日美国之SAT高考可比(此考试似乎有明显的吸金色彩。据介绍,SAT考试在海外,一年中举行六次,是中国高中生进入美国大学读本科最重要的条件之一,考生想要取得更好的SAT成绩,也许会参加几次SAT考试才可以。报名SAT考试的次数并没有限制,但是考生需要根据自己的实际情况和学校的招生情况慎重决定。)

   巴黎综合工科学校作为名牌学校,考取难度很大。据http://www-gap.dcs.st-and.ac.uk/history/Biographies/Hermite.html介绍,米特仅准备一年时间就被录取,只是排名并不是非常突出而已,名列第68位(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.)。仅用一年时间就考上法国顶级名校,称为“不会考试”甚至“考试白痴”(见于附5),国人的想像力不可谓不丰富矣。对于尚未入学、但已才华横溢的埃尔米特、对于公众的期望来说,名校总排名第68确实不够威风"However it was not a glorious pass"。

  《中学数学杂志》2010年第5期《数学是他一生的至爱,但数学考试是他一生的恶梦——不擅长数学考试的数学大师埃尔米特》中称,每年举行两次。

    至于巴黎综合工科技术学院每年举办几次考试的准确说我还不得而知,但一年5次的说法明显太夸张了。另据附16称,巴黎综合工科技术学院一般不接受同一个学生参加第2次(亦即再次,名校选材的风范?)入学考试。

   造成参加5次考试的讹传可能来自本科5年后参加的学位考试。据http://www-gap.dcs.st-and.ac.uk/history/Biographies/Hermite.htmlAfter 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.埃尔米特在本科5年之际(1847年)参加了结业考试顺利通过(据有关消息介绍,法国人习惯于用baccalauréat 加上年限来说明大学学历,比如大一是Bac +1 ,大二是Bac+2, 大三是Bac+3, 如果大三考试合格,得到的学位是Licence,也就是本科学位。法国的学制和欧洲学制是统一的,也就是LMD学制( Licence-Master-Doctorat 分别是Bac+3,Bac+5和Bac+8)),并荣获奖励,很快(即1848年)被巴黎综合工科学校聘用。

   据上海财经大学浙江学院网页http://ggjcjxb.shufe-zj.edu.cn/index.aspx?lanmuid=117&sublanmuid=278&id=1829,“1842年,埃尔米特以总分第68名的较低分数被巴黎综合工科学校录取,虽然他当时已经是一位数学家了,甚至是比一些考他的人水平高得多的数学家.埃尔米特在综合工科学校只读了一年,就由于右腿的残疾而被学校除名.这时,他已经在数学界小有名气了,与JW.亚历山大(Alexadre) JLF.贝特朗(Bertrand) 等人有密切的交往.他希望找到一个教师职业,把它作为可以谋生,同时能继续从事研究工作的根据地.但这需要学位,因此,在他24岁时不得不中断研究工作,去掌握考取学位所必须的那些他不太感兴趣的东西.1847年,他通过考试,取得了学士学位.埃尔米特的数学成就使他受到学界的重视,1848年他被任命为巴黎综合工科学校的入学考试委员.此后10年是他十分活跃的时期, 1856年他当选为巴黎科学院院士,在 48张选票中获得了40张.1862年,通过L.巴斯德(Pasteur) 的工作,巴黎综合工科学校为埃尔米特设了一个大学讲师的职务.次年,他又被任命为该校的主考人,他担任此职直到1867年,这一年他接替JMC.任阿梅尔(Dubamel) 担任巴黎综合工科学校的分析学教授职务.同时他还成为巴黎理学院的教授,先教代数学,后来教分析学.他的分析学讲义在国内外部享有盛名.1876年,埃尔米特辞去他在巴黎综合工科学校的职务,1897年辞去在巴黎理学院的职务而退休.”

   hillside:我认为,上海财经大学浙江学院网页的消息与国外文献(http://www-gap.dcs.st-and.ac.uk/history/Biographies/Hermite.html,英国圣安德鲁大学数学与计算科学学院数学家历史传记库,http://turnbull.mcs.st-and.ac.uk/history/。这个库可能拥有一定的权威性)比较一致,比较可靠。

   据http://www.encyclopedia.com/topic/Charles_Hermite.aspx

In 1848 Hermite was appointed a répétiteur and admissions examiner at the école Polytechnique. The next ten years were his most active period. On 14 July 1856 he was elected a member of the Académie des Sciences, receiving forty out of forty-eight votes.

In 1862, through Pasteur’s influence, a position of maître de conférence was created for Hermite at the école Polytechnique; in 1863 he became an examinateur de sortie et de classement there. He occupied that position until 1869, when he took over J. M. C. Duhamel’s chair as professor of analysis at the école Polytechnique and at the Faculté des Sciences, first in algebra and later in analysis as well. His textbooks in analysis became classics, famous even outside France. He resigned his chair at the école Polytechnique in 1876 and at the Faculté in 1897. 埃尔米特1848年刚一毕业即被巴黎综合工科学校聘用。

   另据http://people.cs.kuleuven.be/~raf.vandebril/ade2008/talks/brezinski.pdf介绍,Hermite had no academic diploma. Hence, in 1847, he  obtained his baccalauréat and a licence in physics one year  later.  But he was already a renowned mathematician, and was  nominated as examinateur temporaire d’admission at école  Polytechnique on July 10, 1848.

   我所以认为“5次”之讹解疑出passed the examinations for the baccalauréat,是因为在法语中,baccalauréat似乎既指“高中”又指“大学”,“examinations”更使部分国人将之混同于国内的大学入学考试。然而,“he  obtained his baccalauréat and a licence”中的“licence”在此处主要指本科学位。

                     伽罗华没有通过的入学考试,埃尔米特通过了,只是成绩平平

http://www.mathematics-in-europe.eu/de/startseite/76-enjoy-maths/strick/981-charles-hermite-december-24-1822-january-14-1901

     Like GALOIS, he hoped to study at the école Polytechnique, but unlike GALOIS, he passed the entrance examination, though to be sure with a rather mediocre performance.


            埃尔米特与伽罗华类似,只是对高校应试科目缺乏兴趣、重视不够,而不是“不会考试”

                    http://apprendre-math.info/anglais/historyDetail.htm?id=Hermite


     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.

hillside:该网页此段英文不太地道,可能翻译自法语。


2.“数学课本就是一堆垃圾,数学考得好的,都是些二流头脑的人,只懂得搬运垃圾。”

   埃尔米特真的说过吗?按照埃尔米特的性格与日后的伯乐作为,他不会随意否定别人,他的两位高徒都是考试顶尖高手。网搜英文网页无法找到类似说法,我估计这是中文故事中的捏造。  

      据http://scienceworld.wolfram.com/biography/Hermite.html称: In 1869, he became a professor at école Normale, and in 1870 at Sorbonne. All during his career, was generous in his help of young mathematicians.

   不过,埃尔米特不喜欢几何与考试倒是真实的。几何教学的繁琐主义使埃尔米特感到厌烦。据http://people.cs.kuleuven.be/~raf.vandebril/ade2008/talks/brezinski.pdf介绍,Hermite hated elementary mathematics, descriptive  geometry, and exams.

   与传闻有悖、非常有趣的是,埃尔米特的两大高足手下名徒庞加莱、阿达玛都是当年的高考状元、考试奇才。1873年,庞加莱以第一名考入巴黎综合理工学院;1884年,阿达玛入学时也以第一名的成绩同时考取高等师范学校和综合工科学校(http://en.wikipedia.org/wiki/Jacques_Hadamard)。然而,据称,阿达玛也在考试场上也并非独孤求败。http://episte.math.ntu.edu.tw/people/p_hadamard/index.html介绍,“

Hadamard(1865~1963)除了數學以外,自小在各方面都有傑出的表現,他自言「一直到七年級,我的算術仍然是全班最後幾名」。但是在碰到一個好數學老師後,士別三日,表現令人刮目相看,在法國最菁英的兩所學校──高等師範學院與綜合工藝學院──的入學考試中,他都名列榜首,最後他選擇前者就讀”。另据中科院吴新谋研究员介绍,到20世纪50年代为止,历史上只有五位法国数学家同时以第一名的成绩考取高等师范学校和综合工科学校,阿达玛是其中之一.虽然他在综合工科学校考得了有史以来的最高分,他还是进了高等师范学校。阿达玛被誉为20世纪以来、庞加莱以后少有的数学多面手。    

  与名列榜首相比,埃尔米特作为尚未入学就已名动巴黎的青年数学家,在名校录取榜高考总排名第68确实不怎么威风(对于普通学子,进入名牌高校录取名单前100可能已是非常荣耀了),但远远谈不上“不会考试”!其实,一般而言,仍然不失为考试高手。

   庞加莱的巴黎综合理工学院高考第一名又是怎么得来的?据有关消息,“1873年,19岁的庞加莱参加了巴黎综合工科学校的入学考试,那是一所以刻板的考试而闻名世界的学校。这时的庞加莱的数学才能已崭露头角,考官们为了试探一下他的能力,有意把考试时间推延了45分钟,他们用这段时间专门为他精心设计了几道数学难题,这个貌不惊人的年轻人没有动笔,在脑袋里就轻松地完成了运算,当他报出答案时,时间之短暂,方法之巧妙,令主考老师们在瞠目结舌之余欣喜若狂。尽管庞加莱的体育成绩欠佳,绘画能力也很差,在几何作图题上得了零分(按录取规定,0分的学生应被淘汰),但惜才的主考官们经过激烈讨论,最终打破惯例,破格给出了第一名的成绩录取了他。”

   哈哈,庞加莱可谓深得乃师遗风,几何作图上继续依葫芦画瓢(鸭蛋的相似形?),不过考试的运气比埃尔米特好得多了。

3. 直到1869年,47岁的埃尔米特才找到一个合适的职位。巴黎高等师范学校聘请这位举世闻名的法兰西科学院院士为教授。不过第二年,他便到了巴黎大学担任教授。
    埃尔米特在这里整整工作了27年。他的数学课堂干脆取消了考试。“学问像大海,考试像鱼钩。老师怎么能把鱼挂在鱼钩上教它在大海中学会自由、平衡的游泳呢?”他解释说。

4.走出校门,埃尔米特不得不为生计发愁。没有地方愿意接受一个瘸子。26岁的年轻人受聘于法兰西学院做一名助教,任务是给学生批改作业。

   就求职而言,阻碍埃尔米特的主要是因为腿有残疾,而与考试无关。放之今日之中土,公务员招考等国字号机构亦不能免例。

   “埃尔米特似乎并未在这里整整工作了27年”也似乎有误。作为一名老师,他是如何取消他的数学考试的,用什么考核成绩?他真的说过“学问像大海,考试像鱼钩。老师怎么能把鱼挂在鱼钩上教它在大海中学会自由、平衡的游泳呢?”吗?

                      实际上是,母校巴黎综合工科学校对埃尔米特仍然关爱

  埃尔米特被强制离开学校是国家的规定、学校的无奈之举,不过学校并未歧视他,通过自学本科毕业后即受母校聘用,而不是所谓的法兰西学院,工作也不是所谓批改作业,而是特意意安排的招生工作。据

http://www.mathematics-in-europe.eu/en/home/76-enjoy-maths/strick/981-charles-hermite-december-24-1822-january-14-1901介绍,It must have been gratifying(关爱) to him indeed when he was appointed to the very commission that decided on which candidates would be admitted!(这是一份优待性的工作)。放之今日,高校招生依然是一个重要岗位。    

    据http://www-gap.dcs.st-and.ac.uk/history/Biographies/Hermite.html介绍,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. 1862年埃尔米特就正式获聘巴黎高等师范学校专门职位,1876年才辞去该校教职。

                                 埃尔米特是一位伟大的教师,“不考试”并不是他的特技 

                             http://www.thefamouspeople.com/profiles/charles-hermite-493.php  


 Apart from being such a great mathematician, Hermite was also known for his teaching skills. He is regarded as one of the most inspiring teachers of the nineteenth century. He kept his topics simple while teaching, which aroused interest in most of his students. Some of his famous students included Henri Poincare and L. Bourguet, to name a few. 

   庞加莱的深情回忆中,根本未谈到“不考试”!

4.别的科目成绩都好,就是数学不及格!

 hillside:埃尔米特真的是“别的科目成绩都好”?!

    据http://global.britannica.com/EBchecked/topic/263303/Charles-Hermite称:Although Hermite had proved himself a creative mathematician at the age of 20, his difficulty in passing his formal examinations forced him to devote five of his most productive years to preparing for his examination for the bachelor of science degree, which he obtained in 1848. 其他科目是否都好,似乎不得而知。

    对于数学的分支,不知道什么原因,埃尔米特对几何学缺乏好感。然而,他是一位伟大的教师,他最出名的学生庞加莱、阿达玛都是数学方面的全才。详细情况可见http://www-gap.dcs.st-and.ac.uk/history/Biographies/Hermite.html

        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.

5.埃尔米特的表现让父母忧心,为了让他把书念好,父亲把他送到巴黎的路易大帝中学

    让埃尔米特父母忧心的并不是他的表现与成绩,而是他那先天残疾的腿!

             http://www.thefamouspeople.com/profiles/charles-hermite-493.php

                                                     Childhood
Hermite was born on December 24th, 1822 at Dieuze, Moselle located in the North-Eastern part of France. He was the sixth son to Ferdinand Hermite and Madeleine Lallemand.  Hermite’s father was an engineer in a salt mine. By the time Charles Hermite turned seven, the family had to move to Nancy, another city in the North-East France, as their family business was moved to there.
Hermite had a defective right leg that crated a difficulty in walking. This caused his parents to worry too much as it was quite evident that this defect would pose a difficulty during the later stages of his life. In fact, they were right about it as it did pose a difficulty at one point of time in his life, when he set out to make his career. However, little Hermite accepted this defect with a broad smile on his face and had a very positive attitude towards life.


附1:http://news.sciencenet.cn/htmlnews/2010/7/234242.shtm

作者:王波 来源:中国青年报 发布时间:2010-7-7 17:34:00
选择字号:  


夏尔·埃尔米特:数学不及格的天才数学家

 
考试结果再次证明,夏尔·埃尔米特(Charles Hermite)是位数学天才,但不是个优秀的数学考生。他差点再次栽在巴黎综合工科学校的数学考试上。
 
这已经是埃米尔特第5次参加考试了。这个20岁的年轻人数学天分过人,在数学杂志上发表文章《对五次方程代数解的探讨》,震惊了数学界,也为他赢得了数学家的名声。
 
在课堂上,埃米尔特却不是好学生。他经常阅读高斯、欧拉和拉格朗日等人的数学著作,然后找老师辩论,还毫不掩饰自己对考试的痛恨。
 
“数学课本就是一堆垃圾,数学考得好的,都是些二流头脑的人,只懂得搬运垃圾。”这位中学生公开宣称。
 
但最终吃亏的仍是他。每次考不好,老师就用木条打他的脚。直到1840年,埃尔米特转学到路易大帝学院。
 
在那里,他遇上了数学老师里夏尔。里夏尔告诉老埃尔米特,他这个喜欢独立思考的儿子就是个“年轻的拉格朗日”。但这位数学老师也明白,在那个注重考试的年代,独创性有时就是一剂毒药。15年前,他那位颇具数学才华的学生伽罗瓦,就是因为太具独创性而一次次败给了考试。
 
里夏尔劝说埃米尔特,从创造性的研究转向为考试做准备,这样才能进入综合工科学校,避免重蹈伽罗瓦的悲剧。
 
埃米尔特接受了老师的劝告,但他确实不适合考试——“年轻的拉格朗日”先后经过了5次考试,才侥幸挤进了工科学校的大门。
 
然而,仅仅过了一年,他便不得不转系。教育当局突然下令,残障者不得在工科学系学习。由于天生右腿残疾,埃米尔特只好转入文学系。
 
但他对数学的兴趣依然未变,他把自己对阿贝尔函数的研究论文寄给了法国大数学家雅可比。对方不仅回信鼓励,还期待着将来有一天能向这个年轻人学习,因为他开辟了一个新领域。
 
已在数学界崭露头角的数学家埃尔米特,数学考试依旧不及格。这差点影响了他从大学里毕业。幸运的是,他最终勉强通过了考试。
 
走出校门,埃尔米特不得不为生计发愁。没有地方愿意接受一个瘸子。
 
埃尔米特想到了当数学老师,但他依然要先参加考试,才能获得任教的资质。好在两位主考的数学家知道埃米尔特是个数学好手,刻意网开一面。否则,埃米尔特也许根本就通不过这次考试。
 
26岁的年轻人受聘于法兰西学院做一名助教,任务是给学生批改作业。这一改,就是20多年。在这20多年里,他在函数论、高等代数、微分方程等方面陆续有重要发现,但是在学校里,这个不会考试也没法获得更高学位的人,只能继续批改作业。
 
直到1869年,47岁的埃尔米特才找到一个合适的职位。巴黎高等师范学校聘请这位举世闻名的法兰西科学院院士为教授。不过第二年,他便到了巴黎大学担任教授。
 
埃尔米特在这里整整工作了27年。他的数学课堂干脆取消了考试。“学问像大海,考试像鱼钩。老师怎么能把鱼挂在鱼钩上教它在大海中学会自由、平衡的游泳呢?”他解释说。
 
这位自称“对数学的开创性研究中毒很深,热爱得无法自拔”的残疾教授,最终赢得了人们的尊重。埃尔米特不仅证明了自然对数的底数e的超越性,还在现代数学各分支中留下好几个以他姓氏命名的概念。更重要的是,他在巴黎大学训练出了庞加莱等整整一代卓越的法国数学家,他的经典著作则在世界各地教育了他的同代人。
 
而这一切,都源于他对知识本身的尊重。1870年,普法战争爆发,获胜的普鲁士人侮辱了法国人。埃尔米特虽然饱含爱国热情,但仍然保持着冷静的头脑,对德意志数学家们取得的成就,给予了高度的肯定和赞赏。在他眼里,科学是超越国界的,对方的知识和智慧的价值,不因双方敌对而在另一方不复存在。
 
“敌人的数学也是数学。”爱国者埃尔米特这样认为。
2010-7-9 8:24:54 匿名
一点也不懂数学,你就不要写道听途说得来的数学和数学家的故事。对于其他学科来说也是这样。最低限度要传播正确的知识,而做到这一点应该不难吧-------花两分钟查查维基,那上面可是什么都有,而且大部分准确。
2010-7-9 8:11:02 匿名
“但最终吃亏的仍是他。每次考不好,老师就用木条打他的脚。直到1840年,埃尔米特转学到路易大帝学院。
”此学院非彼学院,路易大帝严格说应该叫做路易大帝预科,该预科学校现在仍是法国最好的预科学校之一。学生一般读二至三年预科,然后参加竞争异常激烈的工程师大学校入学考试,据说录取率不到1%. 在这样激烈的竞争下,我看一个人的偶尔落选没有什么不正常。还是那句话,是金子总会发光的。我国大数学家华罗庚的数学成绩世界公认,他又考上过什么学校?这篇文章逻辑混乱,所起的作用无非就是误导普通读者而已,害人呀!这种胡乱抄来的文章不写也罢,还发在中国青年报上误导国人。


附2:


附3:数学成绩不佳的数学大师_埃尔米特_陈九威.pdf(刊于《青苹果》,2007年11期  

                                                                         数学成绩不佳的数学大师

                                                                         作者:[陈九威 朱俊峰]  

   他,入学考试重考了五次,大学差点毕不了业,毕业后考不上任何研究所。
   也是他,提出了课本上的“共轭矩阵”,解出了人类一千多年来解不出的“五次方程式的通解”,证明出了自然对数的“超越数性质”。
   埃尔米特从小就是个“问题”学生,上课时老爱找老师辩论;他尤其痛恨数学考试。埃尔米特花许多时间去看牛顿、高斯等数学大师的原著,他认为在那里才能找到“数学的美”。
   埃尔米特的表现让父母忧心,为了让他把书念好,父亲把他送到巴黎的路易大帝中学。因为拥有超人的数学天分,他无法把自己塞入数学教育的牢笼,但是为了顺从父母的意愿,他又必须每天面对那些细微繁琐的计算,这让他痛苦不堪。数学是他一生的至爱,但是数学考试却是他一生的恶梦。这位孝顺的天才,似乎注定终生都要自我折磨。巴黎综合工科技术学院入学考试每年举行两次,他从18岁开始参加,考到第五次才得以勉强通过。其间,在几乎要放弃时,他遇到一位名叫理查的数学老师。理查对埃尔米特说:“我相信你是自拉格朗日以来的第二位数学天才(注:拉格朗日被称为数学界的“贝多芬”,他所作的求根近似解被誉为“数学之诗”),但是埃尔米特,光有天分不够,”理查老师说,“你需要坚持完成学业,才不会被你视为垃圾的传统教育牺牲掉。”因此,他一次又一次落榜,却坚持继续应试。
   埃尔米特进入技术学院读了一年以后,法国教育当局忽然下一道命令:肢障者不得进入工科学习。由于埃尔米特出生后右脚就残障,需拄拐杖行走,他只好转到文学系。文学系里的数学已经容易很多了,但是他的数学还是不及格。有趣的是,与此同时,他在法国的数学研究期刊上发表的《五次方方程式解的思索》引起了数学界的震惊。
   在人类历史上,3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,众多一流数学家埋首苦思四次方程以上到n次方程的解法,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。然而就是这样一个具有开创性的数学天才,直到24岁时,才以及格边缘的成绩从大学毕业。由于不会应付考试,埃尔米特无法继续升学,他只好找一所学校做个批改学生作业的助教。这份助教工作,他做了将近25年,就在这25年中,他发表了关于“代数连分数理论”、“函数论”、“方程论”等方面的论文,名满天下,数学水平远远超过当时所有大学的教授。

   埃尔米特不愤世嫉俗并能坦然前行的动力是什么呢?一是妻子的了解与同心。埃尔米特的妻子是他大学好友勃特伦的妹妹,她无怨无悔地跟随这个不会考试的天才丈夫,一年一年地走下去。二是有人真正地欣赏他,不因他外表的残疾与没有耀人的学位而轻视他。欣赏他的人后来也都在数学界享有盛名。而来自真正行家的惺惺相惜,比考试得高分的一点虚伪荣耀,更能支持一个“失败者”一路走下去。埃尔米特在49岁时,巴黎大学才请他去担任教授。此后的25年,几乎整个法国的大数学家都出自他的门下。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。
    美国加州理工学院数学系的教授贝尔在对历史上的数学伟人进行回顾时,这样描述他:“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,就是埃尔米特,他拥有真正完美的人格。”


附4:数学成绩不佳的数学大师_埃尔米特_卢瑞.pdf(刊于《数学爱好者》,2007·1)


附5:各路关于埃尔米特数学考试的传闻, 有一篇竟冠以"考试白痴"

    [1] 甘志国.  数学是他一生的至爱,但数学考试是他一生的恶梦——不擅长数学考试的数学大师埃尔米特[J]. 中学数学杂志. 2010(05)

    [2] 林革.  痛恨考试的数学天才[J]. 中小学数学(高中版). 2010(09)

    [4] 陈九威,朱俊峰.  数学成绩不佳的数学大师[J]. 教师博览. 2009(07)

    [5] 佚名.  埃尔米特 屡考屡败的数学大师[J]. 师道. 2004(08)

    [6] 毛岁.  数学大师埃尔米特——"考试白痴"也有春天[J]. 中学生百科. 2005(01)  

    [7] 鲁先圣.  不会考试的数学大师[J]. 数学教学通讯. 2011(02)


附5:http://www.ee.cityu.edu.hk/~gchen/pdf/Hermite_GB.pdf

(香港城市大学内部刊物《敬乐》,2005年)

http://www.ee.cityu.edu.hk/~gchen/Anecdotes.htm

名人轶事

大凡名人轶事,故事而已,版本各有不同,不可完全当真。 

Norbert Wiener 维纳  (1894-1964)  [简体] [繁体]

Charles Hermite  厄米特  (1822-1901)  [简体] [繁体]

原文摘录:不过大学未必知道,这个厄尔米特当年参加高考时,考了5次都没考上:别的科目成绩都好,就是数学不及格!

   hillside:以上网页的主人、香港城市大学特意提醒:“大凡名人轶事,故事而已,版本各有不同,不可完全当真。”


附6:上海大学数学系编写的《高等代数中的数学家》

http://math.shu.edu.cn/jpkc/ha/download/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0%E4%B8%AD%E7%9A%84%E6%95%B0%E5%AD%A6%E5%AE%B6/%E9%AB%98%E7%AD%89%E4%BB%A3%E6%95%B0%E4%B8%AD%E7%9A%84%E6%95%B0%E5%AD%A6%E5%AE%B6.pdf

(一) 学习成绩不佳的数学大师─埃尔米特

   埃尔米特是十九世纪最伟大的代数几何学家,但是他大学入学考试重考了五次,每次失败的原因都是数学考不好。他的大学读到几乎毕不了业,每次考不好都是为了数学那一科。他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。

 

附7:科学松鼠会网友的质疑

http://songshuhui.net/archives/64610

novacat220 说道:

英语水平有限,不保证没错,跳着翻译了,谁有兴趣,搞一个准确的完整的版本吧。

从英文版维基百科看到的版本:

Charles Hermite 于 1822年12月24日出生。

Charles Hermite 从小就右脚残疾。

没提到 Charles Hermite 考了五次,才考入他想进入的大学。而是说,为了考入他心仪的 école Polytechnique ,Charles Hermite 请了 Eugène Charles(不是什么 理查德) Catalan 作为自己的辅导老师,在1841年到1842年间,用一年时间精心准备,于1842年考入 école Polytechnique。并且在一年(1843)后,因为残疾而被退学。他为此进行了抗争,但没能成功地保住自己留在école Polytechnique 继续学习的权力,只好在未拿到毕业证的情况下离开了 école Polytechnique 。

也就是在 1842 年,他做出了他在数学上的第一个贡献 :gave a simple proof of the proposition of Niels Abel concerning the impossibility of obtaining an algebraic solution for the equation of the fifth degree。

在1843年至1844年间,通过与 Carl Jacobi 的通讯联系,该数学家完成了另一个数学上的成果。(懒得再 copy 了,我也不懂怎么翻译)

同时,Charles Hermite 在他的一些著名数学家朋友的帮助下,用了五年时间(1843-1847)【PS,这是该人物词条,出现的唯一的一个“five “,或许这就是所谓的“他大学入学考试考了整整五次”的来源 】,通过私底下的学习,在1847年参加并通过了 baccalauréat 学校的考试,取得了学位。然后在1848年,与他一个数学家朋友的姐妹结婚。(After spending five years working privately towards his degree, in which he befriended eminent mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, he took and passed the examinations for the baccalauréat, which he was awarded in 1847. He married Joseph Bertrand's sister, Louise Bertrand in 1848.)

在1848年,Charles Hermite 以 répétiteur and examinateur d'admission(懒得查字典了) 的身份,重返将他退学的 école Polytechnique 。

1856年,In 1856 he contracted smallpox (得了天花?)

1869年,获得 数学教授 职称 (In 1869, he succeeded Jean-Marie Duhamel as professor of mathematics)(此时他 47 岁,没到 49 岁),而他在 école Polytechnique 一直待到 1876年(此时他已经54岁)。

从1876年到他逝世,Charles Hermite 一直待在巴黎(?大学?)(and in the Faculty of Sciences of Paris, which was a post he occupied until his death)

从1862年到1973年,Charles Hermite 在 巴黎高等师范学院( école Normale Supérieure)担任 讲师( lecturer )一职。

维基百科页目:http://en.wikipedia.org/wiki/Charles_Hermite


附8:http://yw.zxxk.com/a32387.html(语文学科网)

    http://sx.zxxk.com/a32387.html(数学学科网)

                         埃尔米特                                录入时间:2008/1/15 16:07:00  

 

       他是十九世纪最伟大的代数几何学家,但是他大学入学考试重考了五次,每次失败的原因都是数学考不好。他的大学读到几乎毕不了业,每次考不好都是为了数学那一科。他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。


附9:百度百科(与其他中文网页类似,充满不实言词)

http://baike.baidu.com/link?url=kVhDsX7YZC_BviTQ8STN1nA1uzC_7hQ7_hXHjBIGhivFLloOOzmgmIAEifVGSM7v


附10:凤凰网及其他各路网页的原始出处基本都出自《中国青年报》。

http://news.ifeng.com/society/2/detail_2010_07/07/1731800_0.shtml

数学家数学考试多次不及格 任教授后取消考试

2010年07月07日 10:31中国青年报本报记者 王波

附11:昔日的巴黎著名两校如何考试(分形几何创始人芒德勃罗的故事,芒德勃罗与埃尔米特与庞加莱不同,他是几何的忠实信徒。)


附12:[中国大百科全书(数学卷)].中国大百科全书出版社编辑部.扫描版



附13:http://global.britannica.com/EBchecked/topic/263303/Charles-Hermite

Charles Hermite,  (born Dec. 24, 1822, Dieuze, Fr.—died Jan. 14, 1901, Paris), French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the generalequation of the fifth degree, the quintic equation.

Although Hermite had proved himself a creative mathematician at the age of 20, his difficulty in passing his formal examinations forced him to devote five of his most productive years to preparing for his examination for the bachelor of science degree, which he obtained in 1848. He was given a minor teaching position at the école ... (100 of 285 words)

hillside:这一篇英文文献值得注意,它提到了埃尔米特在正式考试中存在困难,花了5年时间准备本科结业考试。根据现有材料,我们不能排除埃尔米特每年都参加本科结业考试并屡屡告败,这可能是传言5次高考失败的一条线索。其实,作为一名普遍法国本科生,5年毕业并不说明在考试上存在明显缺陷(hillside:因为埃尔米特已退学,主要是通过自学)。目前,我们也不知道,法国彼时的本科结业考试需要考哪些科目。因此,本文的一个延伸问题是:埃尔米特参加了几次本科结业考试?


附14:因残疾被学校开除使埃尔米特对学校教育感到义愤与失望,客观上影响了结业科目的自学效果与考试成绩

http://www.thefamouspeople.com/profiles/charles-hermite-493.php

                                                    Career
Initially Hermite studied at College de Nancy and later, went on to study in College Henry IV and Lycee Louis-le-Grand in Paris. Hermite’s dream was to study at Ecole Polytechnique for which he prepared all year long. He was trained by Catalan for his exams with Ecole Polytechnique. After a yearlong hard work, Hermite gained entry to Ecole Polytechnique where he was a student for a very short period of time. He was forced to leave the college because of his disability. However, he fought back and won his place at Ecole Polytechnique but with rigid conditions. Such strict conditions angered Hermite and he left the college even without graduating.

Although Hermite lost interest in studies, he never forgot to pay attention to the research work of Lagrange and Gauss, which helped him publish his two papers while at Louis le Grand. In fact, he described in one of the papers that the quintic theory cannot be solved by radicals. He did his graduation privately in a span of five years during which he befriended famous mathematicians like Joseph Bertrand and Carl Jacobi. He had come up with general solutions to the differential equations in terms of theta function. In 1847, he was awarded the certificate after having cleared baccalaureat examination, which most French students take up immediately after secondary education. He was also appointed by Ecole Polytechnique, the same institute that banned him from continuing education, as an admissions examiner and repetiteur.

hillside:上条消息中也提到,大多数法国学生能够顺利通过此项考试(which most French students take up immediately after secondary education. )到底是哪些科目影响了埃尔米特的结业考试?


附15:以下3段出自中文网站、与传言一脉相承的一段疙瘩英文(里面有所谓埃尔米特抨击教科书与考试的原话、以及被老师用木脚踢的描述,但英语既不通顺、语法又很生硬,机器翻译自某段法文?我的联通宽带连GOOGLE都常常登录不了,一时难以追究)。从破案角度,这是一个非常重要的源头性线索。欢迎有兴趣的朋友沿着这几篇拙劣英文进行后续搜索,出处在哪里?是根据传闻的中文进行的英文翻译还是另有外文源头? 我大体判断是根据中文文章进行的洋泾滨翻译。

http://www.sxhxmkl.com/bbs/boke.asp?ba32937n.showtopic.51781.html

http://blog.1688.com/article/i17315775.htm

http://blog.1688.com/article/i17272709.htm

out of school, Hermite had to worry for their livelihood. There is no place willing to accept a cripple.

Alain Richard to persuade Amy Stewart,supra, from the creative turn to prepare for the exam, so as to enter the integrated engineering school, to avoid repeating the tragedy of Galois.

exam results once again proved that Charles Hermite (Charles the Hermite) is a mathematical genius, but not mathematics candidates. He almost planted in the engineering school in Paris on the math test again.

the disability Professor of the self-proclaimed Hermite not only proved the transcendence of the natural logarithm base e, also modern mathematics branch, leaving several concepts named to his last name. More importantly,louboutin pas cher, he trained at the University of Paris, Poincaré, etc. a whole generation of excellent French mathematician, his classic education of his contemporaries around the world.

math textbook is a bunch of garbage, mathematics, and are second-rate minds of the people only know how to garbage removal. Publicly declared that

Hermite in full for 27 years. The mathematics classroom simply cancel the exam.

do well    Mathematics is also a mathematical

Amy Stewart 5th to take the exam. The 20-year-old young mathematical talent extraordinary in mathematics magazine published an article

Hermite thought When the math teacher, but he still must first take the exam in order to obtain the qualification to teach. Fortunately,polo ralph lauren pas cher, the mathematicians of the two examiners know Amy Stewart is a mathematical players deliberately spared. Otherwise, Amy Stewart may simply pass the exam.

until 1869, Hermite, 47-year-old to find a suitable job. Ecole Normale employ the world-famous French Academy of Sciences as a professor. However,franklin marshall, the second year, he went to the University of Paris as a professor.

but his interest in mathematics remained unchanged, his research paper on Abelian functions sent to the French mathematician Ya comparable. The other letter not only to encourage, also look forward to the future one day to the young man to learn, because he opened up a new field.

all of this,burberry pas cher, are derived from his respect for knowledge itself. In 1870, the outbreak of the Franco-Prussian War, Prussian winning an insult to the Frenchman. The Hermite full of patriotic enthusiasm, but still maintained a cool head, a high degree of recognition and appreciation of the achievements of the mathematicians of Germany, to give. In his eyes, science transcends national boundaries, the value of each other's knowledge and wisdom,air jordan femme, not because of hostility in the other no longer exists.

in the classroom,supra chaussures, Amy Stewart is not a good student. He often read the mathematical works of Gauss,franklin marshall pas cher, Euler,air jordan femme British couple houses were 500 bird surrounded by ( ), and Lagrange, and then find a teacher debate, but also no secret of their hatred on the exam.

in the mathematical community-and-coming mathematician Hermite, math test is still failing. This nearly affected his graduation from the university. Fortunately,jordan Rebellious teenage keen surfing conquered the four-storey waves (Photos), he eventually reluctantly passed the exam.

 the  

However,louboutin The hotel day and night play pornographic films , was closed down thre, just over a year, he will have to transfer into a department. Education authorities suddenly ordered with disabilities are not allowed to learn in the Engineering Science Department. Born right leg disability, Amy Stewart had transferred to the Department of Literature.

There, he met a math teacher Alain Richard. Alain Richard told the old Hermite, his favorite son of independent thinking is a young Lagrange. The math teacher but also understand that the exam's focus on that, originality is a poison sometimes. 15 years ago,burberry, he who quite mathematical talented students Galois, too with originality and time lost to the exam.

 

but in the end still lose him. Each well on the exam, the teacher hit him on the foot strips of wood. Until 1840, the Hermite transferred to the College of Louis the Great.

   

Amy Stewart accepted the advice of the teacher,ralph lauren, but he really is not suitable for examination -

 

26-year-old young man employed at the College de France to do a teaching assistant,jordan, the task is to give students correcting homework. This change is more than 20 years. In these 20 years, he successively in terms of function theory,air jordan, advanced algebra, differential equations have an important discovery, but in school, this is not the examination we are unable to get a higher degree, only to continue correcting homework.


附16:为什么埃尔米特数学考试总不及格,依然能成为著名数学家?

http://www.zhihu.com/question/20273552/answer/14655980

http://site.douban.com/120771/widget/notes/3742952/note/221001513/

陳浩 (本科毕业于上海交大物理系,后在巴黎综合理工深造,转修数学,现在柏林自由大学研究离散几何学。)回答:
受邀,怒答。貌似科学松鼠会也在传这事 songshuhui.net/archives
Hermite 是我 Ecole Polytechique(巴黎综合理工,简称 X)的校友。
我知该校在中国鲜为人知,先奉上中英维基页面 [1,2]:

首先对 Hermite 的数学成绩,我提出来源请求。从题目提供的维基页面看,他就读的高中是法国的顶尖高中 [3],基本是 X 的预科班,数学教学应该非常超前。他只花了一年时间准备 X 的竞考并成功(1842年),说明他数学非常了得,因为 X 在法国的竞考以难出名,万里挑一。他在准备过程中如果挂过几次模拟考,那倒正是 X 的风格。Hermite 竞考的名次不出众(68名),但是被录取已经非常厉害了。

注意,传说当年 X 是不能重考的(待验证),至少目前是年龄限制加次数限制 [4],重考五次是万万不可能的。
只有少数特例,比如有人提到的 Galois(和 Hermite 一个高中老师教的)[5]
Galois(伽罗瓦)一共参加了2次Ecole Polytechnique(巴黎理工大学)的考试,第一次,由于口试的时候不愿意做解释,并且显得无理,结果被据了。他当时大概十七八岁,年轻气盛,大部分东西的论证都是马马虎虎,一般懒的写清楚,并且拒绝采取考官给的建议。第二次参加Polytechnique(理工大学)的考试,他口试的时候,逻辑上的跳跃使考官Dinet感到困惑,后来Galois感觉很不好,一怒之下,把黑板擦掷向Dinet,并且直接命中。Galois的天才是不可否认的,不过personality是少一点了,后者在Polytechnique考试中很重要。
X 在科学方面有众多杰出校友 [6,7] ,是当时法国数学最好的学校,所以 Hermite, Galois 等都拼了命考。
其次,就算他在 X 挂过数学课,那也太正常不过了。X 的数学课是世界上最艰深的之一(或者不用加之一)。我的第一堂代数课上的是 P 进数。考试经常一题都写不出,写出半题就是 A 了。挂掉2/3考生是常有的事。X 学生的数学能力在西方是有名的,都是一路打击过来的。我本人也是在 X 挂了数学考试,一气之下转了数学的。

最后,他的确被 X 退过学,原因不是成绩,而是他的残疾。X 是有军校性质的理工学校(拿破仑1805年的命令),所有学生都要参加大量体育运动,我当年参加的是定向越野。法国学生获得军籍,学校日常管理按军队标准,因此残疾学生会有困难。根据维基的资料,Hermite 在这种情况下仍然争取让学校最后网开一面,说明他的能力非同寻常。最后是他认为学校开出的条件过于苛刻,觉得不爽自己退出学校的。他在 X 只呆了一年。

退学前后,他开始了独立的学习和研究,第一篇文章发表于 1842 年。他的研究得到 Jacobi, Liouville, Bertrand 等大神的青睐和帮助,拿了学位。1848年,退学五年后,他重回曾经拒绝他的 X,但是这时是作为助教和录取评审(répétiteur and examinateur d'admission)。再过八年,他获得法兰西科学院院士头衔。传言把他的生平前后顺序完全打乱了。

以上未标注信息全部来自 [8,9,10] 和个人经历,我看到 Hermite 的深造是一条无比豪华的高端路线,拜托不要把他所经历的和一般考试升学相提并论。

[1] en.wikipedia.org/wiki/%
[2] zh.wikipedia.org/wiki/% 
[3] zh.wikipedia.org/wiki/%
[4] admission.polytechnique.edu 谢谢 @维慕 指出
[5] 非正史《Heroes in my heart》newsmth.net/nForum/#
[6] en.wikipedia.org/wiki/L
[7] en.wikipedia.org/wiki/L
[8] en.wikipedia.org/wiki/C
[9] www-history.mcs.st-andrews.ac.uk
[10] encyclopedia.com/topic/


附17:传闻溯源(hillside:就我目前搜索所及,这是传闻、很可能是谎言的最早源头。)

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

发信人: 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。



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