数学家欧拉生平及贡献简介（中英文对照版）

当我年少轻狂时，

我曾拥有自由，但我没有看见它。

我曾拥有时间，但我没有知晓它。

我曾拥有爱情，但我没有感受它。

数十年的时间考验后，我终于理解了三者的真谛。

我已风烛残年，这种理解已经逐渐变成一种满足。

爱，自由和时间，曾一度被我挥霍，而今成为了我前进的动力。

而我将最特别的爱，献给最亲爱的你和我们的孩子们，以及刺客联盟的兄弟姐妹们，

并献给赋予我们生命的那壮美奇妙，让人产生无限遐想的世界。

此爱永恒，Mia Sofia（意大利语：我亲爱的索菲亚） 。

艾吉奥·奥迪托雷。 When I was a young man,

I had liberty, but I did not see it

I had time, but I did not know it

And I had love, but I did not feel it

Many decades would pass before I understood the meaning of all three

And now, the twilight of my life,

this understandinghas passed into contentment

Love, liberty and time, once so disposable,

are the fuels that drive me forward

And love, most especially

For you, our children, our brothers and sisters,

and for the vast and wonderful world that give us life

Endless affections, Mia Sofia

Ezio Auditore Quando ero giovane,

Avevo libertà, ma non me ne ero accorto

Avevo tempo, ma non lo sapevo

Avevo amore, ma non lo sentivo

Sarebbero trascorsi trenta lungi anni prima che riuscissi a comprendere il loro significato

E ora, al crepuscolo della mia vita,

questa comprensione si è trasformata in appagamento

Amore, libertà e tempo, una volta a mia totale disposizione,

sono ora il combustibili che mi spinge avanti

L'amore, soprattutto, mia cara

per te, per i nostri figli, per i nostri fratelli e sorelle

e per il vasto e splendido mondo che ci ha dato la vita e ci tiene sempre sulla corda

Con infinito affetto, Mia Sofia, sono tuo per sempre

Ezio Auditore

您好：不清楚，但是好听的英文歌好多呢~~~本人学英语的推荐这些吧希望你能喜欢。

1、Bubbly--Colbie Caillat（你听过一遍就会非常喜欢的歌）；

2、Burning--Maria Arredondo；

3、Happy--丽安娜 刘易斯；

4、Cry On My Shoulder--出自德国选秀节目（很早的一首，非常好听）；

5、Apologize--Timbaland；

6、The Climb--Miley Cyrus（个人最喜欢的歌手之一）；

7、You Belong With Me--泰勒斯威夫特（绝棒的）；

8、I Stay In Love--玛利亚凯莉；

9、I Didn't Know My Own Strength--Whitney Houston（是非常棒的一首慢歌，也是我非常喜欢的黑人歌手之一。）；

10、A Little Bit Longer--Jonas Brothers（嗓音非常棒的组合，几乎每首都很好听，尤其是这首！强力推荐）；

11、The Little Things--Colbie Caillat；

12、Mad--尼欧；

13、My All--玛丽亚凯莉（据说非常适合作手机铃声的歌）；

14、My Love--WestLife（西域成名金曲，经典老歌，诠释了所有经典的定义。）；

15、Need You Now--Lady Antebellum（时下排行榜热门歌曲）；

16、The Saltwater Room--Owl City（最爱的歌手之一，曲风相当特别）；

17、Take A Bow--Rihanna（听2秒就会爱上的歌手和歌~）；

18、The Technicolor Phase--Owl City（《爱丽丝梦游仙境》的主题曲之一）；

19、This Is It--迈克尔杰克逊（不知到底是翻唱还是遗作，都能再现天王的独特魅力

20、Who Says--John Mayer（类似乡村风以吉他为伴奏，这首非常棒！）；

望采纳~~祝好~~~~

欧拉1707年出生在瑞士的巴塞尔(Basel)城，13岁就进巴塞尔大学读书，得到当时最有名的数学家约翰·伯努利(Johann Bernoulli，1667-1748年)的精心指导

欧拉渊博的知识，无穷无尽的创作精力和空前丰富的著作，都是令人惊叹不已的!他从19岁开始发表论文，直到76岁，半个多世纪写下了浩如烟海的书籍和论文到今几乎每一个数学领域都可以看到欧拉的名字，从初等几何的欧拉线，多面体的欧拉定理，立体解析几何的欧拉变换公式，四次方程的欧拉解法到数论中的欧拉函数，微分方程的欧拉方程，级数论的欧拉常数，变分学的欧拉方程，复变函数的欧拉公式等等，数也数不清他对数学分析的贡献更独具匠心，《无穷小分析引论》一书便是他划时代的代表作，当时数学家们称他为"分析学的化身"

欧拉是科学史上最多产的一位杰出的数学家，据统计他那不倦的一生，共写下了886本书籍和论文，其中分析、代数、数论占40%，几何占18%，物理和力学占28%，天文学占11%，d道学、航海学、建筑学等占3%，彼得堡科学院为了整理他的著作，足足忙碌了四十七年

欧拉著作的惊人多产并不是偶然的，他可以在任何不良的环境中工作，他常常抱着孩子在膝上完成论文，也不顾孩子在旁边喧哗他那顽强的毅力和孜孜不倦的治学精神，使他在双目失明以后，也没有停止对数学的研究，在失明后的17年间，他还口述了几本书和400篇左右的论文19世纪伟大数学家高斯(Gauss，1777-1855年)曾说:"研究欧拉的著作永远是了解数学的最好方法"

欧拉的父亲保罗·欧拉(Paul Euler)也是一个数学家，原希望小欧拉学神学，同时教他一点教学由于小欧拉的才人和异常勤奋的精神，又受到约翰·伯努利的赏识和特殊指导，当他在19岁时写了一篇关于船桅的论文，获得巴黎科学院的奖的奖金后，他的父亲就不再反对他攻读数学了

1725年约翰·伯努利的儿子丹尼尔·伯努利赴俄国，并向沙皇喀德林一世推荐了欧拉，这样，在1727年5月17日欧拉来到了彼得堡1733年，年仅26岁的欧拉担任了彼得堡科学院数学教授1735年，欧拉解决了一个天文学的难题(计算慧星轨道)，这个问题经几个著名数学家几个月的努力才得到解决，而欧拉却用自己发明的方法，三天便完成了然而过度的工作使他得了眼病，并且不幸右眼失明了，这时他才28岁1741年欧拉应普鲁士彼德烈大帝的邀请，到柏林担任科学院物理数学所所长，直到1766年，后来在沙皇喀德林二世的诚恳敦聘下重回彼得堡，不料没有多久，左眼视力衰退，最后完全失明不幸的事情接踵而来，1771年彼得堡的大火灾殃及欧拉住宅，带病而失明的64岁的欧拉被围困在大火中，虽然他被别人从火海中救了出来，但他的书房和大量研究成果全部化为灰烬了

沉重的打击，仍然没有使欧拉倒下，他发誓要把损失夺回来在他完全失明之前，还能朦胧地看见东西，他抓紧这最后的时刻，在一块大黑板上疾书他发现的公式，然后口述其内容，由他的学生特别是大儿子A·欧拉(数学家和物理学家)笔录欧拉完全失明以后，仍然以惊人的毅力与黑暗搏斗，凭着记忆和心算进行研究，直到逝世，竟达17年之久

欧拉的记忆力和心算能力是罕见的，他能够复述年青时代笔记的内容，心算并不限于简单的运算，高等数学一样可以用心算去完成有一个例子足以说明他的本领，欧拉的两个学生把一个复杂的收敛级数的17项加起来，算到第50位数字，两人相差一个单位，欧拉为了确定究竟谁对，用心算进行全部运算，最后把错误找了出来欧拉在失明的17年中;还解决了使牛顿头痛的月离问题和很多复杂的分析问题

欧拉的风格是很高的，拉格朗日是稍后于欧拉的大数学家，从19岁起和欧拉通信，讨论等周问题的一般解法，这引起变分法的诞生等周问题是欧拉多年来苦心考虑的问题，拉格朗日的解法，博得欧拉的热烈赞扬，1759年10月2日欧拉在回信中盛称拉格朗日的成就，并谦虚地压下自己在这方面较不成熟的作品暂不发表，使年青的拉格朗日的工作得以发表和流传，并赢得巨大的声誉他晚年的时候，欧洲所有的数学家都把他当作老师，著名数学家拉普拉斯(Laplace)曾说过:"欧拉是我们的导师" 欧拉充沛的精力保持到最后一刻，1783年9月18日下午，欧拉为了庆祝他计算气球上升定律的成功，请朋友们吃饭，那时天王星刚发现不久，欧拉写出了计算天王星轨道的要领，还和他的孙子逗笑，喝完茶后，突然疾病发作，烟斗从手中落下，口里喃喃地说:"我死了"，欧拉终于"停止了生命和计算"

欧拉的一生，是为数学发展而奋斗的一生，他那杰出的智慧，顽强的毅力，孜孜不倦的奋斗精神和高尚的科学道德，永远是值得我们学习的欧拉在数学上的建树很多，对著名的哥尼斯堡七桥问题的解答开创了图论的研究。欧拉还发现 ，不论什么形状的凸多面体，其顶点数v、棱数e、面数f之间总有v-e+f=2这个关系。v-e+f被称为欧拉示性数，成为拓扑学的基础概念。在数论中，欧拉首先引进了重要的欧拉函数φ(n)，用多种方法证明了费马小定理。以欧拉的名字命名的数学公式、定理等在数学书籍中随处可见, 与此同时，他还在物理、天文、建筑以至音乐、哲学方面取得了辉煌的成就。〔欧拉还创设了许多数学符号，例如π(1736年)，i(1777年)，e(1748年)，sin和cos(1748年)，tg(1753年)，△x(1755年)，∑(1755年)，f(x)(1734年)等

Leonhard Euler (pronounced Oiler; IPA [ˈɔʏlɐ]) (April 15, 1707 – September 18 [OS September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany He published more papers than any other mathematician in history[1]

Euler made important discoveries in fields as diverse as calculus and topology He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function[2] He is also renowned for his work in mechanics, optics, and astronomy

Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time He is also one of the most prolific; his collected works fill 60–80 quarto volumes[3] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is a master for us all"[4]

Euler was featured on the sixth series of the Swiss 10-franc banknote[5] and on numerous Swiss, German, and Russian postage stamps The asteroid 2002 Euler was named in his honor He is also commemorated by the Lutheran Church on their Calendar of Saints on May 24

Contents [hide]

1 Biography

11 Childhood

12 St Petersburg

13 Berlin

14 Eyesight deterioration

15 Last stage of life

2 Contributions to mathematics

21 Mathematical notation

22 Analysis

23 Number theory

24 Graph theory

25 Applied mathematics

26 Physics and astronomy

27 Logic

3 Philosophy and religious beliefs

4 Selected bibliography

5 See also

6 Notes

7 Further reading

8 External links

[edit] Biography

[edit] Childhood

Swiss 10 Franc banknote honoring Euler, the most successful Swiss mathematician in historyEuler was born in Basel to Paul Euler, a pastor of the Reformed Church, and Marguerite Brucker, a pastor's daughter He had two younger sisters named Anna Maria and Maria Magdalena Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, where Euler spent most of his childhood Paul Euler was a family friend of the Bernoullis, and Johann Bernoulli, who was then regarded as Europe's foremost mathematician, would eventually be an important influence on the young Leonhard His early formal education started in Basel, where he was sent to live with his maternal grandmother At the age of thirteen he matriculated at the University of Basel, and in 1723, received a masters of philosophy degree with a dissertation that compared the philosophies of Descartes and Newton At this time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics[6]

Euler was at this point studying theology, Greek, and Hebrew at his father's urging, in order to become a pastor Johann Bernoulli intervened, and convinced Paul Euler that Leonhard was destined to become a great mathematician In 1726, Euler completed his PhD dissertation on the propagation of sound with the title De Sono[7] and in 1727, he entered the Paris Academy Prize Problem competition, where the problem that year was to find the best way to place the masts on a ship He won second place, losing only to Pierre Bouguer—a man now known as "the father of naval architecture" Euler, however, would eventually win the coveted annual prize twelve times in his career[8]

[edit] St Petersburg

Around this time Johann Bernoulli's two sons, Daniel and Nicolas, were working at the Imperial Russian Academy of Sciences in St Petersburg In July 1726, Nicolas died of appendicitis after spending a year in Russia, and when Daniel assumed his brother's position in the mathematics/physics division, he recommended that the post in physiology that he had vacated be filled by his friend Euler In November 1726 Euler eagerly accepted the offer, but delayed making the trip to St Petersburg In the interim he unsuccessfully applied for a physics professorship at the University of Basel[9]

1957 stamp of the former Soviet Union commemorating the 250th birthday of Euler The text says: 250 years from the birth of the great mathematician and academician, Leonhard EulerEuler arrived in the Russian capital on May 17, 1727 He was promoted from his junior post in the medical department of the academy to a position in the mathematics department He lodged with Daniel Bernoulli with whom he often worked in close collaboration Euler mastered Russian and settled into life in St Petersburg He also took on an additional job as a medic in the Russian Navy[10]

The Academy at St Petersburg, established by Peter the Great, was intended to improve education in Russia and to close the scientific gap with Western Europe As a result, it was made especially attractive to foreign scholars like Euler: the academy possessed ample financial resources and a comprehensive library drawn from the private libraries of Peter himself and of the nobility Very few students were enrolled in the academy so as to lessen the faculty's teaching burden, and the academy emphasized research and offered to its faculty both the time and the freedom to pursue scientific questions[8]

However, the Academy's benefactress, Catherine I, who had attempted to continue the progressive policies of her late husband, died the day of Euler's arrival The Russian nobility then gained power upon the ascension of the twelve-year-old Peter II The nobility were suspicious of the academy's foreign scientists, and thus cut funding and caused numerous other difficulties for Euler and his colleagues

Conditions improved slightly upon the death of Peter II, and Euler swiftly rose through the ranks in the academy and was made professor of physics in 1731 Two years later, Daniel Bernoulli, who was fed up with the censorship and hostility he faced at St Petersburg, left for Basel Euler succeeded him as the head of the mathematics department[11]

On January 7, 1734, he married Katharina Gsell, daughter of a painter from the Academy Gymnasium The young couple bought a house by the Neva River, and had thirteen children, of whom only five survived childhood[12]

[edit] Berlin

Stamp of the former German Democratic Republic honoring Euler on the 200th anniversary of his death In the middle, it is showing his polyhedral formulaConcerned about continuing turmoil in Russia, Euler debated whether to stay in St Petersburg or not Frederick the Great of Prussia offered him a post at the Berlin Academy, which he accepted He left St

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