埃尔米特先后在南锡皇家中学(collège royal de Nancy)、巴黎亨利四世中学以及索邦路易大帝中学学习。[3][4]在他还小的时候,他就已经读过一些数学大师所写过的作品,如拉格朗日有关数值方程求解的作品和高斯的数论作品。[1]此外他还涉猎过欧拉的作品。[3]他并不重视自己所在年龄段应该学好的知识,相反地,他与同样毕业于路易大帝中学的伽罗瓦一样,早已把注意力放到了5次方程的可解性问题上。[3]中学就读期间,他曾尝试写过论证5次方程不可能存在根式解的文章。[3]
1842年,他在《新数学年刊》(Nouvelles Annales de Mathématiques)上发表了自己的第1篇原创论文,讨论了阿贝尔关于5次方程代数不可解性的一个引理的简化证明。[1]1843年至1844年,埃尔米特曾与当时正在研究椭圆函数的卡尔·雅可比多次通信。在雅可比最后的成品中,收录了2篇埃尔米特写的文章。其中一篇的内容是如何对阿贝尔曾给出的有关阿贝尔函数的一个定理加以推广,另一篇的内容则涉及椭圆函数的函数变换。[1]埃尔米特曾独立发现一些特殊微分方程的通解可用Θ函数表示,并利用傅里叶级数研究它们的性质。[3]埃尔米特在1843年左右的一些想法还可能直接启发刘维尔在1年后发现了1个刘维尔定理。[3]
执教与后期
1847年,他参加并通过了高中毕业生考试(examinations for the baccalauréat)。[3]1848年,埃尔米特被曾经将他劝退的巴黎综合理工学院聘用,担任教授和入学考试考官。[1]这次他不再是以学生的身份回来,而是摇身一变,直接成为了学校教职员工。1856年,他不幸得了天花,虔诚信教的前辈柯西给了他很大的鼓励以熬过病痛的折磨。[3]1856年,受一位曾照顾他生活的修女和柯西的共同影响,病愈后的埃尔米特决定重拾宗教礼节(practice of his religion)。[1]7月14日,法国科学院因雅可·比内(英语:Jacques Philippe Marie Binet)去世而多出了一个空缺,埃尔米特被选上从而补上了空缺。[1]1869年[1],他继耶安-玛希·杜阿莫(法语:Jean-Marie Duhamel)后也成为巴黎综合理工的数学教授。埃尔米特在岗位上一直干到了1876年[1],而巴黎科学院的职务则伴随了他一生。1862年至1873年间,他常会以演讲者(lecturer,此处应该不是指职称名称)身份在高等师范学校办讲座。[1]70岁生日时,一家国际数学协会为其主办了一场大型的庆祝活动。埃尔米特在活动中被人们选为法国荣誉军团勋章之“大军官勋位”。[1]他的才华受到广泛认可,收获了来自他人的众多赞誉,而这并非是每个科研工作者在有生之年都能享受到的福气。[5]
坊间关于埃尔米特生平经历的文章,认为埃尔米特数学考试成绩经常不及格,大学毕业后考不上好的研究所,且痛恨应试教育。[8][9]台湾网络的一篇类似内容的文章[10]並以E·T·贝尔的书《数学大师:从芝诺到庞加莱(英语:Men of Mathematics)》作为参考资料。但E·T·贝尔的书在介绍埃尔米特的第24章中虽然写了埃尔米特鄙视学校考试,但并未提到一些与本文所引述的内容。[4]科学网(中国科学院和中国工程院等共同主办)在转载时则例行惯例地在正文下方提醒了读者需自己留心文章的真实性。[11]由于历史久远,关于埃尔米特的生平史实数据又流传不多,因此对于这位令人尊敬的数学家在数学专业外的生平,确实有难以精确考究的不确定性,这是对其生平有兴趣者需要留意的地方。
^ 3.003.013.023.033.043.053.063.073.083.093.103.113.123.133.143.153.163.173.183.19J. J. O'Connor; E. F. Robertson. Charles Hermite [夏尔·埃尔米特]. 苏格兰圣安德鲁斯大学(University of St Andrews, Scotland). [2016-01-01]. (原始内容存档于2019-10-22) (英语). 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.","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.","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.","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...he began corresponding with Jacobi and...he was already producing research which was ranking as a leading world-class mathematician.","...show 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...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.","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.引文使用过时参数coauthors (帮助)
^ 5.05.1Halsted, George. Biography: Charles Hermite [人物传:夏尔·埃尔米特]. 美国数学月刊(The American Mathematical Monthly). June - July, 8: 131–133 [2015-12-31]. (原始内容存档于2019-05-21) (英语). The French geometer had the good fortune not granted all great men to see recognized in his lifetime by the scientific world his extraordinary merit. The 24th of December, 1892, his sixtieth birthday, the friends, the disciples, the admirers of the great geometer assembled at the Sorbonne to present him the gold medal struck in his honor by international subscription.","Hermite retained to the last day of his life his privileged intelligence; but his body suffered. In a long letter of his, a few days before his death, he complained of his attacks of asthma and of the lack of appetite and of sleep: he seemed to forsee the nearness of his end...请检查|date=中的日期值 (帮助) 引文格式1维护:日期与年 (link)
^Aubrey J. Kempner. On Transcendental Numbers [论超越数]. Transactions of the American Mathematical Society (American Mathematical Society). October 1916, 17 (4): 476–482. JSTOR 1988833. doi:10.2307/1988833(英语).