数学家传记
恩斯特·弗朗茨·诺伊曼研究晶体学以及数学的其他物理应用。
恩斯特·弗朗茨·诺伊曼的父亲诺伊曼是个农民,后来放弃务农,成为了一名地产代理人。诺伊曼的母亲是一位伯爵夫人,她曾离过婚,她的父母不允许她嫁给诺伊曼,即伯爵夫人的总管,因为他是个平民。诺伊曼的母亲甚至不可能承认诺伊曼是她的儿子。因此,诺伊曼由诺伊曼的父母抚养长大,直到十岁才见到自己的母亲。在我们讨论诺伊曼家族时,应当注意到诺伊曼是卡尔·诺伊曼的父亲,后者在本档案中也有传记。
诺伊曼在柏林文理中学学习,在那里他显示出一些数学才能。然而,由于普鲁士人与法国人之间的战争造成的问题,他未能完成那里的学业。1814年,十六岁的诺伊曼离开了文理中学,志愿加入普鲁士军队。那是普鲁士及其盟国取得胜利的时期,拿破仑率领的法国军队被击退。到1814年5月,盟军已攻占巴黎,签订了巴黎条约,拿破仑被流放。
然而,1815年3月1日,拿破仑逃脱,带着一队卫兵在戛纳登陆。盟军开始集结在法国边境,诺伊曼随普鲁士军队行动。拿破仑集结了一支军队,进军比利时,于1815年6月16日在利尼击败了普鲁士人。诺伊曼参加了这场战斗,受了重伤,被送往杜塞尔多夫的一家医院。因此,他错过了滑铁卢战役的战斗,在那场战役中,拿破仑在利尼战役两天后最终被击败。
受伤并不是降临在诺伊曼身上的唯一不幸,因为他的父亲在一场火灾中失去了所有财产,几乎没有留下什么来支持诺伊曼剩余的教育。尽管有经济困难,诺伊曼还是回到柏林文理中学完成学业,并于1817年进入柏林大学。然而,他并没有注册攻读科学学位,因为他遵从父亲的意愿,开始学习神学。
诺伊曼于1818年4月从柏林大学转到耶拿继续学业。在耶拿,他的兴趣转向了更多的科学课程,他开始学习矿物学和晶体学。他与耶拿的一位老师克里斯蒂安·魏斯成为朋友,魏斯安排了一些经济支持,让诺伊曼能够前往西里西亚进行地质学实地考察。他在1820年夏天进行了第一次旅行,并计划在1822年和1823年进行更多旅行。然而,诺伊曼的父亲去世了,出于对母亲健康和福祉的关心,他从学业中抽出1822-23年这一年时间来管理母亲的农场。
抽出一年时间管理农场并没有阻止诺伊曼撰写他的第一篇关于晶体学的论文,该论文于1823年发表。然后他回到柏林大学,在那里担任矿物陈列馆的管理员,同时完成他的博士学位研究。诺伊曼于1825年11月获得博士学位,次年5月,他与卡尔·古斯塔夫·雅各布·雅可比一起被任命为柯尼斯堡大学的Privatdozent。
1828年,诺伊曼被任命为柯尼斯堡的讲师,次年又被任命为矿物学和物理学讲席。当诺伊曼来到柯尼斯堡时,科学课程由Karl Hagen讲授,而诺伊曼接管了其中一些课程的教学。1830年,他与Karl Hagen的女儿Luise Florentine Hagen结婚,但Luise在生下五个孩子后于1838年去世。五年后,诺伊曼再次结婚,这次娶的是他第一任妻子的表亲Wilhelmina Hagen。
1833年在柯尼斯堡,诺伊曼和卡尔·古斯塔夫·雅各布·雅可比共同创办了一个数学-物理讨论班,用以向他们的学生介绍研究方法。其中一位这样的学生是古斯塔夫·基尔霍夫,他在1843年至1846年间参加了诺伊曼-卡尔·古斯塔夫·雅各布·雅可比讨论班。1847年,诺伊曼因继承第二任妻子父母的遗产而获得钱财。这使他能够在家旁边为自己建造一个物理实验室。他曾多年试图说服大学当局建造一个物理研究所,但直到诺伊曼退休后,物理研究所才得以建造。他为自己建造的物理实验室也被他的学生使用。
诺伊曼的早期工作是在晶体学领域。他使用最小二乘法对仪器进行误差分析,使测量达到了新的精度。然而,他在柯尼斯堡的工作受到弗里德里希·威廉·贝塞尔和卡尔·古斯塔夫·雅各布·雅可比的影响,他转向了数学物理的研究。
1831年,他提出了关于分子热的定律,即化合物的分子热等于其各组分原子热之和。在第二篇论文中,他研究了为什么当热水和冷水混合时,结果温度不是两种温度的平均值。他的解释大体上是正确的,即水的比热随温度升高而增大,但他未能意识到这仅在一定的温度范围内成立。
1832年,诺伊曼研究了光的波动理论,获得了与奥古斯丁·路易·柯西和奥古斯丁·菲涅耳相似的结果。他在两篇论文中发表了他的电感应理论,第一篇在1845年,第二篇在1847年。这些论文假设了超距作用,并推导出了电流感应的数学定律。
诺伊曼只发表了他工作的一小部分,他的发现的主要部分包含在他于柯尼斯堡的讲座中,但从未发表。诺伊曼的儿子卡尔·诺伊曼声称,他父亲在1850年之前(即鲁道夫·克劳修斯关于热力学的第一篇论文发表之年)的柯尼斯堡讲座中提出的未发表研究,证明了他作为热的力学理论创始人之一的优先权。卡尔·诺伊曼在1895年整理了他父亲的讲座准备出版,但它们从未付印。文章[3]包含了诺伊曼在1854-1855学年所作的第三次讲座的摘录。
Franz Neumann's father, Ernst Neumann, was a farmer who later gave up farming and became an estate agent. Franz's mother was a Countess, who had been divorced, and her parents did not allow her to marry Ernst Neumann, the Countess's factotum, since he was a commoner. It was impossible for Franz's mother even to acknowledge that Franz was her son. Therefore Franz was brought up by Ernst Neumann's parents and he did not meet his mother until he was ten years old. While we are discussing the Neumann family we should note that Franz Neumann was the father of Carl Neumann who also has a biography in this archive.
Franz Neumann studied in Berlin Gymnasium where he showed some talent for mathematics. However, he did not complete his studies there because of the problems caused by wars between the Prussians and the French. In 1814, at the age of sixteen, Neumann left the Gymnasium and volunteered for the Prussian army. It was a period of victories for Prussia and its allies as the French army under Napoleon was driven back. By May 1814 the allies had taken Paris, the Treaty of Paris was signed and Napoleon was sent into exile.
However, on 1 March 1815, Napoleon escaped and landed at Cannes with a detachment of his guard. The allied armies began to assemble on the borders of France, and Neumann was with the Prussian forces. Napoleon assembled an army and marched into Belgium where he defeated the Prussians at Ligny on 16 June 1815. Neumann took part in the battle, was seriously wounded, and was taken to a hospital in Düsseldorf. He therefore missed fighting in the battle of Waterloo at which Napoleon was finally defeated two days after the Battle of Ligny.
Being wounded was not the only misfortune to befall Neumann, for his father lost everything he possessed in a fire leaving little to support the rest of Neumann's education. Despite the financial problems, Neumann returned to the Berlin Gymnasium to complete his course and entered the University of Berlin in 1817. He did not enrol for a degree in science, however, for he followed the wishes of his father and began to study theology.
Neumann moved from the University of Berlin to continue his studies at Jena in April 1818. At Jena, his interests turned to more scientific courses and he took up the study of mineralogy and crystallography. He became friendly with one of his teachers at Jena, Christian Weiss, and Weiss arranged for some financial support to allow Neumann to make field trips to Silesia to study geology. He made his first trip in the summer of 1820 and he planned to make further trips in 1822 and 1823. However, Neumann's father died and, concerned about his mother's health and well-being, he took the year 1822-23 out from his studies to manage his mother's farm.
Taking a year out to manage the farm did not stop Neumann writing his first paper on crystallography which was published in 1823. Then he returned to the University of Berlin where he worked as curator of the mineral cabinet while completing the research for his doctorate. Neumann obtained his doctorate in November 1825, and in the following May, together with Jacobi, he was appointed as a Privatdozent at the University of Königsberg.
In 1828 Neumann was appointed as a lecturer at Königsberg, being appointed to the chair of minerology and physics in the following year. When Neumann arrived in Königsberg the science courses were being taught by Karl Hagen, and Neumann took over teaching some of these courses. In 1830, he married Luise Florentine Hagen, Karl Hagen's daughter but Luise died in 1838 having given birth to five children. Five years later Neumann married again, this time to Wilhelmina Hagen, the first cousin of his first wife.
At Königsberg in 1833, Neumann and Jacobi together started up a mathematics-physics seminar which was used to introduce their students to methods of research. One such student was Kirchhoff who attended the Neumann-Jacobi seminar from 1843 to 1846. In 1847 Neumann came into money through an inheritance from his second wife's parents. This enabled him to build a physics laboratory for himself next to his home. He had tried for years to persuade the university authorities to build a Physics Institute but, only after Neumann retired was the Physics Institute built. The physics laboratory which he built for himself was also used by his students.
Neumann's early work was in crystallography. He used least squares methods of error analysis of instruments giving new precision to measurements. However, his work at Königsberg was influenced by Bessel and Jacobi, and he turned towards a study of mathematical physics.
In 1831 he formulated a law on molecular heat, namely that the molecular heat of a compound is equal to the sum of the atomic heats of its constituents. In a second paper he studied why when hot water and cold water are mixed the result does not have a temperature which is the average of the two temperatures. His explanation is broadly correct, namely the specific heat of water increases with temperature, but he failed to realise that this was only true over a certain range of temperatures.
In 1832 Neumann investigated the wave theory of light, obtaining results similar to those of Cauchy and Fresnel. He published his theory of electrical induction in two papers, the first in 1845 and the second in 1847. These assumed action at a distance and deduced the mathematical laws for induction of electric currents.
Neumann only published a fraction of his work, and major portions of his discoveries were contained in his lectures at Königsberg but never published. Carl Neumann, Franz Neumann's son, claimed that the unpublished researches of his father, presented in his Königsberg lectures before 1850, the year of the first memoir of Clausius on thermodynamics, prove his priority as one of the founders of the mechanical theory of heat. Carl Neumann prepared his father's lectures for publication in 1895 but they never appeared in print. The article [3] contains extracts from the third lecture given by Franz Neumann in session 1854-1855.
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