格奥尔格·欧姆Georg Simon Ohm

格奥尔格·欧姆出身于一个新教家庭。他的父亲Johann Wolfgang Ohm是一名锁匠，而他的母亲Maria Elizabeth Beck是一名裁缝的女儿。尽管他的父母没有受过正规教育，欧姆的父亲却是一个相当了不起的人，他自学达到了很高的水平，并能通过自己的教导给儿子们提供极好的教育。如果欧姆的兄弟姐妹都活了下来，他会是一个大家庭中的一员，但正如当时常见的那样，有几个孩子在童年就夭折了。Johann和Maria Ohm所生的七个孩子中只有三个活了下来：欧姆 欧姆、他的弟弟马丁·欧姆（后来成为著名数学家）以及他的妹妹Elizabeth Barbara。

在他们小时候，欧姆 欧姆和马丁·欧姆由他们的父亲教导，父亲使他们在数学、物理、化学和哲学方面达到了很高的水平。这与他们的学校教育形成了鲜明对比。欧姆 欧姆十一岁时进入埃尔朗根文理中学，但他在那里几乎没有受到任何科学训练。事实上，他学校教育的这一正规部分毫无启发性，强调死记硬背和解读文本。这与欧姆 欧姆和Martin从父亲那里受到的富有启发性的教导形成了强烈对比，父亲使他们的数学水平达到了让埃尔朗根大学教授Karl Christian von Langsdorf将他们比作伯努利家族的程度。值得再次强调Johann Wolfgang Ohm的非凡成就：一个完全自学成才的人，竟能给儿子们如此出色的数学和科学教育。

1805年，欧姆进入埃尔朗根大学，但他相当沉迷于学生生活。他并没有专注于学业，而是花大量时间跳舞、滑冰和打台球。欧姆的父亲对儿子浪费他自己从未有幸经历的教育机会感到愤怒，要求欧姆在三个学期后离开大学。欧姆去了（或者更准确地说，被送到）瑞士，1806年9月，他在Gottstadt bei Nydau的一所学校担任数学教师。

Karl Christian von Langsdorf于1809年初离开埃尔朗根大学，前往海德堡大学任职，欧姆本想和他一起去海德堡重新开始数学研究。然而，Langsdorf建议欧姆继续自学数学，并建议欧姆阅读莱昂哈德·欧拉、皮埃尔·西蒙·拉普拉斯和西尔维斯特·佛朗索瓦·拉克鲁瓦的著作。欧姆相当不情愿地接受了他的建议，但他在1809年3月离开了Gottstadt bei Nydau的教学职位，成为纳沙泰尔的一名私人教师。两年来，他一边履行家教职责，一边遵循Langsdorf的建议，继续私下研究数学。然后，在1811年4月，他回到了埃尔朗根大学。

他的私下研究对他大有裨益，因为他在1811年10月25日获得了埃尔朗根大学的博士学位，并立即加入教职员工队伍，担任数学讲师。三个学期后，欧姆放弃了大学职位。他看不到如何在埃尔朗根获得更好的地位，因为那里的前景很差，而他在讲师职位上基本上生活在贫困之中。巴伐利亚政府给他提供了一个在班贝格一所质量较差的学校担任数学和物理教师的职位，他于1813年1月接受了这个职位。

这并不是欧姆所设想的成功职业生涯，他决定必须证明自己的价值远不止于一所差学校的教师。他在极度不快乐的工作中，努力撰写一本关于几何教学的基础书籍。在欧姆忍受了这所学校三年后，它于1816年2月关闭。巴伐利亚政府随后将他送到班贝格一所过度拥挤的学校，帮助进行数学教学。

此处一段未译出，以下为英文原文On 11 September 1817 Ohm received an offer of the post of teacher of mathematics and physics at the Jesuit Gymnasium of Cologne. This was a better school than any that Ohm had taught in previously and it had a well equipped physics laboratory. As he had done for so much of his life, Ohm continued his private studies reading the texts of the leading French mathematicians Lagrange, Legendre, Laplace, Biot and Poisson. He moved on to reading the works of Fourier and Fresnel and he began his own experimental work in the school physics laboratory after he had learnt of Oersted's discovery of electromagnetism in 1820. At first his experiments were conducted for his own educational benefit as were the private studies he made of the works of the leading mathematicians.

科隆的耶稣会中学未能继续保持欧姆开始在那里工作时所具有的高标准，因此到1825年，他决定再次尝试获得他真正想要的工作，即大学里的职位。意识到进入这样一个职位必须通过研究出版物，他改变了对所从事实验工作的态度，并开始系统地朝着发表他的成果而努力[1]：-

学生负担过重，对自己的认真努力鲜有赏识，并意识到自己永远不会结婚，他转向科学，既是为了向世界证明自己，也是为了有一个坚实的基础来支持他在一个更令人振奋的环境中谋求职位的申请。

事实上，他已经确信我们今天称之为“欧姆定律”的真理，即大多数材料中的电流与施加在材料两端的电势差成正比。然而，这一结果并未包含在欧姆于1825年发表的第一篇论文中，因为这篇论文考察的是导线产生的电磁力随导线长度增加而减小。该论文仅基于欧姆所列表的实验证据推导出数学关系。

在1826年的两篇重要论文中，欧姆给出了基于约瑟夫·傅里叶热传导研究的电路传导的数学描述。这些论文延续了欧姆从实验证据推导结果的方法，特别是在第二篇论文中，他能够提出一些定律，这些定律在很大程度上解释了其他人在流电学方面的工作成果。第二篇论文无疑是欧姆在其次年出版的著名著作中提出的综合理论的第一步。

现在被称为欧姆定律的内容出现在这本著名的书Die galvanische Kette, mathematisch bearbeitet Ⓣ（《伽伐尼电路，数学处理》）（1827年）中，他在书中给出了完整的电学理论。该书以理解其余工作所必需的数学背景开始。我们在此应指出，这样的数学背景对于即使是领先的德国物理学家来说也是理解该工作所必需的，因为当时的重点是非数学的物理学方法。我们还应该指出，尽管欧姆在这篇引言中做出了尝试，但他并未真正成功地说服年长的德国物理学家相信数学方法是正确的。正如Caneva在[1]中所解释的，这在某种程度上是欧姆自己的过错：-

……无论是在引言中还是在包含更严格理论发展的正文中，欧姆都没有决定性地阐明整体的内在统一性或基本假设与主要推论之间的联系。例如，尽管他的理论被构想为一个基于三条基本定律的严格演绎系统，但他从未明确指出他希望将其若干数学和文字表述中的哪一个作为规范形式。

有趣的是，欧姆将他的理论呈现为一种接触作用理论，这一理论与超距作用的概念相对立。欧姆认为电的传递发生在“接触粒子”之间，这是欧姆本人使用的术语。论文[8]关注这一思想，特别是阐明欧姆与约瑟夫·傅里叶和克洛德-路易·纳维在科学方法上的差异。对欧姆在表述欧姆定律时所使用的概念框架的详细研究见[6]。

如上所述，欧姆在1825年开始发表重要著作时，正在科隆的耶稣会文理中学任职。从1826年8月起，他获得了一年休假以专注于研究，尽管他只得到了不到半薪的不太慷慨的待遇，但他能够在柏林度过这一年从事他的出版工作。欧姆曾相信他的出版物将使他在不得不返回科隆之前获得大学职位的邀请，但到1827年9月他应该重新开始教学时，他仍然没有收到这样的邀请。

欧姆的工作对理论产生了强烈影响，但并未受到多少热情欢迎。欧姆的感情受到了伤害，他决定留在柏林，并于1828年3月正式辞去了在科隆的职位。他在柏林的一些学校做了一些临时的数学教学工作。

他于1833年在纽伦堡接受了一个职位，尽管这给了他教授的头衔，但这仍然不是他毕生努力追求的大学职位。他的工作最终得到了皇家学会的认可，于1841年授予他科普利奖章。他于1842年成为皇家学会的外籍会员。其他科学院，如Berlin和Turin的科学院，选举他为通讯院士，1845年他成为巴伐利亚科学院的正式院士。

这种迟来的认可令人欣慰，但仍有一个问题：为什么一个今天因其重要贡献而家喻户晓的人，却为获得承认而挣扎了如此之久。这可能没有简单的解释，而是若干不同因素共同作用的结果。一个因素可能是欧姆性格的内向，另一个因素肯定是他对当时在他的国家以非数学方式研究的课题所采取的数学方法。毫无疑问，与当权者的个人纠纷也对欧姆毫无益处。他肯定没有得到Johannes Schultz的青睐，后者是柏林教育部的一位有影响力的人物，也没有得到欧姆 Friedrich Pohl的青睐，后者是该市的一位物理学教授。

电学并不是欧姆进行研究的唯一课题，也不是他最终陷入争议的唯一课题。1843年，他陈述了生理声学的基本原理，涉及人如何听到组合音。然而，他在数学推导中所做的假设并未完全得到证明，这导致了他与物理学家August Seebeck的激烈争论。他成功地使欧姆的假说失去信誉，欧姆不得不承认自己的错误。关于欧姆与Seebeck之间争论的细节，见[10]。

1849年，欧姆在慕尼黑担任巴伐利亚科学院物理陈列室的管理员，并开始在慕尼黑大学讲课。直到1852年，即他去世前两年，欧姆才实现了他毕生的抱负，被任命为慕尼黑大学物理学讲席。

Georg Simon Ohm came from a Protestant family. His father, Johann Wolfgang Ohm, was a locksmith while his mother, Maria Elizabeth Beck, was the daughter of a tailor. Although his parents had not been formally educated, Ohm's father was a rather remarkable man who had educated himself to a high level and was able to give his sons an excellent education through his own teachings. Had Ohm's brothers and sisters all survived he would have been one of a large family but, as was common in those times, several of the children died in their childhood. Of the seven children born to Johann and Maria Ohm only three survived, Georg Simon, his brother Martin who went on to become a well-known mathematician, and his sister Elizabeth Barbara.

When they were children, Georg Simon and Martin were taught by their father who brought them to a high standard in mathematics, physics, chemistry and philosophy. This was in stark contrast to their school education. Georg Simon entered Erlangen Gymnasium at the age of eleven but there he received little in the way of scientific training. In fact this formal part of his schooling was uninspired stressing learning by rote and interpreting texts. This contrasted strongly with the inspired instruction that both Georg Simon and Martin received from their father who brought them to a level in mathematics which led the professor at the University of Erlangen, Karl Christian von Langsdorf, to compare them to the Bernoulli family. It is worth stressing again the remarkable achievement of Johann Wolfgang Ohm, an entirely self-taught man, to have been able to give his sons such a fine mathematical and scientific education.

In 1805 Ohm entered the University of Erlangen but he became rather carried away with student life. Rather than concentrate on his studies he spent much time dancing, ice skating and playing billiards. Ohm's father, angry that his son was wasting the educational opportunity that he himself had never been fortunate enough to experience, demanded that Ohm leave the university after three semesters. Ohm went (or more accurately, was sent) to Switzerland where, in September 1806, he took up a post as a mathematics teacher in a school in Gottstadt bei Nydau.

Karl Christian von Langsdorf left the University of Erlangen in early 1809 to take up a post in the University of Heidelberg and Ohm would have liked to have gone with him to Heidelberg to restart his mathematical studies. Langsdorf, however, advised Ohm to continue with his studies of mathematics on his own, advising Ohm to read the works of Euler, Laplace and Lacroix. Rather reluctantly Ohm took his advice but he left his teaching post in Gottstadt bei Nydau in March 1809 to become a private tutor in Neuchâtel. For two years he carried out his duties as a tutor while he followed Langsdorf's advice and continued his private study of mathematics. Then in April 1811 he returned to the University of Erlangen.

His private studies had stood him in good stead for he received a doctorate from Erlangen on 25 October 1811 and immediately joined the staff as a mathematics lecturer. After three semesters Ohm gave up his university post. He could not see how he could attain a better status at Erlangen as prospects there were poor while he essentially lived in poverty in the lecturing post. The Bavarian government offered him a post as a teacher of mathematics and physics at a poor quality school in Bamberg and he took up the post there in January 1813.

This was not the successful career envisaged by Ohm and he decided that he would have to show that he was worth much more than a teacher in a poor school. He worked on writing an elementary book on the teaching of geometry while remaining desperately unhappy in his job. After Ohm had endured the school for three years it was closed down in February 1816. The Bavarian government then sent him to an overcrowded school in Bamberg to help out with the mathematics teaching.

On 11 September 1817 Ohm received an offer of the post of teacher of mathematics and physics at the Jesuit Gymnasium of Cologne. This was a better school than any that Ohm had taught in previously and it had a well equipped physics laboratory. As he had done for so much of his life, Ohm continued his private studies reading the texts of the leading French mathematicians Lagrange, Legendre, Laplace, Biot and Poisson. He moved on to reading the works of Fourier and Fresnel and he began his own experimental work in the school physics laboratory after he had learnt of Oersted's discovery of electromagnetism in 1820. At first his experiments were conducted for his own educational benefit as were the private studies he made of the works of the leading mathematicians.

The Jesuit Gymnasium of Cologne failed to continue to keep up the high standards that it had when Ohm began to work there so, by 1825, he decided that he would try again to attain the job he really wanted, namely a post in a university. Realising that the way into such a post would have to be through research publications, he changed his attitude towards the experimental work he was undertaking and began to systematically work towards the publication of his results [1]:-

Overburdened with students, finding little appreciation for his conscientious efforts, and realising that he would never marry, he turned to science both to prove himself to the world and to have something solid on which to base his petition for a position in a more stimulating environment.

In fact he had already convinced himself of the truth of what we call today "Ohm's law" namely the relationship that the current through most materials is directly proportional to the potential difference applied across the material. The result was not contained in Ohm's firsts paper published in 1825, however, for this paper examines the decrease in the electromagnetic force produced by a wire as the length of the wire increased. The paper deduced mathematical relationships based purely on the experimental evidence that Ohm had tabulated.

In two important papers in 1826, Ohm gave a mathematical description of conduction in circuits modelled on Fourier's study of heat conduction. These papers continue Ohm's deduction of results from experimental evidence and, particularly in the second, he was able to propose laws which went a long way to explaining results of others working on galvanic electricity. The second paper certainly is the first step in a comprehensive theory which Ohm was able to give in his famous book published in the following year.

What is now known as Ohm's law appears in this famous book Die galvanische Kette, mathematisch bearbeitet Ⓣ (1827) in which he gave his complete theory of electricity. The book begins with the mathematical background necessary for an understanding of the rest of the work. We should remark here that such a mathematical background was necessary for even the leading German physicists to understand the work, for the emphasis at this time was on a non-mathematical approach to physics. We should also remark that, despite Ohm's attempts in this introduction, he was not really successful in convincing the older German physicists that the mathematical approach was the right one. To some extent, as Caneva explains in [1], this was Ohm's own fault:-

... in neither the introduction nor the body of the work, which contained the more rigorous development of the theory, did Ohm bring decisively home either the underlying unity of the whole or the connections between fundamental assumptions and major deductions. For example, although his theory was conceived as a strict deductive system based on three fundamental laws, he nowhere indicated precisely which of their several mathematical and verbal expressions he wished to be taken as the canonical form.

It is interesting that Ohm's presents his theory as one of contiguous action, a theory which opposed the concept of action at a distance. Ohm believed that the communication of electricity occurred between "contiguous particles" which is the term Ohm himself uses. The paper [8] is concerned with this idea, and in particular with illustrating the differences in scientific approach between Ohm and that of Fourier and Navier. A detailed study of the conceptual framework used by Ohm in formulating Ohm's law is given in [6].

As we described above, Ohm was at the Jesuit Gymnasium of Cologne when he began his important publications in 1825. He was given a year off work in which to concentrate on his research beginning in August 1826 and although he only received the less than generous offer of half pay, he was able to spend the year in Berlin working on his publications. Ohm had believed that his publications would lead to his receiving an offer of a university post before having to return to Cologne but by the time he was due to begin teaching again in September 1827 he was still without such an offer.

Although Ohm's work strongly influenced theory, it was received with little enthusiasm. Ohm's feeling were hurt, he decided to remain in Berlin and, in March 1828, he formally resigned his position at Cologne. He took some temporary work teaching mathematics in schools in Berlin.

He accepted a position at Nüremberg in 1833 and although this gave him the title of professor, it was still not the university post for which he had strived all his life. His work was eventually recognised by the Royal Society with its award of the Copley Medal in 1841. He became a foreign member of the Royal Society in 1842. Other academies such as those in Berlin and Turin elected him a corresponding member, and in 1845 he became a full member of the Bavarian Academy.

This belated recognition was welcome but there remains the question of why someone who today is a household name for his important contribution struggled for so long to gain acknowledgement. This may have no simple explanation but rather be the result of a number of different contributary factors. One factor may have been the inwardness of Ohm's character while another was certainly his mathematical approach to topics which at that time were studied in his country a non-mathematical way. There was undoubtedly also personal disputes with the men in power which did Ohm no good at all. He certainly did not find favour with Johannes Schultz who was an influential figure in the ministry of education in Berlin, and with Georg Friedrich Pohl, a professor of physics in that city.

Electricity was not the only topic on which Ohm undertook research, and not the only topic in which he ended up in controversy. In 1843 he stated the fundamental principle of physiological acoustics, concerned with the way in which one hears combination tones. However the assumptions which he made in his mathematical derivation were not totally justified and this resulted in a bitter dispute with the physicist August Seebeck. He succeeded in discrediting Ohm's hypothesis and Ohm had to acknowledge his error. See [10] for details of the dispute between Ohm and Seebeck.

In 1849 Ohm took up a post in Munich as curator of the Bavarian Academy's physical cabinet and began to lecture at the University of Munich. Only in 1852, two years before his death, did Ohm achieve his lifelong ambition of being appointed to the chair of physics at the University of Munich.