约西亚·威拉德·吉布斯Josiah Willard Gibbs

吉布斯的父亲也叫约西亚·威拉德·吉布斯，是耶鲁大学圣典文学教授。事实上，吉布斯家族原籍英格兰沃里克郡，1658年从那里迁往波士顿。不过据说吉布斯的外貌像他的母亲。

吉布斯在当地威廉·霍普金斯文法学校接受教育，在那里他被描述为友善但内向。他对学业的全身心投入，加上相当虚弱的身体，意味着他很少参与学校的社交生活。1854年他进入耶鲁学院，在那里因拉丁语和数学成绩优异而获奖。

吉布斯留在耶鲁，开始从事工程学研究，撰写了一篇论文，其中他用几何方法研究齿轮设计。1863年他从耶鲁获得博士学位时，这是美国授予的第一个工程学博士学位。此后他在耶鲁担任导师三年，头两年教拉丁语，第三年教自然哲学。不过他并不缺钱，因为他的父亲已于1861年去世，而由于他的母亲也已去世，吉布斯和他的两个姐妹继承了一笔相当可观的财产。

1866年至1869年，吉布斯在欧洲学习。他与姐妹们同行，1866—67年冬天在巴黎度过，随后在柏林待了一年，最后于1868—69年在海德堡度过。在海德堡，他受到古斯塔夫·基尔霍夫和赫尔曼·冯·亥姆霍兹的影响。

吉布斯于1869年6月回到Yale，两年后的1871年，他被任命为Yale的数学物理教授。然而，正如Crowther在[2]中指出的：-

他回国时在精神上更像一位欧洲科学家而非美国科学家——这也是他在祖国迟迟未获普遍认可的原因之一。

相当令人意外的是，他被任命为耶鲁大学讲席教授时尚未发表任何著作。或许同样令人意外的是，吉布斯直到1873年、34岁时才发表第一部著作。很少有像吉布斯那样做出如此创新性工作的科学家，在34岁之前还未显露出天才的迹象。

吉布斯在1873年的重要论文是Graphical Methods in the Thermodynamics of Fluids和A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces。1876年，吉布斯发表了他最著名著作On the Equilibrium of Heterogeneous Substances的第一部分，并于1878年发表了该著作的第二部分。

这些论文中的第一篇描述了热力学中的图示。Bumstead（见[11]或[3]）写道：-

他在本文中首次描述的新图示中，从某些方面来说最简单的是以熵和温度为坐标的那一种……任何循环的功或热都与它在图示中任何部分的面积成正比……它在蒸汽机研究中得到了最重要的应用。

第二篇论文将这些图示扩展到三维，这项工作给詹姆斯·克拉克·麦克斯韦留下了深刻印象，以至于他制作了一个吉布斯热力学曲面的三维模型，并在去世前不久将模型寄给了吉布斯。

然而第三篇论文最为非凡。Bumstead在[11]或[3]中写道：-

人们普遍认为，它的出版是化学史上头等重要的事件。……然而，过了许多年它的价值才被普遍知晓，这种延迟在很大程度上是由于它的数学形式和严格的演绎过程使任何人读起来都很困难，尤其是对于最关心它的实验化学专业的学生来说更是如此……

吉布斯在向量分析方面的工作在纯数学中也具有重大意义。他最初于1881年和1884年印制了供自己学生使用的讲义，直到1901年才出现了一个正式出版的版本，是由他的一名学生准备出版的。利用赫尔曼·格拉斯曼的思想，吉布斯建立了一个比威廉·哈密顿的体系更容易应用于物理学的体系。

他应用他的向量方法给出了一种从三次观测中寻找彗星轨道的方法。该方法被应用于寻找1880年Swift彗星的轨道，并且比卡尔·弗里德里希·高斯的方法涉及更少的计算。

吉布斯关于光的电磁理论的五篇系列论文发表于1882年至1889年间。他在统计力学方面的工作也很重要，为quantum theory和詹姆斯·克拉克·麦克斯韦的理论提供了数学框架。事实上，他最后的出版物是Elementary Principles in Statistical Mechanics，这项工作是对统计力学基础进行坚实奠基的精彩论述。

除了早年和在欧洲的三年之外，吉布斯一生都住在同一所房子里，这所房子是他父亲建造的，离吉布斯曾就读的学校、他曾学习的学院以及他终生工作的大学都不远。⟦N3⟧在[2]中这样总结他的一生：-

[吉布斯]终身未婚，住在他尚在世的姐姐家中。晚年时，他是一位身材高大、举止庄重的绅士，步伐矫健，面色红润，承担自己那份家务，对学生平易近人且和善（尽管令人难以理解）。吉布斯深受朋友们的敬重，但美国科学界过于专注于实际问题，以致在他有生之年未能充分利用他深刻的理论工作。他在耶鲁过着平静的生活，深受少数有才华的学生的钦佩，但并未立即对美国科学产生与他的天才相称的影响。

吉布斯用以下热情洋溢的措辞描述了⟦N2⟧的个人品格：-

他举止谦逊，与人交往时和蔼亲切，从不表现出不耐烦或恼怒，没有卑劣的个人野心，也没有丝毫抬高自己的欲望，他近乎实现了无私的基督徒绅士的理想。在认识他的人的心里，他智力成就的伟大永远不会掩盖他生命的美好与尊严。

American Mathematical Society 命名了一个以纪念 吉布斯 的讲座系列。自1923年以来，大多数年份都有一位杰出数学家进行年度讲座。你可以在 THIS LINK 看到讲师及其头衔的列表。

J Willard Gibbs' father, also called Josiah Willard Gibbs, was professor of sacred literature at Yale University. In fact the Gibbs family originated in Warwickshire, England and moved from there to Boston in 1658. However Gibbs is said to have taken after his mother in physical appearance.

Gibbs was educated at the local Hopkins Grammar School where he was described as friendly but withdrawn. His total commitment to academic work together with rather delicate health meant that he was little involved with the social life of the school. In 1854 he entered Yale College where he won prizes for excellence in Latin and Mathematics.

Remaining at Yale, Gibbs began to undertake research in engineering, writing a thesis in which he used geometrical methods to study the design of gears. When he was awarded a doctorate from Yale in 1863 it was the first doctorate of engineering to be conferred in the United States. After this he served as a tutor at Yale for three years, teaching Latin for the first two years and then Natural Philosophy in the third year. He was not short of money however since his father had died in 1861 and, since his mother had also died, Gibbs and his two sisters inherited a fair amount of money.

From 1866 to 1869 Gibbs studied in Europe. He went with his sisters and spent the winter of 1866-67 in Paris, followed by a year in Berlin and, finally spending 1868-69 in Heidelberg. In Heidelberg he was influenced by Kirchhoff and Helmholtz.

Gibbs returned to Yale in June 1869 and, two years later in 1871, he was appointed professor of mathematical physics at Yale. However, as Crowther points out in [2]:-

He returned more a European than an American scientist in spirit-one of the reasons why general recognition in his native country came so slowly.

Rather surprisingly his appointment to the chair at Yale came before he had published any work. Perhaps it is also surprising that Gibbs did not publish his first work until 1873 when he was 34 years old. Few scientists who produce such innovative work as Gibbs did are 34 years of age before producing signs of their genius.

Gibbs' important 1873 papers were Graphical Methods in the Thermodynamics of Fluids and A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces. In 1876 Gibbs published the first part of the work for which he is most famous On the Equilibrium of Heterogeneous Substances, publishing the second part of this work in 1878.

The first of these papers describes diagrams in thermodynamics. Bumstead (see [11] or [3]) writes:-

Of the new diagrams which he first described in this paper, the simplest, in some respects, is that in which entropy and temperature are taken as coordinates... the work or heat of any cycle is proportional to its area in any part of the diagram ... it has found most important applications in the study of the steam engine.

The second paper extended the diagrams into three dimensions and this work impressed Maxwell so much that he constructed a three dimensional model of Gibbs's thermodynamic surface and, shortly before his death, sent the model to Gibbs.

However the third paper is the most remarkable. Bumstead in [11] or [3] writes:-

It is universally recognised that its publication was an event of the first importance in the history of chemistry. ... Nevertheless it was a number of years before its value was generally known, this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficult reading for any one, and especially so for students of experimental chemistry whom it most concerns...

Gibbs' work on vector analysis was also of major importance in pure mathematics. He first produced printed notes for the use of his own students in 1881 and 1884 and it was not until 1901 that a properly published version appeared prepared for publication by one of his students. Using ideas of Grassmann, Gibbs produced a system much more easily applied to physics than that of Hamilton.

He applied his vector methods to give a method of finding the orbit of a comet from three observations. The method was applied to find the orbit of Swift's comet of 1880 and involved less computation than Gauss's method.

A series of five papers by Gibbs on the electromagnetic theory of light were published between 1882 and 1889. His work on statistical mechanics was also important, providing a mathematical framework for quantum theory and for Maxwell's theories. In fact his last publication was Elementary Principles in Statistical Mechanics and this work is a beautiful account putting the foundations of statistical mechanics on a firm foundation.

Except for his early years and the three years in Europe, Gibbs spent his whole life living in the same house which his father had built only a short distance from the school Gibbs had attended, the College at which he had studied and the University where he worked the whole of his life. Crowther, in [2], sums up his life as follows:-

[Gibbs] remained a bachelor, living in his surviving sister's household. In his later years he was a tall, dignified gentleman, with a healthy stride and ruddy complexion, performing his share of household chores, approachable and kind (if unintelligible) to students. Gibbs was highly esteemed by his friends, but U.S. science was too preoccupied with practical questions to make much use of his profound theoretical work during his lifetime. He lived out his quiet life at Yale, deeply admired by a few able students but making no immediate impress on U.S. science commensurate with his genius.

Bumstead describes Gibbs' personal character in the following glowing terms:-

Unassuming in manner, genial and kindly in his intercourse with his fellow-men, never showing impatience or irritation, devoid of personal ambition of the baser sort or of the slightest desire to exalt himself, he went far toward realising the ideal of the unselfish, Christian gentleman. In the minds of those who knew him, the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life.

The American Mathematical Society named a lecture series in honour of Gibbs. An annual lecture has been given by a distinguished mathematician most years since 1923. You can see a list of the lecturers and their titles at THIS LINK.