利斯廷Johann Benedict Listing

利斯廷的家庭有捷克血统。他的父亲，也叫利斯廷，是一名刷子制造商，而他的母亲Caroline Friederike 利斯廷出身于贫苦农民家庭。利斯廷是独生子，在一个经济困难的家庭中长大。

他是个聪明的男孩，天赋出众，因此得到了包括施泰德基金会（艺术与博物馆的资助者）在内的几位资助人的教育资助。他从八岁起就读于模范学校，在那里打下了良好的教育基础。在这所学校里，他最初对科学和数学产生了兴趣，这主要归功于他那位才华横溢的老师埃米尔·穆勒，但他真正有天赋的是艺术。从十三岁起，利斯廷通过绘画和书法赚取一点钱来贴补家用，这让他的父母很高兴。

1825年，利斯廷进入了一所文理中学，在那里学习了五年。他掌握了英语、法语、意大利语和拉丁语，并在这所学校增加了数学和科学知识。他已经决定追求学术生涯，他的才华得到了施泰德基金会颁发的丰厚奖学金的认可。作为一个艺术基金会，他们无法支持利斯廷攻读数学学位，这本来是他的首选，而是授予他学习数学和建筑的奖学金。尽管曾经有一段时间建筑被认为是数学的一个分支，但在利斯廷的时代，它肯定不被这样认为，所以这种组合是相当奇特的，是由利斯廷的愿望和施泰德基金会的职责之间的妥协所决定的。

利斯廷于1830年进入哥廷根大学，参加了非常广泛的课程，比他的奖学金所指定的数学和建筑要广泛得多。除了这两个主题，他还学习了天文学、解剖学、生理学、植物学、矿物学、地质学和化学课程。很快，利斯廷就参加了卡尔·弗里德里希·高斯讲授的数学课程，他很快被卡尔·弗里德里希·高斯发现是一个既非常能干又非常勤奋的学生。卡尔·弗里德里希·高斯邀请他加入他的朋友圈，其中包括威廉·韦伯。

利斯廷并不是唯一被邀请与卡尔·弗里德里希·高斯建立亲密友谊的学生。另一个学生是Sartorius von Walterhausen，他比利斯廷小一岁。Walterhausen对地质学感兴趣，成为利斯廷的终身朋友。然而，卡尔·弗里德里希·高斯对利斯廷的影响非常显著。正是从卡尔·弗里德里希·高斯那里，利斯廷开始学习topological概念。他也是一个有才华的实验者，并与卡尔·弗里德里希·高斯合作进行物理实验，特别是与地磁有关的实验。卡尔·弗里德里希·高斯成为利斯廷的学位论文De superficiebus secundi ordinis Ⓣ（二阶曲面）的导师，该论文是关于二次曲面和三元形式的。他于1834年6月获得博士学位。

Walterhausen正出发前往西西里研究火山。他还同意在这次旅行中为卡尔·弗里德里希·高斯收集地磁数据。利斯廷显然是陪同他的助手的合适人选，两人在利斯廷获得博士学位后不到一个月就出发了。在这次旅行中，利斯廷保持了对许多不同主题的兴趣，以及作为旅行目的的地质学和物理学。他在业余时间研究数学，特别是研究最初由卡尔·弗里德里希·高斯提出的拓扑学思想。他决定总结自己关于这一主题的想法，并在给老学校老师穆勒的一封长信中这样做了。正是在这封信中，“拓扑学”一词首次出现。他不喜欢当时用于拓扑学思想的术语“geometria situs”，并且[4]：-

由于整个学说相当新颖，他觉得自己有理由给它起一个新名字，因此称之为“拓扑学”，他认为这更为恰当。

在旅行期间，利斯廷 被汉诺威高等工业学校联系，询问他是否有兴趣担任应用数学教师一职。他没有明确答复，只是礼貌地感谢了他们的邀请。由于霍乱疫情，Sartorius 和 利斯廷 推迟了返回哥廷根的计划。事实上，他们乘船前往英国，在那里短暂停留后才返回德国。利斯廷 前往汉诺威参加工业学校的职位面试，并被任命，于1837年11月开始了他的教学生涯。

1837年维多利亚成为英国女王时，她的叔叔成为汉诺威的统治者，并废除了自由宪法。威廉·韦伯，哥廷根大学的物理学教授，卡尔·弗里德里希·高斯的亲密合作者，是大学里签署抗议的七位教授之一，七人全部被解雇。威廉·韦伯留在哥廷根，直到1843年都没有职位。然而他的物理学教授职位必须填补，过了一段时间，卡尔·弗里德里希·高斯被要求推荐可能的候选人。他列出了一个三个名字的名单，利斯廷排在第三位。当前两位拒绝了这个提议时，利斯廷于1839年被任命，尽管他从未发表过论文。

作为物理学教授，利斯廷可以选择自己的研究领域。他是一位多才多艺的科学家，在已经涉足过的领域之外又选择了另一个领域，开始研究人眼的光学。他于1845年出版了Beiträge zur physiologischen OptikⓉ（《生理光学贡献》），此书后来成为经典。除了包含细致实验工作所得的数据外，这本书还由利斯廷运用其全部绘画和书法技巧绘制了精美的插图。

1846年9月，利斯廷与保利娜·埃尔弗斯结婚。几乎立刻，这对夫妇就陷入了经济困难，因为保利娜似乎无法将她的开销控制在家庭收入之内。

然而，利斯廷 继续思考拓扑学思想，并于1847年撰写了Vorstudien zur Topologie一书。这是“拓扑学”一词首次在出版物中使用，尽管如上所述，它最早出现在利斯廷 1836年的信中。这门学科多年来被称为analysis situs，直到20世纪20年代末，英文单词topology才被所罗门·莱夫谢茨使用。在这本书中——实际上是一篇扩展的论文，正如标题所示，仅作为初步工作——利斯廷写道：-

所谓拓扑学，我们指的是关于对象的模态特征，或关于空间中点、线、面、体及其部分或集合的连接、相对位置和顺序的规律的学说，始终不考虑度量或数量的问题。

1848年，席卷欧洲的革命产生了后果。最显著的影响是威廉·韦伯被重新任命为哥廷根的讲席，这是他十年前失去的职位。当然，利斯廷已被任命填补威廉·韦伯的讲席，因此必须达成妥协。这就是利斯廷被提升为数学物理普通教授，而威廉·韦伯成为实验物理学教授。尽管利斯廷所进行的研究几乎没有变化，因为他一直朝着自己感兴趣的方向前进，但他确实不得不将实验室的大部分让给威廉·韦伯。

利斯廷的家庭生活并不顺利。这对夫妇有两个女儿——一个在1848年，第二个在次年。然而Pauline Listing的[4]：-

……对待仆人的方式使她多次被带到地方法官面前，而她与房东的关系则导致全家多次搬家。

利斯廷和他的妻子似乎都无法管理家庭财务[4]：-

利斯廷频繁且大量地借钱，有时向高利贷者借；波利娜习惯性地滥用信用，并再次经常性地最终闹上法庭。他们往往入不敷出，有一次几乎避免了破产。

这次几乎破产发生在利斯廷发表另一篇对拓扑学的重要贡献前后。1858年，他几乎与奥古斯特·费迪南德·莫比乌斯同时且独立地发现了Möbius band的性质。1862年，他发表了Der Census raumlicher Complexe oder Verallgemeinerung des Euler'schen Satzes von den PolyedernⓉ（空间复形的考察或莱昂哈德·欧拉多面体定理的推广），其中讨论了将莱昂哈德·欧拉关于定向三维多面体的莱昂哈德·欧拉示性数的公式推广到某些四维单纯复形的情形。利斯廷这第二篇拓扑学著作在[8]中有详细讨论，特里波迪在其中将其与阿瑟·凯莱的一些工作进行了比较。

事实上，破产之所以得以避免，是因为汉诺威的部里救了他。正是萨尔托里乌斯安排了部里的救援行动，而在这里他是在偿还欠利斯廷的债，因为大约三十年前他们旅行期间，利斯廷曾通过护理他度过一场重病而救了他的命。然而，由于利斯廷本人及其妻子的行为，他并未得到同事们的青睐，而且可以肯定的是，他因此获得的科学成就认可较少。然而他是[4]：-

……勤奋而好奇，善良而乐于助人，合群而机智，性情温和到极点，是许多人的真正朋友，不是任何人的敌人。

利斯廷 所作贡献的范围相当惊人。Breitenberger 在 [4] 中写道：-

……他极为细致地研究了地球的形状；他进行了气象学、地磁学和光谱学方面的观测；他撰写了关于定量测定糖尿病患者尿中糖含量的文章；他推动了德国新兴的光学工业以及哥廷根更好的街道照明；他作为政府的观察员前往 1851 年伦敦、1873 年维也纳和 1876 年伦敦的世界博览会；他协助进行了大地测量；……他发明了相当多的术语[拓扑学之外]，其中一些已经通行：“熵现象”、“节点”、“同心光束”、“望远系统”、“大地水准面”……他创造了“一微米”来表示百万分之一米……

利斯廷 确实获得的荣誉包括当选 哥廷根科学院 和 爱丁堡皇家学会。他被图宾根授予荣誉博士学位。

他死于中风。

Johann Benedict Listing's family were of Czech descent. His father, also named Johann Benedict Listing, was a maker of brushes while his mother, Caroline Friederike Listing, came from a poor peasant background. Listing was an only child and brought up in a family which struggled with financial difficulty.

He was a bright boy and his talents were such that he received help with his education from several benefactors including the Städel foundation, supporters of art and museums. He received a good foundation for his education at the Musterschule which he attended from the age of eight. In this school he first became interested in science and mathematics, mainly because of his talented teacher Müller, but he had a real talent for art. Listing pleased his parents by helping out with the family's finances by earning a little money from drawing and calligraphy from the age of thirteen.

In 1825 Listing entered a Gymnasium where he studied for five years. He mastered English, French, Italian and Latin and well as increasing his knowledge of mathematics and science at this school. He had already decided to pursue an academic career and his talents were recognised by the award of a generous scholarship by the Städel foundation. Being an art foundation they could not support Listing to undertake a degree in mathematics, which would have been his preferred option, but instead awarded him the scholarship for the study of mathematics and architecture. Although there was a time when architecture was considered as a branch of mathematics, it certainly was not considered such in Listing's day so the combination was a rather peculiar one dictated by a compromise between Listing's wishes and the remit of the Städel foundation.

Listing entered Göttingen University in 1830 and attended a remarkably broad range of courses, much broader than the mathematics and architecture specified by his scholarship. In addition to these two topics he also took courses on astronomy, anatomy, physiology, botany, mineralogy, geology and chemistry. Soon Listing was attending mathematics courses given by Gauss and he was quickly spotted by Gauss as being both a very able and a very hard working student. Gauss invited him to join his circle of friends who included Weber.

Listing was not the only student invited into close friendship with Gauss. Another student was Sartorius von Walterhausen who was one year younger than Listing. Walterhausen, who was interested in geology, became a lifelong friend of Listing. The influence of Gauss on Listing was, however, very marked. It was from Gauss that Listing began to learn topological concepts. He also was a talented experimenter and collaborated with Gauss in physics experiments, particularly those relating to terrestrial magnetism. Gauss became the supervisor of Listing's dissertation De superficiebus secundi ordinis Ⓣ which was on surfaces of the second degree and ternary forms. He received his doctorate in June 1834.

Walterhausen was setting out on a trip to Sicily to study volcanoes. He had also agreed to collect data on terrestrial magnetism for Gauss on this trip. Listing was an obvious choice for an assistant to accompany him and the pair set off less than a month after Listing had obtained his doctorate. It was a journey on which Listing maintained his interests in many different topics and as well as the geology and physics which were the purpose of the trip. He worked in his spare time on mathematics, in particular working on the topological ideas which had first been suggested by Gauss. He decided to summarise his thoughts on the topic and did so in a long letter to his old school teacher Müller. It is in this letter that the word "topology" appears for the first time. He disliked the term "geometria situs", then used for topological ideas, and [4]:-

The entire doctrine being rather new, he felt justified to give it a new name and therefore called it "topology", which he though more appropriate.

While on his travels Listing was approached by the Höhere Gewerbeschule Hannover asking if he would be interested in a post as a teacher of applied mathematics. Without saying yes or no he politely thanked them for the offer. Because of a cholera epidemic Sartorius and Listing delayed their return to Göttingen. In fact they took a ship to England where they spent a short while before returning to Germany. Listing went to Hannover to be interviewed for the post in the Gewerbeschule and was appointed, starting his teaching career in November 1837.

When Victoria became Queen of Britain in 1837 her uncle became ruler of Hanover and revoked the liberal constitution. Weber, the professor of physics at Göttingen and a close collaborator of Gauss, was one of seven professors at the university to sign a protest and all seven were dismissed. Weber remained at Göttingen without a position until 1843. However his professorship of physics had to be filled and after a while Gauss was asked to suggest possible candidates. He produced a list of three names with Listing in third place. When the first two turned down the offer, Listing was appointed in 1839 despite never having published a paper.

As professor of physics Listing could choose his area for research. A versatile scientist, he chose yet another area to the ones which he had already worked in, and began to study the optics of the human eye. He published Beiträge zur physiologischen Optik Ⓣ in 1845 which became a classic. As well as containing data from careful experimental work, the book was beautifully illustrated by Listing using all his skills in drawing and calligraphy.

In September 1846 Listing married Pauline Elvers. Almost immediately the couple were in financial problems as Pauline seemed unable to keep her spending within the family's income.

Listing continued to think about topological ideas, however, and he wrote the book Vorstudien zur Topologie in 1847. It was the first published use of the word topology although, as we mentioned above, it was first used in Listing's letter of 1836. The subject was known as analysis situs for many years and only in the late 1920s was the English word topology used by Lefschetz. In this book, really an extended essay meant only, as the title states, as a preliminary work, Listing writes:-

By topology we mean the doctrine of the modal features of objects, or of the laws of connection, of relative position and of succession of points, lines, surfaces, bodies and their parts, or aggregates in space, always without regard to matters of measure or quantity.

In 1848 the revolution which swept Europe had its consequences. The most marked effect was that Weber was reappointed to the chair at Göttingen which he had lost ten years before. Of course Listing had been appointed to fill Weber's chair so a compromise had to be reached. This was that Listing was promoted to ordinary professor of mathematical physics while Weber became professor of experimental physics. Although little changed in the research that Listing undertook, since he had always gone in the direction which interested him, he did have to give up a large part of his laboratory to Weber.

However, Listing's family life did not go well. The couple had two daughters - one in 1848 and the second in the following year. However Pauline Listing's [4]:-

... treatment of servants brought her before the magistrates any number of times, while her relations with landlords led to many moves for the family.

Neither Listing nor his wife seemed capable of managing the family finances [4]:-

Listing borrowed frequently and heavily, sometimes from usurers; Pauline habitually abused credit, and again ended up in court with some regularity. They tended to live beyond their means, and on one occasion barely avoided bankruptcy.

The near bankruptcy came around the time that Listing was publishing another remarkable contribution to topology. In 1858 he had discovered the properties of the Möbius band at almost the same time, and independently of, Möbius. In 1862 he published Der Census raumlicher Complexe oder Verallgemeinerung des Euler'schen Satzes von den Polyedern Ⓣ which discusses extensions of Euler's formula for the Euler characteristic of oriented three-dimensional polyhedra to the case of certain four-dimensional simplicial complexes. This second work on topology by Listing is discussed by detail in [8] where Tripodi compares it with some work by Cayley.

In fact bankruptcy was avoided due to the ministry in Hannover saving him. It was Sartorius who had arranged for the rescue act by the ministry and here he was repaying a debt to Listing who had saved his life by nursing him through a serious illness during their journey of nearly thirty years earlier. However, Listing did not find favour with his colleagues because of the behaviour of himself and his wife and it is certain that he received less recognition for his scientific achievements because of it. Yet he was [4]:-

... industrious and inquisitive, kind and helpful, gregarious and witty, good-natured to a degree, a true friend to many, and an enemy to none.

The range of contributions made by Listing is quite remarkable. Breitenberger in [4] writes:-

... he studied the figure of the earth in minute detail; he made observations in meteorology, terrestrial magnetism, and spectroscopy; he wrote on the quantitative determination of sugar in the urine of diabetics; he promoted the nascent optical industry in Germany and better street lighting in Göttingen; he travelled to the world exhibitions in London 1851, Vienna 1873 and London 1876 as an observer for his government; he assisted in geodetic surveys; ... he invented a good many terms [other than topology], some of which have became current: "entropic phenomenona", "nodal points", "homocentric light", "telescopic system", " geoid" ...he coined "one micron" for the millionth of a metre ...

Among the honours which Listing did receive were election to the Göttingen Academy and the Royal Society of Edinburgh. He was awarded an honorary doctorate by Tübingen.

He died of a stroke.