马塞尔·格罗斯曼Marcel Grossmann

马塞尔·格罗斯曼的父母是Jules Grossmann和Katharina Henriette Lichtenhahn。格罗斯曼有一个名叫Eugen的兄弟。Jules Grossmann是瑞士人，但来自一个原籍阿尔萨斯的家庭。1870年，他在布达佩斯创办了一家工厂，在那里他以名字的匈牙利语版本格罗斯曼 Gyula而闻名。这家工厂是与一个名叫Rauschenbach的人共同创办的，位于布达佩斯现在的Lehel广场附近，制造农业机械。Jules Grossmann是这家成功工厂的共同所有者。格罗斯曼在布达佩斯长大，在那里他就读于Dániel Berzsenyi 文理中学（Gymnasium）。这所著名的高中享有极好的教育声誉，为格罗斯曼提供了出色的数学背景。

1893年，格罗斯曼十五岁时，全家迁往瑞士，定居在巴塞尔。1893年至1896年间，他在那里就读于实科中学。在巴塞尔完成中学教育后，格罗斯曼进入苏黎世理工学院（后更名为瑞士联邦理工学院）学习数学，目标是取得文科中学数学教师资格。格罗斯曼的十位同学中有两位是Mileva Maric和阿尔伯特·爱因斯坦。三人成为密友，而不常听课的阿尔伯特·爱因斯坦借用了格罗斯曼的课堂笔记，以便在1898年参加考试。这对阿尔伯特·爱因斯坦来说是个明智的选择，因为格罗斯曼的笔记做得非常仔细——事实上，格罗斯曼的这些笔记保存了下来，因此今天仍能看出其质量。在1900年六名考生参加的毕业文凭考试中，格罗斯曼和阿尔伯特·爱因斯坦都获得了文凭，而Mileva Maric未能通过。到这时，Mileva和阿尔伯特·爱因斯坦无疑已深深相爱。

1900年，格罗斯曼成为苏黎世几何学家奥托·威廉·费德勒的助手。奥托·威廉·费德勒是奥古斯特·费迪南德·莫比乌斯的学生，在布拉格理工学院担任几何学教授之前，曾在苏黎世理工学院担任类似职位。他曾在格罗斯曼、阿尔伯特·爱因斯坦和Maric的本科学习期间教授他们几何学，而正是在几何学课程的考试中格罗斯曼表现优异。格罗斯曼在奥托·威廉·费德勒的指导下进行博士研究，并于1902年凭借学位论文Über die metrischen Eigenschaften kollinearer Gebilde Ⓣ（《共线结构的度量性质》）从苏黎世理工学院获得博士学位。在获得博士学位之前，他于1901年在瑞士北部的弗劳恩费尔德一所学校任教，1905年又迁往巴塞尔担任类似职位。

在阿尔伯特·爱因斯坦和格罗斯曼于1900年毕业后，他们继续保持友谊。阿尔伯特·爱因斯坦正在寻找职位，格罗斯曼于1901年4月13日写信告诉他，自己的父亲是伯尔尼专利局局长的一位朋友，已推荐阿尔伯特·爱因斯坦填补下一个空缺。阿尔伯特·爱因斯坦很高兴得到格罗斯曼的支持，并在同一天的回信中写道：——

亲爱的格罗斯曼！昨天我收到你的来信时，你对不幸的老友的挂念与关怀令我深受感动……若能获得这样一个美好的工作领域，我会非常高兴，并会不遗余力地不负你的推荐。三周前我回到父母这里，想从这里寻找一个大学助教的职位。若不是海因里希·马丁·韦伯对我耍了不诚实的手段，我早就找到了。尽管如此，我还是想尽一切办法，也没有失去幽默感……

格罗斯曼于1903年与工程师Eduard Keller的女儿Anna Keller结婚。他继续从事几何学研究，并于1904年在Frauenfeld出版了Die fundamentalen Konstruktionen der nichteuklidischen Geometrie Ⓣ（非欧几何的基本结构）。次年，他被任命为巴塞尔大学的dozent，于是离开了中学教职。阿尔伯特·爱因斯坦当然没有忘记他的朋友，1905年撰写学位论文时，他在扉页上写道：“献给我的朋友格罗斯曼博士”。1907年，格罗斯曼成为苏黎世联邦理工学院画法几何学教授。

1912年8月，阿尔伯特·爱因斯坦被任命为苏黎世联邦理工学院理论物理学讲席，回到该校。他正努力将狭义相对论推广以纳入引力，并立即开始与老朋友格罗斯曼合作。正是格罗斯曼向他指出，埃尔温·布鲁诺·克里斯托费尔于1864年提出、由格雷戈里奥·里奇-库尔巴斯托罗和图利奥·列维-齐维塔在1901年前后发展的tensor calculus与广义相对论相关。此前轻视数学重要性的阿尔伯特·爱因斯坦，很快被格罗斯曼的专业解释所说服。阿尔伯特·爱因斯坦于1912年10月29日写信给阿诺·索末菲：-

我现在专门研究引力问题，相信在我这里的一位数学家朋友[格罗斯曼]的帮助下，我能克服所有困难。但有一点是肯定的：我一生中从未如此刻苦过，我对数学产生了极大的敬意，而在此之前，由于我的无知，我曾把数学中较为微妙的部分视为纯粹的奢侈品。与这个问题相比，原来的相对论简直是儿戏。

格罗斯曼与阿尔伯特·爱因斯坦的合作产生了1913年关于广义相对论的第一篇论文。那就是发表在Zeitschrift für Mathematik und Physik上的Entwurf einer verallgemeinerten Relativitätsheorie und einer Theorie der Gravitation Ⓣ（广义相对论与引力论纲要）。从一种意义上说，它是一篇联合论文，但从另一种意义上说，它由两篇独立的论文组成，前22页是阿尔伯特·爱因斯坦撰写的“物理学部分”，接下来16页是格罗斯曼撰写的“数学部分”。同样在1913年，格罗斯曼发表了Mathematische Begriffsbildungen zur Gravitationstheorie Ⓣ（引力理论中的数学趋势）。他继续与阿尔伯特·爱因斯坦合作，并于1914年发表了另一篇联合论文，即Kovarianzeigenschaften der Feldgleichungen Ⓣ（场方程的协变性）。我们还应当提到格罗斯曼的其他出版物：教科书Darstellende Geometrie Ⓣ（画法几何）（1915年至1932年间共七版）、Darstellende Geometrie für Maschineningenieure Ⓣ（机械工程师用画法几何）（1915年至1927年间共三版）、Elemente der darstellenden Geometrie Ⓣ（画法几何基础）（1917年）以及Einführung in die darstellende Geometrie Ⓣ（画法几何引论）（1917年）。

1910年，格罗斯曼与巴塞尔大学数学教授Rudolf Fueter以及日内瓦大学代数与高等几何教授Henri Fehr（1870-1954）共同创立了瑞士数学会。Fueter是第一任主席（1910-12），Fehr是第二任主席（1913-15），格罗斯曼是第三任主席（1916-17）。格罗斯曼担任主席的时期特别重要，因为第一次世界大战（1914-18）使法国和德国交战，导致瑞士德语区和法语区之间高度紧张。很大程度上由于格罗斯曼，该学会在紧张局势下仍保持了全瑞士的视角。Swiss Mathematical Society并不是格罗斯曼共同创立的唯一学会。他还在1914年，即第一次世界大战爆发前不久，共同创立了新海尔维第学会。该学会视自己为海尔维第学会的继承者，后者从1761年到1858年为加强联邦以及1848年通过新联邦宪法建立瑞士联邦国家做出了贡献。格罗斯曼和其他创始人意识到瑞士不同地区之间的意见分歧威胁着国家的内部和平，希望创建一个新的海尔维第学会来维护瑞士的统一。除了创立这些重要学会外，格罗斯曼还是报纸Neuen Schweizer Zeitung的共同创始人和编辑。

最后我们应当提到，为表彰格罗斯曼而将一系列会议命名为格罗斯曼会议（关于理论及实验广义相对论、引力与相对论场论最新进展）。这些会议始于1975年，是每三年举行一次的国际会议，为讨论引力、广义相对论和相对论场论的最新进展提供了机会。它们强调数学基础、物理预言和实验检验。

Marcel Grossmann's parents were Jules Grossmann and Katharina Henriette Lichtenhahn. Marcel had a brother named Eugen. Jules Grossmann was Swiss but came from a family originally from Alsace. In 1870, he founded a factory in Budapest where he was known by the Hungarian version of his name, Grossmann Gyula. The factory, founded jointly with someone of the name of Rauschenbach, was situated close to the present Lehel Square in Budapest and manufactured agricultural machinery. Jules Grossmann was the joint owner of this successful factory. Marcel was brought up in Budapest where he attended the Dániel Berzsenyi Gymnasium. This famous high school had an excellent educational reputation and gave Grossmann an excellent background in mathematics.

In 1893, when Marcel was fifteen years old, his family moved to Switzerland and settled in Basel. There he attended the Oberrealschule from 1893 to 1896. After completing his high school education in Basel, Grossmann entered the Zürich Polytechnikum (later named the Eidgenössische Technische Hochschule) to study mathematics with the aim of qualifying as a Gymnasium teacher of mathematics. Two of Grossmann's ten fellow students were Mileva Maric and Albert Einstein. All three became close friends and Einstein, who did not attend many lectures, borrowed Grossmann's lecture notes in order to take his examinations in 1898. This was a good choice by Einstein, for Grossmann took careful notes - in fact these notes by Grossmann have survived so their quality can be seen today. In the final diploma examinations taken by six candidates in 1900 both Grossmann and Einstein were awarded diplomas while Mileva Maric failed. Certainly by this time Mileva and Einstein were deeply in love.

In 1900 Grossmann became an assistant to the geometer Otto Wilhelm Fiedler in Zürich. Fiedler, a student of August Möbius, had been professor of geometry at the Polytechnic Institute of Prague before taking up a similar position at the Polytechnikum at Zürich. He had taught geometry to Grossmann, Einstein and Maric during their undergraduate studies and it was Grossmann who had excelled in the examinations of the geometry course. Grossmann was advised by Fiedler as he undertook research towards his doctorate which he obtained from Zürich Polytechnikum in 1902 for his thesis Über die metrischen Eigenschaften kollinearer Gebilde Ⓣ. Before the award of his doctorate, he became a teacher in a school in Frauenfeld, northern Switzerland, in 1901, moving to take up a similar position in Basel in 1905.

After Einstein and Grossmann graduated in 1900 they continued their friendship. Einstein was looking for position and Grossmann wrote to him on 13 April 1901 telling him that his father, who was a friend of the Director of the Patent Office in Bern, had recommended Einstein for the next vacancy. Einstein was delighted to have Grossmann's support and replied in a letter written on the same day:-

Dear Marcel! When I found your letter yesterday, I was deeply moved by your devotion and compassion which did not let you forget your old luckless friend ... I would be delighted to get such a nice sphere of activity and I would spare no effort to live up to your recommendation. I came here to my parents three weeks ago in order to search from here for an assistant's position at a university. I could have found one long ago had Heinrich Weber not played a dishonest game with me. All the same, I leave no stone unturned and do not give up my sense of humour ...

Grossmann married Anna Keller, the daughter of the engineer Eduard Keller, in 1903. He had continued to undertake research in geometry and he published Die fundamentalen Konstruktionen der nichteuklidischen Geometrie Ⓣ in Frauenfeld in 1904. In the following year he left school teaching when appointed as a dozent at the University of Basel. Einstein certainly did not forget about his friend and when he wrote his thesis in 1905 he wrote on the title page: "Dedicated to my friend Dr Marcel Grossmann". In 1907 Grossmann became professor of descriptive geometry at the Eidgenössische Technische Hochschule in Zürich.

In August 1912, Einstein arrived back at the Eidgenössische Technische Hochschule in Zürich having been appointed to the chair of theoretical physics. He was struggling to extend his special theory of relativity to include gravitation and immediately began collaborating with his old friend Grossmann. It was Grossmann who pointed out to him the relevance to general relativity of the tensor calculus which had been proposed by Elwin Bruno Christoffel in 1864, and developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita around 1901. Einstein, who previously had played down the importance of mathematics, was quickly convinced by Grossmann's expert explanations. Einstein wrote to Arnold Sommerfeld on 29 October 1912:-

I am now working exclusively on the gravitation problem and believe that I can overcome all difficulties with the help of a mathematician friend of mine here [Marcel Grossmann]. But one thing is certain: never before in my life have I toiled any where near as much, and I have gained enormous respect for mathematics, whose more subtle parts I considered until now, in my ignorance, as pure luxury. Compared with this problem, the original theory of relativity is child's play.

The collaboration between Grossmann and Einstein led to the first paper on the general theory of relativity in 1913. It was Entwurf einer verallgemeinerten Relativitätsheorie und einer Theorie der Gravitation Ⓣ published in the Zeitschrift für Mathematik und Physik. In one sense it is a joint paper but in another sense it consists of two separate papers, the first 22 pages being 'Physikalischer Teil' by Einstein and the next 16 pages being 'Mathematischer Teil' written by Grossmann. Also in 1913 Grossmann published Mathematische Begriffsbildungen zur Gravitationstheorie Ⓣ. He continued to collaborate with Einstein and they published another joint paper in 1914, namely Kovarianzeigenschaften der Feldgleichungen Ⓣ. Other publications by Grossmann that we should mention are the textbooks Darstellende Geometrie Ⓣ (seven editions between 1915 and 1932), Darstellende Geometrie für Maschineningenieure Ⓣ (three editions between 1915 and 1927), Elemente der darstellenden Geometrie Ⓣ (1917), and Einführung in die darstellende Geometrie Ⓣ (1917).

In 1910, Grossmann co-founded the Swiss Mathematical Society along with Rudolf Fueter, professor of mathematics at the University of Basel, and Henri Fehr (1870-1954), professor for algebra and higher geometry at the University of Geneva. Fueter was the first president (1910-12), Fehr the second president (1913-15) and Grossmann the third president (1916-17). Grossmann's time as president was a particularly significant one since the First World War (1914-18), which saw France and Germany at war with each other, caused high tension between the German speaking part of Switzerland and the French speaking part. It was in large part due to Grossmann that the Society maintained a Switzerland-wide perspective in spite of the tension. The Swiss Mathematical Society was not the only society that Grossmann co-founded. He was also a co-founder of the Neue Helvetische Gesellschaft in 1914, shortly before the outbreak of World War I. This Society saw itself as a successor of the Helvetic Society, which had contributed from 1761 to 1858 to strengthen the Confederation and the formation of the Swiss Federal State, with its New Federal Constitution, in 1848. Grossmann, and the other founders, realised that differences of opinion between different parts of Switzerland threatened the internal peace of the country and wanted to create a new Helvetic Society to preserve Swiss unity. In addition to founding these important Societies, Grossmann was a co-founder and editor of the newspaper Neuen Schweizer Zeitung.

Finally we should mention the honour given to Marcel Grossmann by naming the series of conferences, the Marcel Grossmann Meetings (on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories). These conferences, begun in 1975, are international meetings held every three years, which provide opportunities for discussing recent advances in gravitation, general relativity and relativistic field theories. They emphasise mathematical foundations, physical predictions and experimental tests.