**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 (1832-1912), 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.

**Article by:** *J J O'Connor* and *E F Robertson*

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