Marcel Grossmann (; April 9, 1878 – September 7, 1936) was a

Swiss Swiss most commonly refers to: * the adjectival form of Switzerland * Swiss people Swiss may also refer to: Places * Swiss, Missouri * Swiss, North Carolina * Swiss, West Virginia * Swiss, Wisconsin Other uses * Swiss Café, an old café located ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who was a friend and classmate of

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

. Grossmann came from an old Swiss family in

Zürich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

. His father managed a textile factory. He became a

Professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...

of Mathematics at the Federal Polytechnic School in Zürich, today the

ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...

, specializing in

descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design an ...

Career

In 1900 Grossmann graduated from the Federal Polytechnic School (ETH) and became an assistant to the geometer Wilhelm Fiedler. He continued to do research on

non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...

and taught in high schools for the next seven years. In 1902, he earned his doctorate from the

University of Zurich The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...

with the thesis ''Ueber die metrischen Eigenschaften kollinearer Gebilde'' (translated ''On the Metrical Properties of Collinear Structures'') with Fiedler as advisor. In 1907, he was appointed full professor of descriptive geometry at the Federal Polytechnic School. As a professor of geometry, Grossmann organized summer courses for high school teachers. In 1910, he became one of the founders of the Swiss Mathematical Society. He was an Invited Speaker of the ICM in 1912 at

Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...

and in 1920 at

Strasbourg Strasbourg ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...

Collaborations with Albert Einstein

's friendship with Grossmann began with their school days in Zürich. Grossmann's careful and complete lecture notes at the Federal Polytechnic School proved to be a salvation for Einstein, who missed many lectures. Grossmann's father helped Einstein get his job at the Swiss Patent Office in

Bern Bern (), or Berne (), ; ; ; . is the ''de facto'' Capital city, capital of Switzerland, referred to as the "federal city".; ; ; . According to the Swiss constitution, the Swiss Confederation intentionally has no "capital", but Bern has gov ...

, and it was Grossmann who helped to conduct the negotiations to bring Einstein back from Prague as a professor of physics at the Zurich Polytechnic. Grossmann was an expert in

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

and

tensor calculus In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

; just the mathematical tools providing a proper mathematical framework for Einstein's work on gravity. Thus, it was natural that Einstein would enter into a scientific collaboration with Grossmann. It was Grossmann who emphasized the importance of a non-Euclidean geometry called

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...

(also

elliptic geometry Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines ...

) to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossmann mentored Einstein in

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

theory as well. Grossmann introduced Einstein to the absolute differential calculus, started by Elwin Bruno Christoffel and fully developed by

Gregorio Ricci-Curbastro Gregorio Ricci-Curbastro (; 12January 1925) was an Italian mathematician. He is most famous as the discoverer of tensor calculus. With his former student Tullio Levi-Civita, he wrote his most famous single publication, a pioneering work on the ...

and

Tullio Levi-Civita Tullio Levi-Civita, (; ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus ( tensor calculus) and its applications to the theory of relativity, but who also made signifi ...

. Grossmann facilitated Einstein's unique synthesis of mathematical and theoretical physics in what is still today considered the most elegant and powerful theory of gravity: the general theory of relativity. The collaboration of Einstein and Grossmann led to a ground-breaking paper, "Outline of a Generalized Theory of Relativity and of a Theory of Gravitation", which was published in 1913 and was one of the two fundamental papers which established Einstein's theory of gravity.

Death

Grossmann died of

multiple sclerosis Multiple sclerosis (MS) is an autoimmune disease resulting in damage to myelinthe insulating covers of nerve cellsin the brain and spinal cord. As a demyelinating disease, MS disrupts the nervous system's ability to Action potential, transmit ...

in 1936. The community of relativists celebrates Grossmann's contributions to physics by organizing Marcel Grossmann meetings every three years.

Legacy

The International Center for Relativistic Astrophysics presents the Marcel Grossmann Awards. Each recipient receives a silver casting of the T. E. S. T. sculpture by the artist A. Pierelli. Each year, an institution is selected and between two and six individual scientists are selected. Past institutional winners include the Planck Scientific Collaboration ( ESA), AlbaNova University Center, Institut des Hautes Etudes Scientifique ( IHES) and others. Past individual winners include

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and professor emeritus at Harvard University. Until 2022, Yau was the William Caspar ...

, Tsung-Dao Lee, Christine Jones Forman and

Stephen Hawking Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...

Notes

References

* *
English translate
* * Graf-Grossmann, Claudia, with T. Sauer, ''Marcel Grossmann: Aus Liebe zur Mathematik'', Römerhof-Verlag, Zürich, 2015, * T. Sauer, ''Marcel Grossmann's contribution to the general theory of relativity'', in: ''Proceedings of the 13th Marcel Grossmann meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories'', July 2012. Edited by Robert T. Jantzen, Kjell Rosquist, Remo Ruffini. World Scientific, 2015, pp. 456–503.(http://arxiv.org/abs/1312.4068) * Graf-Grossmann, Claudia, with T. Sauer, English translation by William D. Brewer, "Marcel Grossmann: For the Love of Mathematics", Springer Biographies, 2018, ,

External links

Marcel Grossmann meetings
* * {{DEFAULTSORT:Grossmann, Marcel 1878 births 1936 deaths Academics from Zurich 20th-century Hungarian mathematicians ETH Zurich alumni Academic staff of ETH Zurich Geometers Jewish scientists Hungarian Jews Hungarian people of Swiss descent Mathematicians from Budapest Relativity theorists Swiss expatriates in Hungary 20th-century Swiss mathematicians Neurological disease deaths in Switzerland Deaths from multiple sclerosis People with multiple sclerosis Swiss people with disabilities Hungarian people with disabilities