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

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, structure, space, models, and change. History On ...

and a friend and classmate of

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...

. Grossmann was a member of an old Swiss family from Zurich. His father managed a textile factory. He became a

Professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professo ...

of Mathematics at the

Federal Polytechnic School (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , aca ...

in Zurich, today the ETH Zurich, 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 and ...

Career

In 1900 Grossmann graduated from the

(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 g ...

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

University of Zurich The University of Zürich (UZH, german: Universität Zürich) is a public research university located in the city of Zürich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 f ...

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 UK and in 1920 at Strasbourg.

Collaborations with Albert Einstein

's friendship with Grossmann began with their school days in Zurich. 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 german: Berner(in)french: Bernois(e) it, bernese , neighboring_municipalities = Bremgarten bei Bern, Frauenkappelen, Ittigen, Kirchlindach, Köniz, Mühleberg, Muri bei Bern, Neuenegg, Ostermundigen, Wohlen bei Bern, Zollikofen , website ...

, 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 mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and mult ...

and

tensor calculus In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi ...

; 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, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point ...

(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 General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...

Abraham Pais Abraham Pais (; May 19, 1918 – July 28, 2000) was a Dutch-American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II. ...

'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 related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...

theory as well. Grossmann introduced Einstein to the absolute differential calculus, started by

Elwin Bruno Christoffel Elwin Bruno Christoffel (; 10 November 1829 – 15 March 1900) was a German mathematician and physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provi ...

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 th ...

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 signi ...

. 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 (cerebral) sclerosis (MS), also known as encephalomyelitis disseminata or disseminated sclerosis, is the most common demyelinating disease, in which the insulating covers of nerve cells in the brain and spinal cord are damaged. This ...

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 ICRA, the International Center for Relativistic Astrophysics is an international research institute for relativistic astrophysics and related areas. Its members are seven Universities and four organizations. The center is located in Rome, Italy. ...

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 and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathem ...

, T. D. Lee, Christine Jones and Stephen Hawking.

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 20th-century Hungarian mathematicians ETH Zurich alumni ETH Zurich faculty 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