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Einstein's Italian Mathematicians: Ricci, Levi-civita, and the Birth of General Relativity
In the first decade of the twentieth century as Albert Einstein began formulating a revolutionary theory of gravity, the Italian mathematician Gregorio Ricci was entering the later stages of what appeared to be a productive if not particularly memorable career, devoted largely to what his colleagues regarded as the dogged development of a mathematical language he called the absolute differential calculus. In 1912, the work of these two dedicated scientists would intersect-and physics and mathematics would never be the same. Einstein's Italian Mathematicians chronicles the lives and intellectual contributions of Ricci and his brilliant student Tullio Levi-Civita, including letters, interviews, memoranda, and other personal and professional papers, to tell the remarkable, little-known story of how two Italian academicians, of widely divergent backgrounds and temperaments, came to provide the indispensable mathematical foundation-today known as the tensor calculus-for general relativity.
211 pages, Paperback
Published July 20, 2018
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January 19, 2023
~~~ Cast ~~~
There are four major characters in this tale which is arguably one of the best stories on success of mathematics as a language to understand nature. Out of four, three are mathematicians; Gregorio Ricci-Curbastro (Italian), Tullio Levi-Civita (Italian), Marcel Grossmann (Swiss) and a physicist; Albert Einstein (German-born).
~~~ Trailer ~~~
This is a story of two desperate researchers; Ricci and Einstein. Ricci wanted his mathematical discovery, the absolute differential calculus, to see the light of application in physics and be accepted as important work by mathematicians. Einstein, on the other hand, was looking for a mathematical formalism for his general theory of relativity. They both had the tenacity of the bulldog on their respective fields. Ricci nurtured and developed his mathematics, detail by detail, for more than a decade. Einstein did same to his theory; philosophically advancing but with attempts and failure to model it mathematically. It was when they crossed path, the fundamental perception of the nature would never be the same again.
~~~ Plot ~~~
This book starts with the vivid portrait of the life of Ricci which was virtually spent in two towns Lugo and Padua, his hometown and university where he taught respectively. He devoted most of his active career in developing the absolute differential calculus which aimed at representing the equations in such a way that same equation would be valid for any choice of coordinate system (inertial or non-inertial). This independence in the choice of the coordinate system is what suggests the word 'absolute' in the absolute calculus. In modern terms this calculus is called tensor calculus.
In his working life, Ricci did not enjoy the amount of respect and acknowledgement from his discovery of absolute differential calculus. It was mainly because the mathematics looked promising but lacked application which could demonstrate its effectiveness. Obviously Ricci applied his calculus on some problems of physics but this application did not show much insight as compared to the methods that were already being used.
His absolute differential calculus was in dark but this was soon to be changed and this is where Levi-Civita, one of his brightest students, later collaborator, and life long friend, comes into play. In 1900 when they published a joint review paper titled "Methods of the absolute differential calculus and their applications" which presented tutorial of absolute differential calculus with all necessary mathematical foundations lucidly explained. "Applications to Mechanics" and "Applications to Physics" were included as final two chapters in the hope that the application be applied to wide range of more important problems.
“Grossmann, you must help me or else I’ll go crazy.”
A. Einstein to M. Grossmann, summer 1912
In 1912 Einstein went to Zürich where he was professor of theoretical physics at the ETH Zürich under the recommendation of his old friend and a brilliant mathematician in non-Euclidian geometry; Marcell Grossmann. Einstein presented the problem he has been grappling for 5 years to Grossmann who suggested that the work of two Italian mathematicians Ricci and Levi-Civita could be useful. According to Grossmann, a differential calculus that is independent to the coordinate system was something Einstein needed and the very same mathematics was offered in the 1900 paper of Ricci and Levi-Civita.
No doubt that Einstein was first rate physicist and great philosopher but when it came to mathematics, he was a humble man. It was clear that he needed help with this absolute differential calculus which Grossman was happy to offer. They published a joint paper "Outline of a Generalized Theory of Relativity and of a Theory of Gravitation" in 1913 on which Einstein expounded physical aspects of his theory and Grossman did same in mathematical language using the tools discovered by Ricci and his student. (The paper has been translated into English and is present in the collected works of Einstein. The clarity in the line of reasoning of Grossman as he uses the mathematics to explain gravity is evident to the readers with mathematical inclination.) This paper, as it is, had some issues which was solved by Einstein in November of 1915. It is very important to note that the final presentation of general theory of relativity contains the same mathematical architecture what was drafted by Grossmann in their 1913 paper. From 1912 to 1914, Einstein had equipped himself with the necessary mathematical tools with the help of Grossmann.
Einstein left Zürich and moved to Berlin in 1914. Levi-Civita, who got in touch with Einstein with regards to what he saw as a fault in his paper of November 1914 (which Einstein wrote after he moved to Berlin), corresponded with Einstein for six month till the fall of 1915. In the November of 1915 he gave set of four lectures to the members of the Prussian Academy. In the course of these lectures, for four weeks, Einstein wrestled with a succession of tensors, equations, corrections, and updates, before presenting his final version of the gravitational equations on November 25th ... and the rest, as they say, is the history.
~~~ Epilogue ~~~
With the success of general theory of relativity, Ricci got to witness the grandness of his mathematical discovery (the pleasure which not many mathematicians has been able to witness in the history of mathematics). He later died at the age of 73 in 1925.
In case of Levi-Civita, he went on to contribute on various problems of general relativity and popularized the field in Italy. The ending, however, was not so happy for Levi-Civita. Inspite of his contributions and mathematical fame, as a Jew, he could not survive the Italian Fascist government. His professorship and of his membership of all scientific societies were stripped. Tullio Levi-Civita, one of the best mathematician of his time, died in 1941 aged 68 in his home country as if he were nobody.
~~~ My thoughts ~~~
I loved the narrative for its graphic portrayal of Italy and the rigidity of Italian academics during the time of Ricci and the struggles he went through to establish himself as competent mathematician. Reading through the book, I had started to miss the amount of detailed mathematical exploration on the works of Ricci and Levi-Civita. All this changed when I reached APPENDIX-A, which provides good amount of mathematical insights to absolute differential calculus and its use in general theory of relativity. The appendix was a beautiful surprise to me. This book, in my view, is equally accessible to general readers (u can skip Appendix-A) and those who are into mathematics.
Personally, the book would have been more exciting to me if the line of mathematical reasoning had extended from works of Gauss to Riemann to Christoffel to Ricci. It sure does mentions the link but I would love to read more about the work of first three mathematicians and how they were useful to the latter. But again, the book is not titled "On the Complete History of Tensor Calculus", so I should limit my expectations.
I am currently learning differential geometry and I got interested in this book as the source of historical background on the field. I enjoyed it a lot and certainly would recommend the book to other interested readers.
[Thank you Sriza for helping me edit this review.]
There are four major characters in this tale which is arguably one of the best stories on success of mathematics as a language to understand nature. Out of four, three are mathematicians; Gregorio Ricci-Curbastro (Italian), Tullio Levi-Civita (Italian), Marcel Grossmann (Swiss) and a physicist; Albert Einstein (German-born).
~~~ Trailer ~~~
This is a story of two desperate researchers; Ricci and Einstein. Ricci wanted his mathematical discovery, the absolute differential calculus, to see the light of application in physics and be accepted as important work by mathematicians. Einstein, on the other hand, was looking for a mathematical formalism for his general theory of relativity. They both had the tenacity of the bulldog on their respective fields. Ricci nurtured and developed his mathematics, detail by detail, for more than a decade. Einstein did same to his theory; philosophically advancing but with attempts and failure to model it mathematically. It was when they crossed path, the fundamental perception of the nature would never be the same again.
~~~ Plot ~~~
This book starts with the vivid portrait of the life of Ricci which was virtually spent in two towns Lugo and Padua, his hometown and university where he taught respectively. He devoted most of his active career in developing the absolute differential calculus which aimed at representing the equations in such a way that same equation would be valid for any choice of coordinate system (inertial or non-inertial). This independence in the choice of the coordinate system is what suggests the word 'absolute' in the absolute calculus. In modern terms this calculus is called tensor calculus.
In his working life, Ricci did not enjoy the amount of respect and acknowledgement from his discovery of absolute differential calculus. It was mainly because the mathematics looked promising but lacked application which could demonstrate its effectiveness. Obviously Ricci applied his calculus on some problems of physics but this application did not show much insight as compared to the methods that were already being used.
His absolute differential calculus was in dark but this was soon to be changed and this is where Levi-Civita, one of his brightest students, later collaborator, and life long friend, comes into play. In 1900 when they published a joint review paper titled "Methods of the absolute differential calculus and their applications" which presented tutorial of absolute differential calculus with all necessary mathematical foundations lucidly explained. "Applications to Mechanics" and "Applications to Physics" were included as final two chapters in the hope that the application be applied to wide range of more important problems.
“Grossmann, you must help me or else I’ll go crazy.”
A. Einstein to M. Grossmann, summer 1912
In 1912 Einstein went to Zürich where he was professor of theoretical physics at the ETH Zürich under the recommendation of his old friend and a brilliant mathematician in non-Euclidian geometry; Marcell Grossmann. Einstein presented the problem he has been grappling for 5 years to Grossmann who suggested that the work of two Italian mathematicians Ricci and Levi-Civita could be useful. According to Grossmann, a differential calculus that is independent to the coordinate system was something Einstein needed and the very same mathematics was offered in the 1900 paper of Ricci and Levi-Civita.
No doubt that Einstein was first rate physicist and great philosopher but when it came to mathematics, he was a humble man. It was clear that he needed help with this absolute differential calculus which Grossman was happy to offer. They published a joint paper "Outline of a Generalized Theory of Relativity and of a Theory of Gravitation" in 1913 on which Einstein expounded physical aspects of his theory and Grossman did same in mathematical language using the tools discovered by Ricci and his student. (The paper has been translated into English and is present in the collected works of Einstein. The clarity in the line of reasoning of Grossman as he uses the mathematics to explain gravity is evident to the readers with mathematical inclination.) This paper, as it is, had some issues which was solved by Einstein in November of 1915. It is very important to note that the final presentation of general theory of relativity contains the same mathematical architecture what was drafted by Grossmann in their 1913 paper. From 1912 to 1914, Einstein had equipped himself with the necessary mathematical tools with the help of Grossmann.
Einstein left Zürich and moved to Berlin in 1914. Levi-Civita, who got in touch with Einstein with regards to what he saw as a fault in his paper of November 1914 (which Einstein wrote after he moved to Berlin), corresponded with Einstein for six month till the fall of 1915. In the November of 1915 he gave set of four lectures to the members of the Prussian Academy. In the course of these lectures, for four weeks, Einstein wrestled with a succession of tensors, equations, corrections, and updates, before presenting his final version of the gravitational equations on November 25th ... and the rest, as they say, is the history.
~~~ Epilogue ~~~
With the success of general theory of relativity, Ricci got to witness the grandness of his mathematical discovery (the pleasure which not many mathematicians has been able to witness in the history of mathematics). He later died at the age of 73 in 1925.
In case of Levi-Civita, he went on to contribute on various problems of general relativity and popularized the field in Italy. The ending, however, was not so happy for Levi-Civita. Inspite of his contributions and mathematical fame, as a Jew, he could not survive the Italian Fascist government. His professorship and of his membership of all scientific societies were stripped. Tullio Levi-Civita, one of the best mathematician of his time, died in 1941 aged 68 in his home country as if he were nobody.
~~~ My thoughts ~~~
I loved the narrative for its graphic portrayal of Italy and the rigidity of Italian academics during the time of Ricci and the struggles he went through to establish himself as competent mathematician. Reading through the book, I had started to miss the amount of detailed mathematical exploration on the works of Ricci and Levi-Civita. All this changed when I reached APPENDIX-A, which provides good amount of mathematical insights to absolute differential calculus and its use in general theory of relativity. The appendix was a beautiful surprise to me. This book, in my view, is equally accessible to general readers (u can skip Appendix-A) and those who are into mathematics.
Personally, the book would have been more exciting to me if the line of mathematical reasoning had extended from works of Gauss to Riemann to Christoffel to Ricci. It sure does mentions the link but I would love to read more about the work of first three mathematicians and how they were useful to the latter. But again, the book is not titled "On the Complete History of Tensor Calculus", so I should limit my expectations.
I am currently learning differential geometry and I got interested in this book as the source of historical background on the field. I enjoyed it a lot and certainly would recommend the book to other interested readers.
[Thank you Sriza for helping me edit this review.]
Displaying 1 of 1 review