Einstein’s Italian Mathematicians: Ricci, Levi-civita, and the Birth of General Relativity (Monograph Books) by Judith R. Goodstein (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review A wonderfully written chronicle of the lives of two great mathematicians and how their work shaped Einstein’s masterpiece as well as ushering in new fields of mathematics. The book is also an intriguing and insightful portrait of Italy during the period from Italian independence in 1870 until the onset of World War II. –Gino Segre, Physics Department, University of PennsylvaniaGalileo said that mathematics is the language of nature. Einstein might have found himself mute when it came to describing gravity if it weren’t for the mathematics of covariant derivatives developed by Galileo’s countrymen Gregorio Ricci-Curbastro and Tullio Levi-Civita. Judy Goodstein tells their stories and their connection to Einstein with clarity and grace in a most readable book. –Barry Simon, California Institute of TechnologyThe theory of general relativity would never have seen the light without the absolute differential calculus invented by the Italian mathematicians Gregorio Ricci Curbastro and Tullio Levi-Civita. This wonderful book carefully examines the academic, cultural, political, and historical framework in Italy of that time, and explores the deep relation always fed with sincere respect, admiration, and affection between these two great mathematicians at the turn of the twentieth century. –Tullio Ceccherini-Silberstein, Università del Sannio, Benevento, Italy About the Author Judith R. Goodstein, California Institute of Technology, Pasadena, CA.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Primarily covering the lives and the relativity-related mathematics of Gregorio Ricci and Levi-Civita. Very well researched and clear writing. Goodstein describes the environments in which they worked, and provides a vivid picture of their personal and academic backgrounds.

⭐In the fall of 1915, after 3 years wrestling “with a succession of tensors, equations, corrections, and updates”, Einstein was finally coming close to his dream – a natural mathematical theory that would demonstrate the equivalence of gravity and acceleration, opening the door to a world of cosmology far beyond Newton’s laws. Finally, when it all seemed to fit, tried his hand at computing the “perihelion of Mercury” which had baffled astronomer’s for so long. When he realized that his theory of general relativity computed exactly the observed value, “His heart skipped a beat. ‘I was beside myself with joy and excitement for days’, he later told a friend”. He’d hit jackpot, “the strongest emotional experience … of his life”, the masterpiece that to this day is the gold standard for mathematical physics. Einstein was a physicist, not a mathematician, yet he’d gotten his head around a difficult and obscure branch of mathematics. How did this extraordinary development come about? The book at hand gives an eloquent answer to this question by exploring the lives and mathematics of the two Italian mathematicians behind it all, Gregorio Ricci Curbastro and Tullio Levi-Civita. Ricci pioneered the mathematics, now known as differential geometry, building on the foundational work by Riemann (of Riemannian manifold fame), and was later joined by Levi-Civita, the one who actually corresponded with Einstein. Yet it was another mathematician, Marcel Grossman, who acted as the intermediary and first collaborator, who Einstein had turned to for help, and who realized the importance of the work of Ricci and Levi-Civita. Goodstein writes interesting personal and scientific biographies of Ricci and Levi-Civita, illuminating both the mathematical and geo-political developments of the era, ending with a brief overview of the math for mathematical readers. Long ago I’d read an entire book on differential geometry, without fully grasping what it was all about. The fascinating historical context in this book makes the math itself more accessible. It was Einstein and Grossman who adopted the terminology of “tensors” and the “summation” notation, along with “covariant” and “contravariant” tensors, versus the more common word “invariant”. Highly recommended.

⭐I am just amazed on how well she writes, how much she knows and understands about Italy and it’s culture (and byzantine educational system), and her pretty good understanding of some fine points of differential geometry (I suspect she got some help there from her husband). Highly recommended !!

⭐If you’ve studied physics you’ll know about tensors, transformations and relativity. But it’s all neatly packaged for you now. Early 20th C and young Einstein has no idea how to generalise his E=mc^2 ‘special relativity’ which should be called (Euclidean spacetime invariance) to non-inertial frames, non-Euclidian geometry ie curved space ie gravity. A circle of friends and fellow academics point him to the work of italian mathematical physicists who extended ideas of Riemann, Gauss and Christoffel, and whose work, re-packaged and with Einstein and Grossman’s inventive notation, led to the equations of General Relativity whose consequences continue to surprise to this day. Meticulously researched and written, this book is a valuable contribution to Einsteinology and history of science.

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