Tensor - History

History

The concepts of later tensor analysis arose from the work of Carl Friedrich Gauss in differential geometry, and the formulation was much influenced by the theory of algebraic forms and invariants developed during the middle of the nineteenth century. The word "tensor" itself was introduced in 1846 by William Rowan Hamilton to describe something different from what is now meant by a tensor. The contemporary usage was brought in by Woldemar Voigt in 1898.

Tensor calculus was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential calculus, and originally presented by Ricci in 1892. It was made accessible to many mathematicians by the publication of Ricci and Tullio Levi-Civita's 1900 classic text Méthodes de calcul différentiel absolu et leurs applications (Methods of absolute differential calculus and their applications).

In the 20th century, the subject came to be known as tensor analysis, and achieved broader acceptance with the introduction of Einstein's theory of general relativity, around 1915. General relativity is formulated completely in the language of tensors. Einstein had learned about them, with great difficulty, from the geometer Marcel Grossmann. Levi-Civita then initiated a correspondence with Einstein to correct mistakes Einstein had made in his use of tensor analysis. The correspondence lasted 1915–17, and was characterized by mutual respect:

I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot. —Albert Einstein, The Italian Mathematicians of Relativity

Tensors were also found to be useful in other fields such as continuum mechanics. Some well-known examples of tensors in differential geometry are quadratic forms such as metric tensors, and the Riemann curvature tensor. The exterior algebra of Hermann Grassmann, from the middle of the nineteenth century, is itself a tensor theory, and highly geometric, but it was some time before it was seen, with the theory of differential forms, as naturally unified with tensor calculus. The work of Élie Cartan made differential forms one of the basic kinds of tensors used in mathematics.

From about the 1920s onwards, it was realised that tensors play a basic role in algebraic topology (for example in the Künneth theorem). Correspondingly there are types of tensors at work in many branches of abstract algebra, particularly in homological algebra and representation theory. Multilinear algebra can be developed in greater generality than for scalars coming from a field, but the theory is then certainly less geometric, and computations more technical and less algorithmic. Tensors are generalized within category theory by means of the concept of monoidal category, from the 1960s.

Read more about this topic:  Tensor

Other articles related to "history":

Xia Dynasty - Modern Skepticism
... The Skeptical School of early Chinese history, started by Gu Jiegang in the 1920s, was the first group of scholars within China to seriously question the traditional story of its early history "the later the time ... early Chinese history is a tale told and retold for generations, during which new elements were added to the front end" ...
Voltaire - Works - Historical
... History of Charles XII, King of Sweden (1731) The Age of Louis XIV (1751) The Age of Louis XV (1746–1752) Annals of the Empire – Charlemagne, A.D ... on the Manners of Nations (or 'Universal History') (1756) History of the Russian Empire Under Peter the Great (Vol ... II 1763) History of the Parliament of Paris (1769) ...
Spain - History - Fall of Muslim Rule and Unification
... The breakup of Al-Andalus into the competing taifa kingdoms helped the long embattled Iberian Christian kingdoms gain the initiative ... The capture of the strategically central city of Toledo in 1085 marked a significant shift in the balance of power in favour of the Christian kingdoms ...
Casino - History of Gambling Houses
... form or another has been seen in almost every society in history ... the Ancient Greeks and Romans to Napoleon's France and Elizabethan England, much of history is filled with stories of entertainment based on games of chance ... In American history, early gambling establishments were known as saloons ...
History of Computing
... The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate ...

Famous quotes containing the word history:

    The greatest honor history can bestow is that of peacemaker.
    Richard M. Nixon (1913–1995)

    The history of his present majesty, is a history of unremitting injuries and usurpations ... all of which have in direct object the establishment of an absolute tyranny over these states. To prove this, let facts be submitted to a candid world, for the truth of which we pledge a faith yet unsullied by falsehood.
    Thomas Jefferson (1743–1826)

    The reverence for the Scriptures is an element of civilization, for thus has the history of the world been preserved, and is preserved.
    Ralph Waldo Emerson (1803–1882)