Search Results for tensor*

Biographies

1. Schmidt Harry biography
   
   • After Schmidt died his colleagues completed the manuscript he was writing giving an introduction to vector and tensors.
     
   • This was published as Einfuhrung in die Vektor und Tensorrechnung unter besonderer Berucksichtigung ihrer physikalischen Bedeutung (1953).
     
   • The third chapter deals briefly with tensors as vector triples and as matrices, using the stress tensor as an illustration.
     

2. Christoffel biography
   
   • Christoffel published papers on function theory including conformal mappings, geometry and tensor analysis, Riemann's o-function, the theory of invariants, orthogonal polynomials and continued fractions, differential equations and potential theory, light, and shock waves.
     
   • He wrote important papers which contributed to the development of the tensor calculus of C G Ricci-Curbastro and Tullio Levi-Civita.
     
   • The Christoffel symbols [ij,k] which he introduced are fundamental in the study of tensor analysis.
     
   • The procedure Christoffel employed in his solution of the equivalence problem is what Gregorio Ricci-Curbastro later called covariant differentiation, Christoffel also used the latter concept to define the basic Riemann-Christoffel curvature tensor.
     
   • Indeed this influence is clearly seen since this allowed Ricci-Curbastro and Levi-Civita to develop a coordinate free differential calculus which Einstein, with the help of Grossmann, turned into the tensor analysis mathematical foundation of general relativity.
     
   • Christoffel not only contributed to all these fields, but his interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light.
     

3. Grothendieck biography
   
   • He presented his doctoral thesis Produits tensoriels topologiques et espaces nucleaires.
     
   • The mere enumeration of Grothendieck's best known contributions is overwhelming: topological tensor products and nuclear spaces, sheaf cohomology as derived functors, schemes, K-theory and Grothendieck-Riemann-Roch, the emphasis on working relative to a base, defining and constructing geometric objects via the functors they are to represent, fibred categories and descent, stacks, Grothendieck topologies (sites) and topoi, derived categories, formalisms of local and global duality (the 'six operations'), etale cohomology and the cohomological interpretation of L-functions, crystalline cohomology, 'standard conjectures', motives and the 'yoga of weights', tensor categories and motivic Galois groups.
     

4. Levi-Civita biography
   
   • He wrote a dissertation, which was supervised by Ricci-Curbastro, on absolute invariants but this also marks the beginning of his use of the tensor calculus [Historia Math.
     
   • In 1886 he published a famous paper in which he developed the calculus of tensors, following on the work of Christoffel, including covariant differentiation.
     
   • In 1900 he published, jointly with Ricci-Curbastro, the theory of tensors in Methodes de calcul differential absolu et leures applications in a form which was used by Einstein 15 years later.
     

5. Littlewood Dudley biography
   
   • interest in invariant theory had flagged somewhat, one reason for this being the introduction of tensors.
     
   • Another reason was certainly the work of Hilbert, but Littlewood tried to remedy the "tensor reason" in a series of papers on tensors and invariant theory.
     

6. Eisenhart biography
   
   • Important contributions to it were made by Bianchi, Beltrami, Christoffel, Schur, Voss, and others, and Ricci-Curbastro coordinated and extended the theory with the use of tensor analysis and his absolute calculus.
     
   • In 1933 Eisenhart published Continuous Groups of Transformations which continues the work of his earlier books looking at Lie's theory using the methods of the tensor calculus and differential geometry.
     
   • The new chapter began about 1920 with the extended studies of tensor analysis, Riemannian geometry and its generalizations, and the application of the theory of continuous groups to the new physical theories.
     

7. Schouten biography
   
   • Schouten's doctoral thesis, presented in 1914, was on tensor analysis, a topic he worked on all his life.
     
   • Schouten produced 180 papers and 6 books on tensor analysis.
     
   • An important figure in the development of the tensor calculus, Schouten was president of the 1954 International Congress of Mathematicians at Amsterdam.
     

8. Kagan biography
   
   • In 1927, Kagan organised a seminar on vector and tensor analysis.
     
   • He founded a publication associated with this seminar Transactions of the seminar on Vector and Tensor Analysis with its applications to Geometry, Mechanics and Physics in 1933.
     
   • Kagan studied tensor differential geometry after going to Moscow because of an interest in relativity.
     

9. Milne-Thomson biography
   
   • The paper treats compressible or incompressible fluids of constant viscosity and finds the density, velocity and stress distribution in terms of an arbitrary function and a second rank arbitrary tensor.
     
   • He gave two lectures in Madrid in 1951 on the elements of finite elasticity theory, the first lecture covering the topics of deformation tensors, stress, equations of motion, and energy.
     

10. Einstein biography
    
    • About 1912, Einstein began a new phase of his gravitational research, with the help of his mathematician friend Marcel Grossmann, by expressing his work in terms of the tensor calculus of Tullio Levi-Civita and Gregorio Ricci-Curbastro.
      
    • I never realised that so many Americans were interested in tensor analysis.
      

11. Sasaki biography
    
    • He discovered a tensor, now called Weyl's conformal curvature tensor, whose vanishing is a necessary condition that the space be conformally flat, that is to say, that the space can be mapped conformally on the Euclidean space.
      

12. Daubechies biography
    
    • In 1978 An application of hyperdifferential operators to holomorphic quantization appeared, then a number of papers written jointly with Dirk Aerts: A characterization of subsystems in physics; Physical justification for using the tensor product to describe two quantum systems as one joint system; A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation; and A connection between propositional systems in Hilbert spaces and von Neumann algebras.
      
    • One of the basic rules of Hilbert space quantum mechanics is that when two physical systems, say S1 and S, are viewed as the pieces of a compound system S, then the Hilbert space to be associated to S is the tensor product of the Hilbert spaces H1 and H associated to S1 and S.
      

13. Infeld biography
    
    • He used tensor notation at that time a novelty to me.
      
    • (Infeld liked to quip that mankind can be classified into two categories: those who knew what a tensor was, and all the rest; and he would add "I don't much care about that rest".) .
      

14. Vagner biography
    
    • His research activities were connected with the Seminar on Vector and Tensor Analysis at Moscow University.
      
    • The theory is applied to affine hyperspheres (all normals through one point) and hyperquadrics (Darboux tensor vanishes).
      

15. Mathisson biography
    
    • Mathisson proved that the variational equation can be solved when it has been defined so that the equations to be imposed upon the characteristic tensor will be compatible with the variations allowed in the fields.
      
    • The transition from the characteristic tensor to the dynamical variables is conveyed by an analysis of the physical meaning of the constituents.
      

16. Frenkel biography
    
    • He had already published a number of major books: The structure of matter I (1922), The theory of relativity (1923), The structure of matter II (1924), Vector and tensor analysis (1925), Electricity and matter (1925), and Electrodynamics (1926).
      
    • Other major books included Analytical mechanics (1935) and Theoretical mechanics based on vector and tensor analysis (1940).
      

17. Carmeli biography
    
    • We represent the spin coefficients and the Riemann tensor in the form of linear combinations of the infinitesimal generators of the group SL(2, C).
      
    • The spin coefficients take the role of the Yang-Mills-like potentials, whereas the Riemann tensor takes the role of the fields.
      

18. Spencer Tony biography
    
    • The authors use general tensors associated with a curvilinear coordinate system moving with the body.
      
    • After introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress, the author examines the mathematical statements of the laws of conservation of mass, momentum and energy and the formulation of the mechanical constitutive equations for various classes of fluids and solids.
      

19. Van Kampen biography
    
    • Schouten worked all his life on tensor analysis and although this seems quite far removed from the topics that van Kampen had been undertaking research on, nevertheless he collaborated with Schouten on three papers on tensor analysis, published in 1930, 1931 and 1933.
      

20. Nikodym biography
    
    • Some of his other books were: Introduction to differential calculus, (Warsaw, 1936) (jointly with his wife), Theory of tensors with applications to geometry and mathematical physics, I, (Warsaw, 1938), Differential Equations, (Poznan, 1949).
      
    • Three of other his books: the second volume of Theory of Tensors and two volumes of Mechanics disappeared during World War II.
      

21. Golab biography
    
    • In 1956 Golab published the book Tensor calculus (Polish).
      
    • This is a careful book, in the classical style and the usual best traditions of the Polish school, on the Tensor Calculus, written from a geometrical point of view, and intended for students of Physics and Engineering as well as those of Mathematics.
      

22. Struik biography
    
    • Struik decided to change to the topic he was studying with Schouten, tensor analysis, for his doctoral thesis and he presented his dissertation on applications of tensor methods to Riemannian manifolds in 1922.
      

23. Ricci-Curbastro biography
    
    • Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity.
      

24. Du Val biography
    
    • He published on the De Sitter model of the universe and Grassmann's tensor calculus.
      

25. Kostrikin biography
    
    • Tensor products.
      

26. Coolidge biography
    
    • A great number of special topics are briefly or amply discussed, from the geometry of the spider's web to modern criticism of enumerative geometry, Douglas' work on the Plateau problem, quaternions and some tensor analysis.
      

27. Frobenius biography
    
    • Over the years 1897-1899 Frobenius published two papers on group representations, one on induced characters, and one on tensor product of characters.
      

28. Pars biography
    
    • His prize essay was entitled Vector and Tensor Fields and was in two parts.
      

29. Penrose biography
    
    • of the mathematical apparatus of gravitation theory, with emphasis on the geometrical theory of the Riemann tensor.
      

30. Weatherburn biography
    
    • He published An Introduction to Riemannian Geometry and the Tensor Calculus in 1938 and it was reissued in 1966.
      

31. Seidel Jaap biography
    
    • Spherical designs and tensors.
      

32. Love biography
    
    • The treatment throughout is severely analytical, but it took form too early to incorporate the tensor calculus.
      

33. Zaremba biography
    
    • He showed how to make tensorial definitions of stress rate that were invariant to spin and thus were suitable for use in relations between the stress history and the deformation history of a material.
      

34. Jeffreys biography
    
    • In pure mathematics he studied operational methods (where he improved on Heaviside's operational calculus and Laplace transforms), cartesian tensors and asymptotic approximations.
      

35. Chevalley biography
    
    • But at least two things, now clearly of central importance, were completely missing: the tensor product of modules, and the generalization of every object to a graded object.
      

36. Nash biography
    
    • Soon, however, his growing interest in mathematics had him take courses on tensor calculus and relativity.
      

37. Bromwich biography
    
    • Some of this work is described in [Tensor (NS) 55 (2) (1994), 192-196.',6)">6] where its history is explained:- .
      

38. Eilenberg biography
    
    • The basic principles of homological algebra, and in particular the full functorial control over the manipulation of tensor products and modules of operator homomorphisms, will undoubtedly become standard algebraic technique already on the elementary level.
      

39. Warner biography
    
    • The following year her second paper appeared The homology of tensor products and her next two papers, published in 1975 and 1976, were the results of work she undertook while in Malaysia, the last overseas posting her husband was to have, during 1974-76.
      

40. Kolosov biography
    
    • In 1908 Kolosov began working on the theory of elasticity and his doctoral thesis (equivalent to the German habilitation standard) contains Kolosov's formulas expressing the components of the stress tensor and the displacement vector in terms of two analytic functions of one complex variable.
      

41. Northcott biography
    
    • It focuses on the construction of the tensor, exterior and symmetric algebras of a module over a commutative ring and, by bringing out some of their relationships, develops the theory of several associated structures.
      

42. Yano biography
    
    • Here he collaborated with J A Schouten and they published four joint papers on almost complex manifolds and the Nijenhuis tensor.
      

43. Mises biography
    
    • He introduced a stress tensor which was used in the study of the strength of materials.
      

44. Grossmann biography
    
    • Grossmann discovered the relevance of the tensor calculus of Christoffel, Ricci-Curbastro and Levi-Civita to relativity.
      

45. Beltrami biography
    
    • Beltrami indirectly influenced the development of tensor analysis by providing a basis for the ideas of Ricci-Curbastro and Levi-Civita on the topic.
      

46. Riemann biography
    
    • In fact the main point of this part of Riemann's lecture was the definition of the curvature tensor.
      

47. Murnaghan biography
    
    • Over the period up to 1936, in addition to the major texts we have already mentioned, Murnaghan undertook research and published papers on a wide variety of topics such as electrodynamics, relativity, tensor analysis, elasticity, dynamics, aerodynamics, quantum mechanics, and celestial mechanics.
      

48. Schatten biography
    
    • Schatten's principal mathematical achievement was that of initiating the study of tensor products of Banach spaces.
      

49. Cohn biography
    
    • He generalised a theorem due to Magnus, and worked on the structure of tensor spaces.
      

History Topics

1. General relativity
   
   • In 1913 Einstein and Grossmann published a joint paper where the tensor calculus of Ricci and Levi-Civita is employed to make further advances.
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   • Grossmann gave Einstein the Riemann-Christoffel tensor which, together with the Ricci tensor which can be derived from it, were to become the major tools in the future theory.
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   • Progress was being made in that gravitation was described for the first time by the metric tensor but still the theory was not right.
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   • Before that however he had written a paper in October 1914 nearly half of which is a treatise on tensor analysis and differential geometry.
     
   • This paper led to a correspondence between Einstein and Levi-Civita in which Levi-Civita pointed out technical errors in Einstein's work on tensors.
     

2. Quantum mechanics history
   
   • It had been Christoffel's discovery of 'covariant differentiation' in 1869 which let Ricci extend the theory of tensor analysis to Riemannian space of n dimensions.
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   • The Ricci and Levi-Civita definitions were thought to give the most general formulation of a tensor.
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   • Up to this stage quantum theory was set up in Euclidean space and used Cartesian tensors of linear and angular momentum.
     
   • Pauli realised that spin, one of the states proposed by Bose, corresponded to a new kind of tensor, one not covered by the Ricci and Levi-Civita work of 1901.
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3. Bolzano publications.html
   
   • algebra y Analysis, Vectorial y Tensorial [Vector and Tensor Algebra and Analysis] 4 (Friedrich Frommann Verlag (Gunther Holzboog), Stuttgart, 1982).
     

4. Bourbaki 2
   
   • This chapter on multilinear algebra covers tensor products, tensor spaces, Grassmann algebra and determinants.
     

5. Ledermann interview
   
   • One of these things I picked on, it had something to do with tensors of matrices, quite a complicated problem which was not entirely correct, so I did my thesis on this Turnbull and Aitken book.
     

6. Special relativity
   
   • Also in 1908 Minkowski published an important paper on relativity, presenting the Maxwell-Lorentz equations in tensor form.
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Famous Curves

Societies etc

1. BMC 1974
   
   • Epstein, D B ANatural tensors in Riemannian manifolds .
     

2. BMC 1980
   

3. European Mathematical Society Prizes
   
   • This enabled him to extend Hadwiger's theorem to tensor valued valuations.
     

References

1. References for Einstein
   
   • T Levi-Chivita, Analytic expression for the gravitation tensor in Einstein's theory (Russian), in Einstein collection, 1980-1981 'Nauka' (Moscow, 1985), 191-203, 335.
     
   • G Maltese, The rejection of the Ricci tensor in Einstein's first tensorial theory of gravitation, Arch.
     

2. References for Schouten
   
   • A Nijenhuis, J A Schouten : A Master at Tensors, Nieuw archief voor wiskunde 20 (1972), 1-19.
     
   • D J Struik, J A Schouten and the tensor calculus, Nieuw Arch.
     

3. References for Ricci-Curbastro
   
   • D J Struik, From Riemann to Ricci : the origins of the tensor calculus, in Analysis, geometry and groups : a Riemann legacy volume (Palm Harbor, FL, 1993), 657--674.
     
   • L Dell'Aglio, The concept of tensor in Ricci-Curbastro (Italian), Boll.
     

4. References for Levi-Civita
   
   • D J Struik, Schouten, Levi-Civita, and the emergence of tensor calculus, in The history of modern mathematics, Vol.
     

5. References for Schatten
   
   • W A Light and E W Cheney, Approximation Theory in Tensor Product Spaces (Berlin, 1985) .
     

6. References for Ruse
   
   • A Kawaguchi, Professor Harold Stanley Ruse, Tensor (N.S.) 29 (3) (1975), i.
     

7. References for Bromwich
   
   • J D Zund and J M Wilkes, Bromwich's method for solving the source-free Maxwell equations, Tensor (NS) 55 (2) (1994), 192-196.
     

8. References for Davies
   
   • A Kawaguchi, Professor Evan Tom Davies, Tensor (N.S.) 28 (1974), i-ii.
     

Additional material

1. H S Ruse papers
   
   • On the line-geometry of the Riemann tensor (1944).
     
   • When Vn is Riemannian the metric tensor gjk and Riemann tensor Rijkl define in each Sn-1 a quadric and a quadratic line complex, respectively.
     
   • Sets of vectors in a V defined by the Riemann tensor (1944).
     
   • J L Vanderslice writes: The components of the Riemann tensor at a nonsingular point of a Riemannian Vn define a quadratic complex in the space at infinity in the affine tangent space An associated with the point.
     
   • Multivectors and catalytic tensors (1947).
     
   • Light is thrown on the nature of catalytic tensors, and we have an illustration of the value of geometric methods in discovering tensor formulae which involve covariant derivatives.
     
   • Tensor extensions of metrisable local Lie groups (1959).
     
   • Then A tensor L is a Lie algebra and hence corresponds to a Lie group G(A tensor L).
     
   • Assume the Lie group G(L) has a left and right invariant non-degenerate Riemann metric; when will a group with Lie algebra A tensor L have the same property? The author shows that if we restrict ourselves to local groups, the existence of the desired Riemann metric on the local group is implied by the existence of a non-singular bilinear form on A.
     

2. Levi-Civita: 'Lezioni di calcolo differenziale assoluto
   
   • In 1925 Levi-Civita published Lezioni di calcolo differenziale assoluto and, two years later an English translation appeared entitled The Absolute Differential Calculus (Calculus of Tensors).
     
   • A similar standpoint was subsequently adopted by the most distinguished workers in the field of general relativity, in particular by Weyl, Laue, Eddington, and Birkhoff, all of whom made conspicuous original contributions, both of idea and of method, to the physical theories, in addition to useful and elegant developments of the tensor calculus.
     
   • For instance, the definition of a tensor, and some algebraic anticipations of the results intended to simplify the proofs, are to be found in Weyl, Laue, and Marais, all of whom, like Eddington, establish a more or less intimate connection between co-variant differentiation and parallelism.
     
   • But the association with the algebraico-tensorial notation and with the elements of differential geometry is always less detailed and systematic than what I tried to establish in my lectures.
     

3. Eddington: 'Mathematical Theory of Relativity' Introduction
   
   • It might well seem impossible to realise so comprehensive an outlook; but we shall find that the mathematical calculus of tensors does represent and deal with world-conditions precisely in this way.
     
   • A tensor expresses simultaneously the whole group of measure-numbers associated with any world-condition; and machinery is provided for keeping the various codes distinct.
     
   • For this reason the somewhat difficult tensor calculus is not to be regarded as an evil necessity in this subject, which ought if possible to be replaced by simpler analytical devices; our knowledge of conditions in the external world, as it comes to us through observation and experiment, is precisely of the kind which can be expressed by a tensor and not otherwise.
     
   • And, just as in arithmetic we can deal freely with a billion objects without trying to visualise the enormous collection; so the tensor calculus enables us to deal with the world-condition in the totality of its aspects without attempting to picture it.
     

4. EMS obituary
   
   • At Padua, one of his Professors had been Gregorio Ricci-Curbastro, who in 1892 had published the first work on the subject now often known as tensor analysis.
     
   • Certainly he himself never fell a victim to the fascinations of notation, which, among some tensorists, led to a tangled undergrowth of symbolism which rendered their work all but unreadable.
     
   • By his early work with Ricci on tensor analysis and by his later discovery of infinitesimal parallelism, Levi-Civita laid the foundations both for relativity and for the establishment of differential geometry as one of the great branches of modern mathematics.
     

5. Donald C Spencer's publications
   
   • G F D Duff and D C Spencer, Harmonic tensors on manifolds with boundary, Proc.
     
   • G F D Duff and D C Spencer, Harmonic tensors on Riemannian manifolds with boundary, Ann.
     
   • P R Garabedian and D C Spencer, A complex tensor calculus for Kahler manifolds, Acta Math.
     

6. Tullio Levi-Civita
   

7. Levi-Civita: 'Absolute Differential Calculus
   
   • In 1925 Levi-Civita published Lezioni di calcolo differenziale assoluto and, two years later an English translation appeared entitled The Absolute Differential Calculus (Calculus of Tensors).
     
   • (Calculus of Tensors) .
     
   • This method has seemed to me to be preferable to the procedure of enunciating the postulates of relativistic Mechanics in abstract tensorial form, which is so comprehensive in physical content as to be almost inaccessible to ordinary intuition, except with ample comment and illustration.
     

8. Levi-Civita.html
   
   • At Padua, one of his Professors had been Gregorio Ricci-Curbastro, who in 1892 had published the first work on the subject now often known as tensor analysis.
     
   • Certainly he himself never fell a victim to the fascinations of notation, which, among some tensorists, led to a tangled undergrowth of symbolism which rendered their work all but unreadable.
     
   • By his early work with Ricci on tensor analysis and by his later discovery of infinitesimal parallelism, Levi-Civita laid the foundations both for relativity and for the establishment of differential geometry as one of the great branches of modern mathematics.
     

9. Bolzano's publications
   
   • algebra y Analysis, Vectorial y Tensorial [Vector and Tensor Algebra and Analysis] 4 (Friedrich Frommann Verlag (Gunther Holzboog), Stuttgart, 1982).
     

10. Oswald Veblen Publications
    
    • (c) (With T Y Thomas) "Extensions of Relative Tensors", Trans.
      
    • 1928 (a) "Projective Tensors and Connections", Proc.
      
    • (b) "Conformal Tensors and Connections", Proc.
      

11. Malcev: 'Foundations of Linear Algebra' Introduction
    
    • Linear algebra proper usually encompasses linear and bilinear forms, and the very beginnings of the theory of multilinear forms as tensor algebras.
      
    • At about the same time the development of differential geometry for many -dimensional spaces and of the theory of transformations of algebraic forms of higher powers led to the creation of the tensor calculus, upon which was built the theory of relativity.
      

12. G C McVittie papers
    
    • J L Synge writes: The author employs the technique of tensor calculus to transform the equations of classical hydrodynamics to moving curvilinear coordinates.
      
    • H P Robertson writes: The first three of the five chapters present a rapid survey of our knowledge of extra-galactic nebulae, of the tensor calculus and of the principles of the general theory of relativity.
      

13. Sheppard Papers
    
    • From Determinant to Tensor.
      

14. Whittaker EMS Obituary.html
    
    • His interest in Relativity manifested itself also at the undergraduate level, for the Honours course entitled Higher Algebra and Geometry contained neither Algebra nor Geometry in the ordinary sense of these terms but comprised Tensor Calculus with Riemannian Geometry and its generalisations.
      

15. EMS obituary
    
    • Unlike Einstein's theory, it was based on flat space-time and involved a gravitational tensor potential governed by a linear differential equation.
      

16. Caius Iacob: 'Applied mathematics and mechanics
    
    • Generalizations concerning the tensor of inertia of a system of mass points.
      

17. Zariski and Samuel: 'Commutative Algebra
    
    • The last two sections deal respectively with tensor products of rings and free joins of integral domains.
      

18. H Weyl: 'Theory of groups and quantum mechanics'Preface to Second Edition
    
    • This extension already leads so far away from the fundamental purpose of the book that I felt forced to omit the formulation of the quantum laws in accordance with the general theory of relativity, as developed by V Fock and myself, in spite of its desirability for the deduction of the energy-momentum tensor.
      

19. G H Hardy's schedule of lectures in the USA
    
    • He and Milne were two of the four lecturers giving courses at a symposium on theoretical physics at the University of Michigan, 24 June-16 August, 1929: Milne spoke on problems in astrophysics and vector and tensor methods in statics and dynamics; Dirac gave an introduction to quantum mechanics.
      

20. Herstein: Preface to 'Topics in algebra
    
    • Likewise, there is no mention of tensor products or related constructions.
      

Quotations

Chronology

1. Mathematical Chronology
   
   • Levi-Civita publishes a paper developing the calculus of tensors.
     
   • Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.
     

2. Chronology for 1890 to 1900
   
   • Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.
     

3. Chronology for 1900 to 1910
   
   • Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.
     

4. Chronology for 1880 to 1890
   
   • Levi-Civita publishes a paper developing the calculus of tensors.