George David Birkhoff | Academic Influence

George David Birkhoff's AcademicInfluence.com Rankings

George David Birkhoff

Mathematics

#166

Historical Rank

Measure Theory

#114

Historical Rank

mathematics Degrees

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Mathematics

George David Birkhoff's Degrees

PhD Mathematics University of Chicago

Why Is George David Birkhoff Influential?

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According to Wikipedia, George David Birkhoff was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and during his time he was considered by many to be the preeminent American mathematician.

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George David Birkhoff's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Proof of the Ergodic Theorem (1931) (759)
Relativity And Modern Physics (1925) (415)
A Determinant Formula for the Number of Ways of Coloring a Map (404)
Surface transformations and their dynamical applications (1922) (290)
The restricted problem of three bodies (1915) (273)
On the asymptotic character of the solutions of certain linear differential equations containing a parameter (1908) (260)
Boundary value and expansion problems of ordinary linear differential equations (1908) (257)
Proof of Poincaré’s geometric theorem (246)
The Generalized Riemann Problem for Linear Differential Equations and the Allied Problems for Linear Difference and q-Difference Equations (185)
Dynamical systems with two degrees of freedom (1917) (172)
On the Integral Divisors of a n - b n (1904) (172)
General theory of linear difference equations (1911) (147)
Analytic theory of singular difference equations (1933) (141)
An extension of Poincaré's last geometric theorem (1926) (132)
Dynamical Systems with Two Degrees of Freedom. (1917) (126)
On the periodic motions of dynamical systems (1927) (122)
Formal theory of irregular linear difference equations (1930) (114)
Note on the gamma function (1913) (112)
General mean value and remainder theorems with applications to mechanical differentiation and quadrature (108)
The Boundary Problems and Developments Associated with a System of Ordinary Linear Differential Equations of the First Order (101)
The Reducibility of Maps (1913) (99)
Invariant points in function space (94)
Singular points of ordinary linear differential equations (1909) (92)
A Set of Postulates for Plane Geometry, Based on Scale and Protractor (1932) (82)
Proof of a Recurrence Theorem for Strongly Transitive Systems. (1931) (76)
A theorem on matrices of analytic functions (1913) (72)
Structure Analysis of Surface Transformations (71)
Recent Contributions to the Ergodic Theory. (1932) (68)
On the periodic motions near a given periodic motion of a dynamical system (1934) (66)
Physical aspects of dynamical systems (1927) (65)
General Ergodic Theorems. (1939) (63)
Note on a Canonical Form for the Linear q-Difference System. (1941) (49)
One the Solutions of Ordinary Linear Homogeneous Differential Equations of the Third Order (1911) (44)
Matter, Electricity and Gravitation in Flat Space-Time. (1943) (32)
Natural Isoperimetric Conditions in the Calculus of Variations. (1935) (29)
Dynamical Systems (Colloquium Publications) (28)
FIFTY YEARS OF AMERICAN MATHEMATICS. (1938) (28)
Equivalent singular points of ordinary linear differential equations (1913) (28)
Metric Foundations of Geometry. (1941) (25)
RECENT ADVANCES IN DYNAMICS. (1920) (24)
Existence and oscillation theorem for a certain boundary value problem (1909) (22)
What is the Ergodic Theorem (1942) (21)
On a simple type of irregular singular point (1913) (21)
On the Number of Ways of Colouring a Map (1930) (17)
Stability and the Equations of Dynamics (15)
SOME UNSOLVED PROBLEMS OF THEORETICAL DYNAMICS. (1941) (15)
An elementary double inequality for the roots of an algebraic equation having greatest absolute value (1915) (14)
Flat Space-Time and Gravitation. (1944) (13)
Probability and physical systems (1932) (13)
An Ergodic Theorem for General Semi-Groups. (1939) (12)
A theorem on matrices of analytic functions (12)
Note on the expansion problems of ordinary linear differential equations (1913) (12)
On the polynomial expressions for the number of ways of coloring a map (1934) (12)
Generalized Minimax Principle in the Calculus of Variations. (1935) (11)
A simplified treatment of the regular singular point (1910) (11)
Distributive postulates for systems like Boolean algebras (1946) (10)
Infinite products of analytic matrices (1916) (8)
Poincaré's Göttingen Lectures (8)
Dependent Probabilities and Spaces (L). (1938) (8)
Stability of periodic motions (1927) (8)
Stability in Causal Systems (1935) (7)
A New Theory of Vortex Streets. (1952) (7)
Divergent series and singular points of ordinary differential equations (7)
General theory of dynamical systems (1927) (6)
A mathematical approach to ethics (1941) (6)
Some Remarks Concerning Schrödinger's Wave Equation. (1933) (5)
On Birkhoff's New Theory of Gravitation (1944) (5)
Effective Conformal Transformation of Smooth, Simply Connected Domains. (1951) (5)
A MATHEMATICAL CRITIQUE OF SOME PHYSICAL THEORIES. (1927) (5)
Review: E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies; with an Introduction to the Problem of Three Bodies (4)
Intuition, Reason and Faith in Science (1938) (4)
The scientific work of Maxime Bôcher (1919) (4)
Variational principles and applications (1927) (4)
A Theorem on Series of Orthogonal Functions with an Application to Strum-Liouville Series. (1917) (4)
Relation of the theory to earlier aesthetic theories (1932) (3)
The mathematical work of Oliver Dimon Kellogg (1933) (3)
A new criterion of stability (2)
The Hydrogen Atom and the Balmer Formula. (1927) (2)
The New Haven Colloquium Lectures (1911) (2)
The Work of Poincaré on Differential Equations (1934) (2)
Note on Linear Difference and Differential Equations. (1941) (1)
SIR JOSEPH LARMOR AND MODERN MATHEMATICAL PHYSICS. (1943) (1)
The Work of Poincaré on Automorphic Functions (1)
Differential and Integral Calculus (1937) (1)
Note on the expansion of the Green's function (1912) (1)
A Theory of Matter and Electricity. (1927) (1)
CI. Circular plates of variable thickness (1922) (1)
Newton's philosophy of gravitation (0)
Formal aspects of dynamics (1927) (0)
CHAPTER X. FOUR-DIMENSIONAL SPACE-TIME (1927) (0)
Electricity as a fluid (1938) (0)
CHAPTER VI. VECTORS AND TENSORS IN TWO DIMENSIONS (0)
An Introduction to the Theory of Numbers . By G. H. Hardy and E. M. Wright. The Oxford University Press. Octavo: xvi + 403 pp. $8.00. (1939) (0)
CHAPTER V. THE DIATONIC CHORDS (1933) (0)
CHAPTER IX. EARLIER AESTHETIC THEORIES (1933) (0)
CHAPTER VII. ONE-DIMENSIONAL HYDRODYNAMICS (1927) (0)
Geometry of Time and Space . By Alfred A. Robb. vii+408 pp. Cambridge University Press, 1936. (1936) (0)
Topology: Algebraic Topology . By Solomon Lefschetz. vi + 389 pp. Vol. 27. Colloquium Publications of the American Mathematical Society. 1942. $6.00. (1942) (0)
CHAPTER I. THE BASIC FORMULA (1933) (0)
William Fogg Osgood and American Mathematics (1943) (0)
CHAPTER VIII. TENSOR ANALYSIS (1927) (0)
CHAPTER I. CLASSICAL PHYSICS (1927) (0)
Note on a Preceding Paper (1932) (0)
Book Review: Das Relativitätsprinzip@@@Book Review: Raum. Zeit. Materie@@@Book Review: Relativity. The special and the general Theory@@@Book Review: The Theory of Relativity@@@Book Review: Das Relativitätsprinzip@@@Book Review: The Concept of Nature@@@Book Review: Wiskunde, Waarheid, Werkelijkheid (0)
CHAPTER XIV. THE GRAVITATIONAL FIELD (1927) (0)
LIST OF PLATES (1933) (0)
The musical quality and poetry (1932) (0)
CHAPTER VIII. THE MUSICAL QUALITY IN POETRY (1933) (0)
Books on Relativity (1922) (0)
The origin, nature, and influence of relativity : Lowell Institute lectures, Lowell Institute -- Boston and Los Angeles lectures, University of California -- Southern Branch (0)
Application of Poincaré’s geometric theorem (1927) (0)
Existence of periodic motions (1927) (0)
CHAPTER IV. ISOTROPIC AND AEOLOTROPIC SPACE-TIME (1927) (0)
Edward Burr Van Vleck—In memoriam (1944) (0)
CHAPTER II. POLYGONAL FORMS (1933) (0)
CHAPTER VII. MELODY (1933) (0)
The principle of sufficient reason (1941) (0)
CHAPTER XIII. LINEAR TENSOR EQUATIONS (1927) (0)
Ideals in Algebraic Rings. (1934) (0)
CHAPTER XII. ELECTROMAGNETISM (1927) (0)
CHAPTER VI. DIATONIC HARMONY (1933) (0)
CHAPTER II. INTRODUCTION TO SPACE-TIME (1927) (0)
CHAPTER IV. VASE (1933) (0)
CHAPTER IX. GRAVITATION IN TWO-DIMENSIONAL SPACE-TIME (1927) (0)
The problem of three bodies (1927) (0)
An Elementary Treatment of Fourier's Series (1921) (0)
On the Integration of Operators. (1937) (0)
An Introduction to the Theory of Numbers (1939) (0)
CHAPTER XVI. APPLICATIONS IN THE SOLAR FIELD (1927) (0)
CHAPTER Χ. ART AND AESTHETICS (1933) (0)
The visiting lectureship of the American Mathematical Society (0)
Calculus. (Scientific Books: Differential and Integral Calculus) (1937) (0)
The diatonic chords (1932) (0)
CHAPTER III. ORNAMENTS AND TILINGS (1933) (0)
CHAPTER III. THE ISOMETRIC ASSUMPTION (0)
Geometry of Time and Space (1936) (0)
The case of two degrees of freedom (1927) (0)
A Theorem Concerning Uniform Convergence (1905) (0)
CHAPTER XV. THE SOLAR GRAVITATIONAL FIELD (1927) (0)
Theorem Concerning the Singular Points of Ordinary Linear Differential Equations. (1915) (0)
CHAPTER V. DYNAMICS OF A LINEAR SET OF PARTICLES (1927) (0)
CHAPTER XI. DYNAMICS, HYDRODYNAMICS, ELASTICITY (1927) (0)

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