Harry Bateman
Encyclopedia
Harry Bateman FRS was an English
mathematician
.
, and in his final year, won a scholarship to Trinity College, Cambridge
. There he distinguished himself in 1903 as Senior Wrangler (tied with P.E. Marrack) and by winning the Smith's Prize
(1905). He studied in Göttingen and Paris, taught at the University of Liverpool and University of Manchester before moving to the US in 1910. First he taught at Bryn Mawr College
and then Johns Hopkins University
. There, working with Frank Morley in geometry, he achieved the Ph.D. In 1917 he took up his permanent position at California Institute of Technology
, then still called Throop Polytechnic Institute.
Eric Temple Bell
says, "Like his contemporaries and immediate predecessors among Cambridge mathematicians of the first decade of this century [1901–1910]... Bateman was thoroughly trained in both pure analysis
and mathematical physics
, and retained an equal interest in both throughout his scientific career."
In 1907 Harry Bateman was lecturing at the University of Liverpool
together with another senior wrangler, Ebenezer Cunningham
. Together they came up with the idea of a conformal group of spacetime which involved an extension of the method of images
.
For his part, in 1910 Bateman published "The transformation of the electrodynamical equations" (Proc. London Math. Soc. 8:223–264). He showed that the Jacobian matrix
of a spacetime
diffeomorphism
which preserves the Maxwell equations is proportional to an orthogonal matrix
, hence conformal. The transformation group
of such transformations has 15 parameters and extends both the Poincaré group
and the Lorentz group
.
In evaluating this paper, one of his students, Clifford Truesdell
, wrote
In 1914 Bateman published The Mathematical Analysis of Electrical and Optical Wave-motion. As Murnaghan says, this book "is unique and characteristic of the man. Into less than 160 small pages is crowded a wealth of information which would take an expert years to digest."
The following year he published a textbook
Differential Equations, and sometime later Partial differential equations of mathematical physics. Bateman is also author of Hydrodynamics and Numerical integration of differential equations.
Harry Bateman wrote two significant articles on the history of applied mathematics:
In his Mathematical Analysis of Electrical and Optical Wave-motion (p. 131) he describes the charged-corpuscle trajectory as follows:
This figure of speech is not to be confused with a string in physics
, for the universes in string theory
have dimensions inflated beyond four, something not found in Bateman's work.
Bateman received many honors for his contributions, including election to the Royal Society
of London
in 1928, election to the National Academy of Sciences
in 1930. He was elected as vice-president of the American Mathematical Society
in 1935. He was on his way to New York
to receive an award from the Institute of Aeronautical Science when he died of coronary thrombosis
. The Harry Bateman Research Instructorships at the California Institute of Technology are named in his honour (see external link below).
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Life and work
Harry Bateman first grew to love mathematics at Manchester Grammar SchoolManchester Grammar School
The Manchester Grammar School is the largest independent day school for boys in the UK . It is based in Manchester, England...
, and in his final year, won a scholarship to Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
. There he distinguished himself in 1903 as Senior Wrangler (tied with P.E. Marrack) and by winning the Smith's Prize
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in theoretical Physics, mathematics and applied mathematics at the University of Cambridge, Cambridge, England.- History :...
(1905). He studied in Göttingen and Paris, taught at the University of Liverpool and University of Manchester before moving to the US in 1910. First he taught at Bryn Mawr College
Bryn Mawr College
Bryn Mawr College is a women's liberal arts college located in Bryn Mawr, a community in Lower Merion Township, Pennsylvania, ten miles west of Philadelphia. The name "Bryn Mawr" means "big hill" in Welsh....
and then Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
. There, working with Frank Morley in geometry, he achieved the Ph.D. In 1917 he took up his permanent position at California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
, then still called Throop Polytechnic Institute.
Eric Temple Bell
Eric Temple Bell
Eric Temple Bell , was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life...
says, "Like his contemporaries and immediate predecessors among Cambridge mathematicians of the first decade of this century [1901–1910]... Bateman was thoroughly trained in both pure analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
and mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, and retained an equal interest in both throughout his scientific career."
In 1907 Harry Bateman was lecturing at the University of Liverpool
University of Liverpool
The University of Liverpool is a teaching and research university in the city of Liverpool, England. It is a member of the Russell Group of large research-intensive universities and the N8 Group for research collaboration. Founded in 1881 , it is also one of the six original "red brick" civic...
together with another senior wrangler, Ebenezer Cunningham
Ebenezer Cunningham
Ebenezer Cunningham was a British mathematician who is remembered for his research and exposition at the dawn of special relativity....
. Together they came up with the idea of a conformal group of spacetime which involved an extension of the method of images
Method of images
See also Method of image charges for applications in electrostatics and magnetostaticsMethod of images is a mathematical tool for solving differential equations in which the domain of the sought function is extended by the addition of its mirror image with respect to a symmetry hyperplane, with...
.
For his part, in 1910 Bateman published "The transformation of the electrodynamical equations" (Proc. London Math. Soc. 8:223–264). He showed that the Jacobian matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
of a spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
diffeomorphism
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth.- Definition :...
which preserves the Maxwell equations is proportional to an orthogonal matrix
Orthogonal matrix
In linear algebra, an orthogonal matrix , is a square matrix with real entries whose columns and rows are orthogonal unit vectors ....
, hence conformal. The transformation group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
of such transformations has 15 parameters and extends both the Poincaré group
Poincaré group
In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime.-Simple explanation:...
and the Lorentz group
Lorentz group
In physics , the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical setting for all physical phenomena...
.
In evaluating this paper, one of his students, Clifford Truesdell
Clifford Truesdell
Clifford Ambrose Truesdell III was an American mathematician, natural philosopher, historian of science, and polemicist.-Life:...
, wrote
- The importance of Bateman's paper lies not in its specific details but in its general approach. Bateman, perhaps influenced by Hilbert’s point of view in mathematical physics as a whole, was the first to see that the basic ideas of electromagnetism were equivalent to statements regarding integrals of differential forms, statements for which Grassmann’s calculus of extension on differentiable manifolds, Poincaré's theories of Stokesian transformations and integral invariants, and Lie’s theory of continuous groups could be fruitfully applied.
In 1914 Bateman published The Mathematical Analysis of Electrical and Optical Wave-motion. As Murnaghan says, this book "is unique and characteristic of the man. Into less than 160 small pages is crowded a wealth of information which would take an expert years to digest."
The following year he published a textbook
Textbook
A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...
Differential Equations, and sometime later Partial differential equations of mathematical physics. Bateman is also author of Hydrodynamics and Numerical integration of differential equations.
Harry Bateman wrote two significant articles on the history of applied mathematics:
- "The influence of tidal theory upon the development of mathematics"
- National Mathematics Magazine 18:14–26 (1943)
- "Hamilton's work in dynamics and its influence on modern thought"
- Scripta MathematicaScripta MathematicaScripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics...
10:51–63 (1944)
- Scripta Mathematica
In his Mathematical Analysis of Electrical and Optical Wave-motion (p. 131) he describes the charged-corpuscle trajectory as follows:
- a corpuscle has a kind of tube or thread attached to it. When the motion of the corpuscle changes a wave or kink runs along the thread; the energy radiated from the corpuscle spreads out in all directions but is concentrated round the thread so that the thread acts as a guiding wire.
This figure of speech is not to be confused with a string in physics
String (physics)
A string is a hypothetical vibrating one-dimensional sub-atomic structure and one of the main objects of study in string theory, a branch of theoretical physics. There are different string theories, many of which are unified by M-theory. A string is an object with a one-dimensional spatial extent,...
, for the universes in string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
have dimensions inflated beyond four, something not found in Bateman's work.
Bateman received many honors for his contributions, including election to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
of London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
in 1928, election to the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1930. He was elected as vice-president of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
in 1935. He was on his way to New York
New York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
to receive an award from the Institute of Aeronautical Science when he died of coronary thrombosis
Thrombosis
Thrombosis is the formation of a blood clot inside a blood vessel, obstructing the flow of blood through the circulatory system. When a blood vessel is injured, the body uses platelets and fibrin to form a blood clot to prevent blood loss...
. The Harry Bateman Research Instructorships at the California Institute of Technology are named in his honour (see external link below).
See also
- Bateman Manuscript ProjectBateman Manuscript ProjectThe Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthur Erdélyi....
- Bateman function
- Bateman polynomialsBateman polynomialsIn mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by . The Bateman–Pasternack polynomials are a generalization introduced by ....
- Bateman transformBateman transformIn the mathematical study of partial differential equation, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables...
Publications
- The Conformal Transformations of a Space of Four Dimensions and their Applications to Geometrical Optics, 1908, Proceedings of the London Mathematical Society, 7, 70-89
External links
- Harry Bateman Research Instructorships
- Mathematical genealogy from Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
.