Editing Harry Bateman

{{short description|British-American mathematician}}
{{for|the artist|Harry Bateman (artist)}}
{{EngvarB|date=August 2014}}
{{Use dmy dates|date=August 2014|cs1-dates=y}}
{{Infobox scientist
| name              = Harry Bateman
| image             = Harry Bateman sketch 1931.png
| caption           = 1931 drawing of Harry Bateman
| birth_date        = {{birth date|df=yes|1882|05|29}}
| birth_place       = [[Manchester, England|Manchester]], England
| death_date        = {{death date and age|df=yes|1946|01|21|1882|05|29}}
| death_place       = Milford, Utah, USA
| fields            = [[Geometrical optics]]<br>[[Partial differential equation]]s<br>[[Fluid dynamics]]<br>[[Electromagnetism]]
| workplaces        = [[Bryn Mawr College]]<br />[[Johns Hopkins University]]<br />[[California Institute of Technology]]
| education         = {{nowrap|[[Trinity College, Cambridge]] ([[Bachelor of Arts|BA]], [[Master of Arts (Oxford, Cambridge, and Dublin)|MA]])<br />[[Johns Hopkins University]] ([[PhD]])}}
| thesis_title      = The Quartic Curve and {{nowrap|Its Inscribed Configurations}}
| thesis_url        = https://www.jstor.org/stable/2370369
| thesis_year       = 1913
| doctoral_advisor  = [[Frank Morley]]
| doctoral_students = [[Clifford Truesdell]]<br>[[Howard P. Robertson]]<br>[[Albert George Wilson]]
| known_for         = [[Bateman Manuscript Project]]<br>[[Burgers' equation|Bateman–Burgers equation]]<br>[[Bateman equation]]<br>[[Bateman function]]<br>[[Bateman polynomials]]<br>[[Bateman transform]]
| awards            = [[Senior Wrangler (University of Cambridge)|Senior Wrangler]] (1903)<br>[[Smith's Prize]] (1905)<br>[[Gibbs Lecture]] (1943)
}}

'''Harry Bateman''' [[Fellow of the Royal Society|FRS]]<ref name="Erdélyi_1947" /> (29 May 1882 – 21 January 1946) was an English [[mathematician]] with a specialty in [[differential equation]]s of [[mathematical physics]].<ref name="Erdélyi_1946" /><ref name="Murnaghan_1948" /> With [[Ebenezer Cunningham]], he expanded the views of spacetime symmetry of Lorentz and Poincare to a more expansive [[conformal group of spacetime]] leaving [[Maxwell's equations]] invariant. Moving to the US, he obtained a Ph.D. in geometry with [[Frank Morley]] and became a professor of mathematics at [[California Institute of Technology]]. There he taught [[fluid dynamics]] to students going into [[aerodynamics]] with [[Theodore von Karman]]. Bateman made a broad survey of applied differential equations in his [[Gibbs Lecture]] in 1943 titled, "The control of an elastic fluid".

==Biography==
Bateman was born in [[Manchester]], England, on 29 May 1882. He first gained an interest in mathematics during his time at [[Manchester Grammar School]]. In his final year, he won a scholarship to [[Trinity College, Cambridge]]. Bateman studied with coach [[Robert Alfred Herman]] to prepare for the [[Cambridge Mathematical Tripos]]. He distinguished himself in 1903 as [[Wrangler (University of Cambridge)|Senior Wrangler]] (tied with P.E. Marrack) and by winning the [[Smith's Prize]] (1905).<ref name="acad" />

His first paper, "The determination of curves satisfying given conditions", was published when he was still an undergraduate student.<ref name="PCPS_1903" /> He studied in Göttingen and Paris, and taught at the University of Liverpool and University of Manchester. After moving to the US in 1910, he taught at [[Bryn Mawr College]] and then [[Johns Hopkins University]]. There, working with [[Frank Morley]] in geometry, he achieved his Ph.D., prior to which he had already published more than 60 papers, including some of his celebrated papers. In 1917, he took up his permanent position at the [[California Institute of Technology]], which was then known as the "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 [[mathematical analysis|pure analysis]] and [[mathematical physics]], and retained an equal interest in both throughout his scientific career."<ref name="Bell_1946" />

[[Theodore von Kármán]] was called in as an advisor for a projected aeronautics laboratory at Caltech and later gave this appraisal of Bateman:<ref name="Kármán_1967" />
{{blockquote|In 1926 Cal Tech{{sic}} had only a minor interest in [[aeronautics]]. The professorship that came nearest to aeronautics was occupied by a shy, meticulous Englishman, Dr. Harry Bateman. He was an applied mathematician from Cambridge who worked in the field of [[fluid mechanics]]. He seemed to know everything but did nothing important. I liked him.}}

Harry Bateman married Ethel Horner in 1912 and had a son named Harry Graham, who died as a child. Later, the couple adopted a daughter named Joan Margaret. He died on his way to New York in 1946 of [[coronary thrombosis]].

==Scientific contributions==
In 1907, Harry Bateman was lecturing at the [[University of Liverpool]] together with another senior wrangler, [[Ebenezer Cunningham]]. In 1908, together they came up with the idea of a [[conformal group of spacetime]] (now usually denoted as {{math|C(1,3)}})<ref name="Kosyakov_2007" /> which involved an extension of the [[method of images]].<ref name="Warwick_2003" />

[[File:DecayChain241Pu-eng.svg|thumb|Quantity calculation with the Bateman function for 241Pu]]
In nuclear physics, the [[Bateman equation]] is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 and the analytical solution was provided by Harry Bateman in 1910.<ref>Bateman, H. (1910, June). The solution of a system of differential equations occurring in the theory of radioactive transformations. In Proc. Cambridge Philos. Soc (Vol. 15, No. pt V, pp. 423–427) [https://archive.org/details/cbarchive_122715_solutionofasystemofdifferentia1843]</ref>

For his part, in 1910 Bateman published ''[[:s:The Transformation of the Electrodynamical Equations|The Transformation of the Electrodynamical Equations]]''.<ref name="Bateman_1910" /> He showed that the [[Jacobian matrix and determinant|Jacobian]] [[Matrix (mathematics)|matrix]] of a [[spacetime]] [[diffeomorphism]] which preserves the [[Maxwell equations]] is proportional to an [[orthogonal matrix]], hence [[conformal transformation|conformal]]. The transformation [[Lie group|group]] of such transformations has 15 parameters and extends both the [[Poincaré group]] and the [[Lorentz group]]. Bateman called the elements of this group [[spherical wave transformation]]s.<ref name="Bateman_1909" />

In evaluating this paper, one of his students, [[Clifford Truesdell]], wrote:
{{blockquote|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 form]]s, 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.<ref name="Truesdell_1984" />}}
Bateman was the first to apply [[Laplace transform]] to the integral equation in 1906. He submitted a detailed report on integral equations in 1911 to the British association for the advancement of science.<ref name="Bateman_1911" /> [[Horace Lamb]] in his 1910 paper<ref name="Lamb_1910" /> solved an integral equation 
:<math>2\int_0^\infty f(y-\zeta^2)\,d\zeta = F(y)</math>  
as a double integral, but in his footnote he says, "Mr. H. Bateman, to whom I submitted the question, has obtained a simpler solution in the form" 
:<math>f(y) = \frac 1 \pi \int_{-y}^\infty \frac{F'(-z)}{\sqrt{z+x}}dz</math>.

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 year to digest."<ref name="Murnaghan_1948" />
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''. Bateman studied the [[Burgers' equation]]<ref name="Bateman_1915_1" /> long before [[Jan Burgers]] started to study.

Harry Bateman wrote two significant articles on the history of applied mathematics: "The influence of tidal theory upon the development of mathematics",<ref name="Bateman_1943" /> and "Hamilton's work in dynamics and its influence on modern thought".<ref name="Bateman_1944" />

In his ''Mathematical Analysis of Electrical and Optical Wave-motion'' (p.&nbsp;131), he describes the charged-corpuscle trajectory as follows:
{{blockquote|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 (physics)|string in physics]], for the universes in [[string theory]] have dimensions inflated beyond four, something not found in Bateman's work. Bateman went on to study the [[luminiferous aether]] with an article "The structure of the Aether".<ref name="Bateman_1915_2" /> His starting point is the [[bivector (complex)|bivector]] form of an [[electromagnetic field]], <math>\mathbf{E} + i \mathbf{B}</math>. He recalled [[Alfred-Marie Liénard]]'s electromagnetic fields, and then distinguished another type he calls "aethereal fields":
{{blockquote|When a large number of "aethereal fields" are superposed their singular curves indicate the structure of an "aether" which is capable of supporting a certain type of electromagnetic field.}}

Bateman received many honours for his contributions, including election to the [[American Philosophical Society]] in 1924, election to the [[Royal Society]] of London in 1928, and election to the [[United States National Academy of Sciences|National Academy of Sciences]] in 1930.<ref>{{Cite web |title=Harry Bateman |url=http://www.nasonline.org/member-directory/deceased-members/20000657.html |access-date=2023-08-23 |website=www.nasonline.org}}</ref> He was elected as vice-president of the [[American Mathematical Society]] in 1935 and was the Society's Gibbs Lecturer for 1943.<ref name="Murnaghan_1948" /><ref name="Bateman_1945" /> 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 is named in his honour.<ref name="caltech" />

After his death, his notes on higher transcendental functions were edited by [[Arthur Erdélyi]], [[Wilhelm Magnus]], {{ill|Fritz Oberhettinger|de}}, and [[Francesco Giacomo Tricomi|Francesco G. Tricomi]], and published in 1953.<ref name="Erdélyi_1953" />

==Publications==
In a review of Bateman's book ''Partial Differential Equations of Mathematical Physics'', [[Richard Courant]] says that "there is no other work which presents the analytical tools and the results achieved by means of them equally completely and with as many original contributions" and also "advanced students and research workers alike will read it with great benefit".
{{Div col|colwidth=32em}}
* 1908: [[s:en:The Conformal Transformations of a Space of Four Dimensions and their Applications to Geometrical Optics|The Conformal Transformations of a Space of Four Dimensions and their Applications to Geometrical Optics]], ''[[Proceedings of the London Mathematical Society]]'' 7: 70–89.
* 1910: [https://www.biodiversitylibrary.org/item/94115#page/506/mode/1up History and Present State of the Theory of Integral Equations], ''Report of the [[British Association]]''.
* 1914: (dissertation) [http://quod.lib.umich.edu/u/umhistmath/ABQ9961.0001.001/1?rgn=works;view=pdf;rgn1=author;q1=Bateman The Quartic Curve and its Inscribed Configurations], [[American Journal of Mathematics]] 36(4)<!-- link from University of Michigan Historical Math Collection -->.
* 1915: [http://trove.nla.gov.au/work/3563964 The Mathematical Analysis of Electrical and Optical Wave-motion on the Basis of Maxwell's Equations], [[Cambridge University Press]].
* 1918: ''Differential equations'', Longmans, Green, London, Reprint Chelsea 1966.
* 1932: ''Partial Differential Equations of Mathematical Physics'', Cambridge University Press 1932,<ref name="Walsh_1933" /> Dover 1944, 1959.
* 1933: (with Albert A. Bennett, William E. Milne) ''Numerical Integration of Differential Equations'', ''Bulletin of the National Research Council'', Dover 1956.
* 1932: (with [[Hugh Latimer Dryden|Hugh Dryden]], [[Francis Dominic Murnaghan (mathematician)|Francis Murnaghan]]) [https://books.google.com/books?id=rSixAAAAIAAJ Report of the Committee on Hydrodynamics], ''Bulletin of the National Research Council'', Washington D.C.
* 1945: [https://projecteuclid.org/euclid.bams/1183507238 The Control of an Elastic Fluid], [[Bulletin of the American Mathematical Society]] 51(9):601–646 via [[Project Euclid]], also found in ''Selected Papers on Mathematical Trends in Control Theory'' ([[Richard Bellman]] & Robert Kalaba editors).
* [[Bateman Manuscript Project]]: ''Higher Transcendental Functions'', 3 vols., McGraw Hill 1953/1955, Krieger 1981.
* [[Bateman Manuscript Project]]: ''Tables of Integral Transforms'', 2 vols., McGraw Hill 1954.
{{colend}}

==See also==
* [[Bateman Manuscript Project]]

==References==
{{reflist|refs=
<ref name="Erdélyi_1947">{{cite journal |author-last=Erdélyi |author-first=Arthur |author-link=Arthur Erdélyi |doi=10.1098/rsbm.1947.0020 |title=Harry Bateman. 1882–1946 |journal=[[Obituary Notices of Fellows of the Royal Society]] |volume=5 |issue=15 |pages=590–618 |date=1947|s2cid=179356952 }}</ref>
<ref name="Murnaghan_1948">{{cite journal |author-last=Murnaghan |author-first=Francis Dominic |author-link=Francis Dominic Murnaghan (mathematician) |doi=10.1090/S0002-9904-1948-08955-8 |title=Harry Bateman 1882–1946 |journal=[[Bulletin of the American Mathematical Society]] |volume=54 |pages=88–103<!-- some sources state 88–94 --> |date=1948 |doi-access=free}}</ref>
<ref name="Erdélyi_1946">{{cite journal |author-last=Erdélyi |author-first=Arthur |author-link=Arthur Erdélyi |doi=10.1112/jlms/s1-21.4.300 |title=Harry Bateman |journal=[[Journal of the London Mathematical Society]] |issue=4 |pages=300–310 |date=1946 |volume=s1-21}}</ref>
<ref name="acad">{{acad|id=BTMN900H|name=Bateman, Harry}}</ref>
<ref name="PCPS_1903">2. 1903. The determination of curves satisfying given conditions. ''[[Proceedings of the Cambridge Philosophical Society]]'' 12, 163</ref>
<ref name="Bell_1946">{{cite journal |author-first=Eric |author-last=Temple Bell |author-link=Eric Temple Bell |date=1946 |title=Harry Bateman|journal=Quarterly of Applied Mathematics |issue=4 |pages=105–111}}</ref>
<ref name="Kármán_1967">{{cite book |author-first1=Theodore |author-last1=von Kármán |author-link1=Theodore von Kármán |author-first2=Lee |author-last2=Edson  |date=1967 |title=The Wind and Beyond |page=124 |publisher=[[Little, Brown and Company]]}}</ref>
<ref name="Kosyakov_2007">{{cite book |author-first=Boris Pavlovich |author-last=Kosyakov |title=Introduction to the Classical Theory of Particles and Fields |publisher=[[Springer Science+Business Media|Springer]] |publication-place=Berlin / Heidelberg, Germany |date=2007 |isbn=978-3-540-40933-5 |doi=10.1007/978-3-540-40934-2 |page=216|url=https://cds.cern.ch/record/1338975 }}</ref>
<ref name="Warwick_2003">{{cite book |author-last=Warwick |author-first=Andrew |title=Masters of theory: Cambridge and the rise of mathematical physics |url=https://archive.org/details/mastersoftheoryc0000warw |url-access=registration |publisher=[[The University of Chicago Press]] |location=Chicago, Illinois, USA |date=2003 |isbn=0-226-87375-7 |pages=416–424}}</ref>
<ref name="Bateman_1910">{{cite journal |author-last=Bateman |author-first=Harry |author-link=Harry Bateman |title=The Transformation of the Electrodynamical Equations |doi=10.1112/plms/s2-8.1.223 |journal=Proceedings of the London Mathematical Society |pages=223–264 |date=1910 |volume=s2-8 |url=https://zenodo.org/record/1433552}}</ref>
<ref name="Bateman_1909">{{cite journal |author-last=Bateman |author-first=Harry |author-link=Harry Bateman |title=The Conformal Transformations of a Space of Four Dimensions and Their Applications to Geometrical Optics |doi=10.1112/plms/s2-7.1.70 |journal=[[Proceedings of the London Mathematical Society]] |pages=70–89 |date=1909 |volume=s2-7 |url=https://zenodo.org/record/1447802}}</ref>
<ref name="Truesdell_1984">{{cite book |author-last=Truesdell III |author-first=Clifford Ambrose |author-link=Clifford Ambrose Truesdell III |title=An idiot's fugitive essays on science: methods, criticism, training, circumstances |publisher=[[Springer-Verlag]] |location=Berlin, Germany |date=1984 |isbn=0-387-90703-3 |pages=403–438 |quote=Genius and the establishment at a polite standstill in the modern university: Bateman}}</ref>
<ref name="Bateman_1911">{{cite journal |author-last=Bateman |author-first=Harry |author-link=Harry Bateman |date=1911 |title=Report on the history and present state of the theory of integral equations |journal=Report of the British Association for the Advancement of Science |page=345 |url=https://archive.org/stream/reportofbritisha11scie/reportofbritisha11scie_djvu.txt}}</ref>
<ref name="Lamb_1910">{{cite journal |author-last=Lamb |author-first=Horace |date=1910-02-10 |orig-date=1910-02-06 |title=On the diffraction of a solitary wave |url=https://zenodo.org/record/2369668 |journal=Proceedings of the London Mathematical Society |volume=2 |issue=1 |pages=422–437 |doi=10.1112/plms/s2-8.1.422}}</ref>
<ref name="Bateman_1915_1">{{Cite FTP |author-last=Bateman |author-first=Harry |author-link=Harry Bateman |date=1915 |title=Some recent researches on the motion of fluids |url=ftp://ftp.library.noaa.gov/docs.lib/htdocs/rescue/mwr/043/mwr-043-04-0163.pdf |volume=43 |issue=4 |pages=163–170 |doi=10.1175/1520-0493(1915)43<163:srrotm>2.0.co;2 |bibcode=1915MWRv...43..163B|server=[[Monthly Weather Review]] |url-status=dead |doi-access=free }}</ref>
<ref name="Bateman_1943">{{cite journal |author-last=Bateman |author-first=Harry |author-link=Harry Bateman |title=The Influence of Tidal Theory upon the Development of Mathematics |journal=[[National Mathematics Magazine]] |volume=18 |issue=1 |pages=14–26 |doi=10.2307/3029913 |date=1943 |jstor=3029913}}</ref>
<ref name="Bateman_1944">{{cite journal |author-first=Harry |author-last=Bateman |author-link=Harry Bateman |date=1944 |title=Hamilton's work in dynamics and its influence on modern thought |journal=[[Scripta Mathematica]] |issue=10 |pages=51–63}}</ref>
<ref name="Bateman_1915_2">{{cite journal |author-first=Harry |author-last=Bateman |author-link=Harry Bateman |date=1915 |url=https://www.ams.org/journals/bull/1915-21-06/S0002-9904-1915-02631-5/S0002-9904-1915-02631-5.pdf |title=The Structure of the Aether |journal=[[Bulletin of the American Mathematical Society]] |volume=21 |issue=6 |pages=299–309|doi=10.1090/S0002-9904-1915-02631-5 |doi-access=free }}</ref>
<ref name="Bateman_1945">{{cite journal |author-last=Bateman |author-first=Harry |author-link=Harry Bateman |title=The control of an elastic fluid |journal=[[Bulletin of the American Mathematical Society]] |date=1945 |volume=51 |issue=9 |pages=601–646 |mr=0014548 |doi=10.1090/s0002-9904-1945-08413-4 |doi-access=free}}</ref>
<ref name="caltech">{{cite web |url=http://www.math.caltech.edu/general/08-09postdoc.html |title=Instructorships in Mathematics 2008–2009 |access-date=2012-01-30}}</ref>
<ref name="Erdélyi_1953">{{cite book |author-first1=Arthur |author-last1=Erdélyi |author-link1=Arthur Erdélyi |author-first2=Wilhelm |author-last2=Magnus |author-link2=Hans Heinrich Wilhelm Magnus |author-first3=Fritz |author-last3=Oberhettinger |author-link3=:de:Fritz Oberhettinger |author-first4=Francesco Giacomo |author-last4=Tricomi |author-link4=Francesco Giacomo Tricomi |title=Higher Transcendental Functions |publisher=[[McGraw-Hill Book Company, Inc.]] |date=1953<!-- vol. I+II -->–1955<!-- vol. III -->|bibcode=1953hft1.book...59E }}</ref>
<ref name="Walsh_1933">{{cite journal |author-last=Walsh |author-first=Joseph L. |author-link=Joseph L. Walsh |title=Bateman on Mathematical Physics |journal=[[Bulletin of the American Mathematical Society]] |date=1933 |volume=39 |issue=3 |pages=178–180 |url=http://projecteuclid.org/euclid.bams/1183496570 |doi=10.1090/s0002-9904-1933-05561-1 |doi-access=free}}</ref>
}}

==External links==
{{Wikisourceauthor}}
* [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/bateman-harry.pdf Academy of Sciences Biographical Memoir]
* {{MathGenealogy|id=8181}}
* {{MacTutor Biography|id=Bateman}}

{{Authority control}}

{{DEFAULTSORT:Bateman, Harry}}
[[Category:1882 births]]
[[Category:1946 deaths]]
[[Category:Alumni of Trinity College, Cambridge]]
[[Category:Bryn Mawr College faculty]]
[[Category:California Institute of Technology faculty]]
[[Category:English mathematicians]]
[[Category:Fluid dynamicists]]
[[Category:Fellows of the Royal Society]]
[[Category:Johns Hopkins University faculty]]
[[Category:People educated at Manchester Grammar School]]
[[Category:Scientists from Manchester]]
[[Category:Senior Wranglers]]
[[Category:Deaths from coronary thrombosis]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:International members of the American Philosophical Society]]