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Thomas Craig (1855–1900) was an American mathematician. He was a professor at Johns Hopkins University and a proponent of the methods of
differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
.


Biography

Thomas Craig was born December 20, 1855, in Pittston, Pennsylvania. His father Alexander Craig immigrated from Scotland, and worked as an engineer in the mining industry. Thomas Craig first studied civil engineering at Lafayette College in Pennsylvania, where a teacher William J. Bruce was a mentor to him. Thomas took his C.E. degree in 1875. He taught high school in Newton, New Jersey while continuing to study
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
. He entered into correspondence with Benjamin Peirce and Peter Guthrie Tait. Thomas Craig was one of the prime movers of Johns Hopkins University when it was launched by Daniel Coit Gilman in 1876. Craig and
George Bruce Halsted George Bruce Halsted (November 25, 1853 – March 16, 1922), usually cited as G. B. Halsted, was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States through his own work and ...
were the first Hopkins Fellows in mathematics.
James Joseph Sylvester James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership ro ...
had been invited to lead a graduate program in
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
but would only be doing that. Craig was needed to teach
differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...
and integral calculus. The first year there were only fifteen students studying mathematics, but by 1883 there were 35. In 1878 Craig took his Ph.D. degree with a dissertation ''The Representation of One Surface Upon Another, and Some Points in the theory of the Curvature of Surfaces''. He became an instructor at Johns Hopkins that year, but also took up work at the
U. S. Coast and Geodetic Survey The National Geodetic Survey (NGS) is a United States federal agency that defines and manages a national coordinate system, providing the foundation for transportation and communication; mapping and charting; and a large number of applications ...
. In that capacity he produced the text for ''A Treatise on Projections'' for workers at the Geodetic Survey. Craig and Simon Newcomb read Leo Königsberger's ''Theory of Functions'' also. Thomas married Louise Alford, daughter of General Benjamin Alvord, on May 4, 1880. The couple raised two daughters, Alisa and Ethel. After 1881 Craig was totally committed to Johns Hopkins, particularly anticipating
Arthur Cayley Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific United Kingdom of Great Britain and Ireland, British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, C ...
's lectures on theta functions when he came over for the Spring semester of 1882. Besides the calculus courses, Craig taught differential equations,
elliptic function In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those in ...
s,
elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...
,
partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...
s,
calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
,
definite integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...
s,
mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects ...
, dynamics, hydrodynamics,
sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
,
spherical harmonic In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics for ...
s, and
Bessel function Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...
s. When the
American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United ...
was launched in 1877 Craig was tasked with recording expenses, as these were underwritten by Johns Hopkins University. His report at the end of 1882 gave the total just under ten thousand dollars. Thomas Craig died May 8, 1900. With information supplied by
Luther P. Eisenhart Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry. Life Eisenhart was born in York, Pennsylvania, and graduated from Gettysburg Coll ...
, Simon Newcomb wrote the notice in the ''American Journal of Mathematics'' Simon Newcomb (1900
Thomas Craig
obituary in
American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United ...
from
Jstor JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ...
early materials


Works

Thomas Craig wrote the following contributions to the ''American Journal of Mathematics'': * 1880: AJM 3:114 to 27: Orthomorphic projections of an ellipsoid on a sphere * 1881: AJM 4: 297 to 320: On certain metric properties of surfaces * 1881: AJM 4:358 to 78: The counter-pedal surface of an ellipsoid * 1882: AJM 5:62 to 75: Some elliptic function formula * 1882: AJM 5:76 to 8: Note on the counter-pedal surface of an ellipsoid * 1882:
Crelle's Journal ''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by Au ...
93:251 to 70: On the parallel surface to an ellipsoid * 1883: Crelle's 94:162 to 70: Note on parallel surfaces * 1879
Wave and Vortex Motion
D. Van Nostrand Publishing, from
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* 1882
A Treatise on Projections
from
University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...
Historical Math Collection * 1889
A Treatise on Linear Differential Equations
John Wiley & Sons John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, i ...
, from Historical Math Monographs at
Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to ...


Notes and references

*
Karen Parshall Karen Hunger Parshall (born 1955, Virginia; ''née'' Karen Virginia Hunger) is an American historian of mathematics. She is the Commonwealth Professor of History and Mathematics at the University of Virginia with a joint appointment in the Corcor ...
& David E. Rowe (1994) ''The Emergence of the American Mathematical Research Community'', Chapter 2: "J.J. Sylvester and Johns Hopkins", . * F.P. Matz (1901
Professor Thomas Craig
American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an ...
8:183 to 7, from
Jstor JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ...
early content. * {{DEFAULTSORT:Craig, Thomas 19th-century American mathematicians 1855 births 1900 deaths