Thomas Craig (1855–1900) was an American mathematician. He was a professor at

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...

and a proponent of the methods of differential geometry.

Biography

Thomas Craig was born December 20, 1855, in

Pittston, Pennsylvania Pittston is a city in Luzerne County, Pennsylvania, United States. It is situated between Scranton and Wilkes-Barre in Northeastern Pennsylvania. The city gained prominence in the late 19th and early 20th centuries as an active anthracite coal ...

. His father Alexander Craig immigrated from

Scotland Scotland (, ) is a Countries of the United Kingdom, country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a Anglo-Scottish border, border with England to the southeast ...

, and worked as an

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the limit ...

in the mining industry. Thomas Craig first studied

civil engineering Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...

Lafayette College Lafayette College is a private liberal arts college in Easton, Pennsylvania. Founded in 1826 by James Madison Porter and other citizens in Easton, the college first held classes in 1832. The founders voted to name the college after General Laf ...

Pennsylvania Pennsylvania (; ( Pennsylvania Dutch: )), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. It borders Delaware to its southeast, ...

, where a teacher William J. Bruce was a

mentor Mentorship is the influence, guidance, or direction given by a mentor. A mentor is someone who teaches or gives help and advice to a less experienced and often younger person. In an organizational setting, a mentor influences the personal and p ...

to him. Thomas took his C.E. degree in 1875. He taught

high school A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both '' lower secondary education'' (ages 11 to 14) and ''upper seconda ...

Newton, New Jersey Newton, officially the ''Town of Newton'', is an incorporated municipality located in Sussex County, in the U.S. state of New Jersey. It is situated approximately by road northwest of New York City. As the location of the county's administrat ...

while continuing to study mathematics. He entered into correspondence with

Benjamin Peirce Benjamin Peirce (; April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philoso ...

and

Peter Guthrie Tait Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook ''Treatise on Natural Philosophy'', which he co-wrote wi ...

. Thomas Craig was one of the prime movers of

when it was launched by

Daniel Coit Gilman Daniel Coit Gilman (; July 6, 1831 – October 13, 1908) was an American educator and academic. Gilman was instrumental in founding the Sheffield Scientific School at Yale College, and subsequently served as the second president of the University ...

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 had been invited to lead a graduate program in mathematics but would only be doing that. Craig was needed to teach differential calculus and

integral calculus In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding ...

. 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. In that capacity he produced the text for ''A Treatise on Projections'' for workers at the Geodetic Survey. Craig and

Simon Newcomb Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian–American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins University. Born in N ...

read

Leo Königsberger Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject. In 20 ...

'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's lectures on

theta function In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field ...

s when he came over for the Spring semester of 1882. Besides the calculus courses, Craig taught

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s, elliptic functions, elasticity, partial differential equations, calculus of variations, definite integrals,

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 object ...

, 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'' b ...

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 form ...

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 arbitrar ...

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 S ...

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,

wrote the notice in the ''American Journal of Mathematics''

(1900
Thomas Craig
obituary in

from Jstor 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 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

Google Books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical ...

* 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, ...

, 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 tea ...

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 Corco ...

& 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 8:183 to 7, from Jstor early content. * {{DEFAULTSORT:Craig, Thomas 19th-century American mathematicians 1855 births 1900 deaths