4-21. Thomas Craig

Thomas Craig (1855–1900) was the son of immigrant Scots; his father worked as a mining engineer in the coal industry of Pennsylvania. He obtained a degree in civil engineering from Lafayette College in 1875, then taught mathematics in a high school in New Jersey, before winning a doctoral fellowship to study mathematics at the newly-opened Johns Hopkins University in 1876.

Craig successfully defended his thesis on “The representation of one surface upon another, and some points in the theory of the curvature of surfaces” in 1878, and joined the teaching staff of Johns Hopkins. He obtained a concurrent, part-time position with the Coast and Geodetic Survey, which he held until 1881. While with the Survey, he published several works on fluid mechanics (Craig, 1879b, a; Thomson, 1880). Craig then continued to teach mathematics at Johns Hopkins, along with James Joseph Sylvester, Arthur Cayley, William Story, and Charles Sanders Peirce; he also attended the lectures of Sylvester and Cayley.

Craig’s mathematical interests beyond fluid mechanics included elliptic functions and differential geometry, topics on which he published in Crelle’s Journal. Craig also published a treatise on projections, and another on linear differential equations.

Craig served as associate editor of the Hopkins-published American Journal of Mathematics (AJM), first under Sylvester, then, upon the latter’s move to Oxford, under Simon Newcomb. It is in this editorial capacity that Craig came to exchange several dozens of letters with Poincaré, in the period from 1883 to 1892. Poincaré greatly admired a paper that appeared in the first volume of the AJM, George William Hill’s “Researches in the lunar theory,” where Hill presented a novel technique for solving the eponymous differential equation, involving an infinite determinant. Craig’s interest in Poincaré’s work was not just editorial, however. He studied Poincaré’s papers, and found he was not able to understand all of them to his satisfaction. This led him to ask Poincaré for help, not by letter, but in person, after steaming to Paris in June, 1884.

Thanks in part to Craig’s constant badgering, four papers by Poincaré appeared in the AJM, along with a portrait (in 1889). Among these is one of Poincaré’s most celebrated papers, describing the “sweeping method”, or méthode de balayage, for solving the Dirichlet problem (Poincaré, 1890). In fact, it was the latter paper that Gaston Darboux and others put forward first among the several works meriting the 1910 Nobel Prize in Physics in their letter of nomination.

Craig took over the editorship of the AJM from Newcomb in 1894, and was promoted to professor of pure mathematics at Hopkins. His editorial policy favoring submissions from European mathematicians displeased members of the American Mathematical Society, and consequently spurred the foundation in 1899 of the Transactions of the American Mathematical Society (Batterson, 2017). Already in 1898, Craig relinquished his position as editor on grounds of poor health, and he expired from heart failure at the age of forty-four on 8 May, 1900.

Notes

• 1 For an overview of the mathematics department at Johns Hopkins in the last quarter of the nineteenth century, see Parshall and Rowe (1994, chap. 3).
• 2 See Hill (1878a, b, c), and the biographical note on Hill.
• 3 See Darboux et al. to the Nobel Committee for Physics, ca. 1 January 1910 (§ 2-62-24).
• 4 The title page of the second number of AJM 16 (April, 1894) lists Craig as the editor, “with the cooperation of Simon Newcomb”.
• 5 For Craig’s biography, see MacTutor, and the obituaries by Newcomb (1900), and Matz (1901).