The time when he was an undergraduate at Cambridge was one of great activity in mathematical physics. Maxwell's classical memoir, "A Dynamical Theory of the Electromagnetic Field," appeared in 1865; the representation of physical phenomena dynamically was being rapidly extended, and the suitability of Lagrange's methods for such representations more widely recognised. This influence is clearly marked in Professor Niven's scientific work; his first paper "On the Application of Lagrange's Equations to the Solution of Questions of Impact," published in the 'Messenger of Mathematics' in 1868, demonstrated the advantages of Lagrange's method in such problems. A succession of papers followed on subjects covering a wide range - the wave surface, the theory of elasticity, the parallax of double stars, conduction of heat and electricity. In these papers, more especially in the two papers published in the 'Philosophical Transactions,' "On the Conduction of Heat in Ellipsoids of Revolution," 1881, and "0n the Conduction of Electric Currents in Infinite Plates and Spherical Shells," 1882, great analytical power is shown, though the analysis is not allowed to obscure the real objective of the investigations.
In 1880 Professor Niven was appointed to the Chair of Natural Philosophy in the University of Aberdeen, and with his transference to Aberdeen his activity in research work was necessarily diminished. The changes which were made in the arrangement of the work of a Scottish University after his appointment left little leisure to the occupants of some of the chairs, Natural Philosophy being one of those affected by the changes. Whether these changes have proved beneficial to the students is somewhat doubtful, but that the changes have rendered it almost impossible for the Professors in question to find time both for original investigations and for the efficient discharge of their teaching duties is certain.
During Professor Niven's long tenure of the Chair of Natural Philosophy the department has grown considerably; at the beginning of his term of office it was inadequately housed at King's College, but, the department is now at Marischal College, where new laboratories were built for it towards the end of last century, and it was largely owing to him that this improvement was carried out. Formerly instruction in experimental physics was of necessity confined to a small number; with the greater facilities at Marischal College a larger number can have practical training and consequently a more thorough instruction in Natural Philosophy.
Professor Niven's many students appreciated his unsparing efforts on their behalf; the greater part of every day during term found him in his department engaged either in teaching or in preparing the demonstration experiments for the next lectures, and apart from occasional fishing expeditions he was there during the vacations also.
In the spring of 1922 he became seriously ill, and, although he was able to take some of his honours classes at his house during the summer term, he retired from the Professorship at the end of the academical year. To the regret of his many friends he did not enjoy a long evening of leisure; gradually becoming weaker, he died on May 11, 1923.