Thomas received his Ph.D., supervised by Frederick Wahn Beal, from the University of Pennsylvania with thesis Congruences of Circles, Studied with reference to the Surface of Centers. He was a mathematics professor at Duke University for many years. His graduate students include Mabel Griffin (later married to L. B. Reavis) and Ruth W. Stokes. In 1935 he was one of the founders of the Duke Mathematical Journal. For the academic year 1936–1937 was a visiting scholar at the Institute for Advanced Study.
- with Oswald Veblen: Veblen, O.; Thomas, J. M. (1925). "Projective Normal Coördinates for the Geometry of Paths". Proceedings of the National Academy of Sciences. 11 (4): 204–7. doi:10.1073/pnas.11.4.204. PMC 1085921. PMID 16576871.
- Note on the projective geometry of paths. Proceedings of the National Academy of Sciences 11, no. 4 (1925): 207–209.
- The number of even and odd absolute permutations of n letters. Bull. Amer. Math. Soc. 31 (1925) 303–304. MR1561049
- Conformal correspondence of Riemann spaces. Proceedings of the National Academy of Sciences 11, no. 5 (1925): 257–259.
- Conformal invariants. Proceedings of the National Academy of Sciences 12, no. 6 (1926): 389–393.
- Asymmetric displacement of a vector. Trans. Amer. Math. Soc. 28 (1926) 658–670. MR1501370
- with Oswald Veblen: Projective invariants of affine geometry of paths. Annals of Mathematics 27 (1926): 279–296. doi:10.2307/1967848
- Riquier's existence theorems. Annals of Mathematics 30 (1928): 285–310. doi:10.2307/1968282
- Matrices of integers ordering derivatives. Trans. Amer. Math. Soc. 33 (1931) 389–410. MR1501594
- The condition for an orthonomic differential system. Trans. Amer. Math. Soc. 34 (1932) 332–338. MR1501640
- Pfaffian systems of species one. Trans. Amer. Math. Soc. 35 (1933) 356–371. MR1501689
- Riquier's existence theorems. Annals of Mathematics 35 (1934): 306–311. doi:10.2307/1968434 (addendum to 1928 publication in Annals of Mathematics)
- An existence theorem for generalized pfaffian systems. Bull. Amer. Math. Soc. 40 (1934) 309–315. MR1562842
- The condition for a pfaffian system in involution. Bull. Amer. Math. Soc. 40 (1934) 316–320. MR1562843
- Sturm's theorem for multiple roots. National Mathematics Magazine 15, no. 8 (1941): 391–394. JSTOR 3028551
- Equations equivalent to a linear differential equation. Proc. Amer. Math. Soc. 3 (1952) 899–903. MR0052001
- Differential systems. 1937.
- Theory of equations. McGraw-Hill. 1938; 211 pages
- Elementary mathematics in artillery fire, by Joseph Miller Thomas with tables prepared by Vincent H. Haag. McGraw-Hill. 1942; 256 pages
- Systems and roots. William Byrd Press. 1962; 123 pages
- A primer on roots. William Byrd Press. 1974; 106 pages
- Thomas Decomposition of Algebraic and Differential Systems by Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann, Daniel Robertz, 2010
- Joseph Miller Thomas at the Mathematics Genealogy Project
- Green, Judy; LaDuke, Jeanne (2009). Pioneering Women in American Mathematics: The Pre-1940 PhD's. American Mathematical Society. ISBN 9780821843765. (Griffin) Reavis and Stokes biographies on p.513-515 and p.580-582 of the Supplementary Material at AMS, respectively.
- Joseph Miller Thomas | Institute for Advanced Study
- Kondratieva, M. V. (1998). Differential and Difference Dimension Polynomials. Springer Science & Business Media. p. ix (preface). ISBN 978-0-7923-5484-0.
- Astrelin, A. V.; Golubitsky, O. D.; Pankratiev, E. V. (2000). "Involutive bases of ideals in the ring of polynomials". Programming and Computer Software. 26 (1): 31–35. doi:10.1007/bf02759177.
- Bochner, Salomon (1938). "Review: Differential systems by J. M. Thomas" (PDF). Bull. Amer. Math. Soc. 44 (5): 314–315. doi:10.1090/s0002-9904-1938-06724-9.