Terng has been an active member of the Association for Women in Mathematics (AWM). She served as AWM President from 1995 to 1997, chaired the Julia Robinson Celebration of Women in Math Conference, which was held July 1–3, 1996,[6] and chaired the Michler Prize and Travel/Mentoring Grant Committees.[7]
Terng has served on the editorial boards of the Transactions of the AMS, the Taiwanese Journal of Mathematics, Communications of Analysis and Geometry, the Proceedings of the AMS, and the Journal of Fixed Point Theory and its Applications.[8]
Her early research concerned the classification of naturalvector bundles and natural differential operators between them. She then became interested in submanifold geometry. Her main contributions are developing a structure theory for isoparametric submanifolds in and constructing soliton equations from special submanifolds. Recently, Terng and Karen Uhlenbeck (University of Texas at Austin) have developed a general approach to integrable PDEs that explains their hidden symmetries in terms of loop group actions. She is co-author of the book Submanifold Geometry and Critical Point Theory and an editor of the Journal of Differential Geometry survey volume 4 on "Integrable systems".
Professor Terng served as president of the Association for Women in Mathematics (AWM) from 1995 to 1997 and as Member-at-Large of the Council of the American Mathematical Society (AMS) from 1989 to 1992. She is currently on the Advisory Board of the National Center for Theoretical Sciences in Taiwan, the Steering Committee of the Institute for Advanced Study Park City Summer Institute, and the Editorial Board of the Transactions of the AMS.
^Shaw, Mei-Chi (2014), "A woman mathematician's journey", ICCM Notices, 2 (1): 59–74, doi:10.4310/ICCM.2014.v2.n1.a11, MR3237703. Reprinted in Casazza, Peter; Krantz, Steven G.; Ruden, Randi D. (2015), I, Mathematician, MAA Spectrum, Washington, DC: Mathematical Association of America, pp. 227–250, ISBN978-0-88385-585-0, MR3362652. See in particular p. 70 of ICCM Notices or pp. 243–244 of I, Mathematician.