Wanner grew up in Seefeld in Tirol and studied mathematics at the University of Innsbruck, where he received his doctorate in 1965 with advisor Wolfgang Gröbner and dissertation Ein Beitrag zur numerischen Behandlung von Randwertproblemen gewöhnlicher Differentialgleichungen (A contribution to the numerical treatment of boundary value problems of ordinary differential equations).[2] He taught in Innsbruck and from 1973 at the University of Geneva.
Wanner's research deals with numerical analysis of ordinary differential equations (about which he wrote a two-volume monograph with Ernst Hairer). Wanner is the co-author of an analysis undergraduate textbook and a geometry undergraduate textbook, both of which give historically oriented explanations of mathematics.
In 2003 he was awarded, jointly with Ernst Hairer, the Peter Henrici Prize. In 2015 Wanner received SIAM's George Pólya Prize for Mathematical Exposition.[3]
Hairer, E.; Wanner, G. (1973). "Multistep-multistage-multiderivative methods for ordinary differential equations". Computing. 11 (3): 287–303. doi:10.1007/BF02252917. ISSN0010-485X.
Hairer, E.; Wanner, G. (1975). "A theory for Nyström methods". Numerische Mathematik. 25 (4): 383–400. doi:10.1007/BF01396335. ISSN0029-599X.
Hairer, E.; Wanner, G. (1981). "Algebraically Stable and Implementable Runge-Kutta Methods of High Order". SIAM Journal on Numerical Analysis. 18 (6): 1098–1108. doi:10.1137/0718074. ISSN0036-1429.
Hairer, Ernst; Wanner, Gerhard (1999). "Stiff differential equations solved by Radau methods". Journal of Computational and Applied Mathematics. 111 (1–2): 93–111. doi:10.1016/S0377-0427(99)00134-X. ISSN0377-0427.
with Ernst Hairer and Christian Lubich: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. 2002. 2nd edition. Springer, Berlin/Heidelberg 2010, ISBN978-3-642-05157-9. pbk reprint
with Ernst Hairer and Sylvert Nørsett: Solving Ordinary Differential Equations I. Nonstiff Problems (1st ed.). 1987. Hairer, Ernst; Nørsett, Syvert P.; Wanner, Gerhard (1993). Revised 2nd edition. ISBN9783540566700. 3rd corrected printing. Springer, Berlin/Heidelberg 2009, ISBN978-3-642-05163-0.
with Ernst Hairer and Sylvert Nørsett: Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems (1st ed.). 1991. 2nd edition. Springer, Berlin/Heidelberg 1996, ISBN978-3-642-05220-0. 2013 pbk reprint