[1][2] Duistermaat attended primary school in Jakarta, at the time capital of the Dutch East Indies, where his family moved after the end of World War II.

[5] His original supervisor was the applied mathematician Günther K. Braun, who passed away one year before the thesis defense, so the official supervision was taken over by geometer Hans Freudenthal.

These topics exerted an important influence for his future pioneering works in microlocal analysis,[6][8][10] most prominently during his collaboration with Lars Hörmander, when they developed the theory of Fourier integral operators and proved the Propagation of singularities theorem [de].

[20] In symplectic geometry he is well known[9][15][7] for his article with his PhD student Gert Heckman [de] on the Duistermaat–Heckman formula,[21] which will later be placed in the more general framework of equivariant cohomology,[22] independently by Berline and Vergne[23] and by Atiyah and Bott.

[30] He also worked on barrier functions in convex programming,[31] collaborated with biomedical technologists on computer vision[32] and with geophysicists on modeling the polarity reversals of the Earth's magnetic field.