Cheng is a professor of Applied Mathematics in the theoretical physics group of the Department of Mathematics at the Massachusetts Institute of Technology (MIT).
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He received the B.Sc and the Ph.D. degrees from California Institute of Technology, in 1959 and 61. He had post-doctorate research appointments at Caltech, Princeton University and Harvard University before joining the MIT faculty in applied mathematics in 1965. In 1978, Professor Cheng was elected Member of Taiwan's Academia Sinica.
He has also served as the Chairman of the Applied Mathematics Committee at the MIT Department of Mathematics. He is on the Editorial Board of the Journal Studies in Applied Mathematics