He started teaching at Harvard University in 1982 and is currently the T. Jefferson Coolidge Professor of Computer Science and Applied Mathematics in the Harvard School of Engineering and Applied Sciences.
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Jerrum, Valiant, and Vazirani showed that every #P-complete problem either has an FPRAS, or is essentially impossible to approximate; if there is any polynomial-time algorithm which consistently produces an approximation of a #P-complete problem which is within a polynomial ratio in the size of the input of the exact answer, then that algorithm can be used to construct an FPRAS.