Work
LeVeque's research interest was number theory, specifically transcendental numbers, uniform distribution, and Diophantine approximation.
He wrote a number of number theory textbooks and reference books, which influenced the development of number theory in the United States. A long-term project was to update Leonard Eugene Dickson's History of the Theory of Numbers. This project eventually produced a six-volume collection titled Reviews in Number Theory. The Special Libraries Association's Physics-Astronomy-Mathematics Division awarded LeVeque its Division Award in 1978 for his contributions to the bibliography of mathematics.
The American Mathematical Society grew rapidly during LeVeque's time as executive director (1977–1988). Revenues tripled from $5 million in 1977 to $14.9 million in 1988. The Society began computerizing at a rapid rate during this period, with Mathematical Reviews first becoming available electronically through existing academic dial-up services; this system later evolved into MathSciNet. Most of the headquarters staff received computer terminals for use in the new operations.
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