Caviness graduated from the University of North Carolina at Chapel Hill with a B.S. with honors in Mathematics in 1962 and from Carnegie Mellon University with an M.S. in Mathematics in 1964 and a Ph.D. in Computer Science / Mathematics in 1968. His Ph.D. Thesis entitled ``On Canonical Forms and Simplification'' was supervised by Alan J. Perlis. Caviness held faculty positions at Duke University, the University of Wisconsin at Madison, the Illinois Institute of Technology, Rensselaer Polytechnic Institute and the University of Delaware. He held visiting positions Bell Laboratories, Murray Hill, General Electric Research and Development, Schenectady, the ETH Zurich, the IBM T. J. Watson Research Center and was a Program Director at NSF.
Caviness's research includes the design and analysis of algebraic algorithms, in particular, algorithmic decision procedures for integration in finite terms and for computing closed form solutions of differential equations. Among his results, jointly with his Ph.D. students, are so-called structure theorems that prescribe the possible candidates of formulas if an integral has a closed form solution. After having been department chair, Caviness turned to web-based technologies with an eye on pedagogical applications such as mathematical mark-up and searching documents in pdf format. He supervised five Ph.D. theses and several master theses.
In 1988 Caviness co-edited a Report to NSF on Future Directions for Research in Symbolic Computation, which among others laid the path of funding in what we today call hybrid symbolic-numeric computation. In 1998 Caviness co-edited a collection of papers on Quantifier Elimination and Cylindrical Algebraic Decomposition which has become the standard reference on the subject today.
Caviness engaged in numerous service activities for the symbolic computation community, among which are: he was the 7th Chair of the ACM Special Interest Group on Symbolic and Algebraic Manipulation (SIGSAM) from 1977-79. He was the Editor-in-Chief of the Journal of Symbolic Computation from 1995-2000, and an editorial board member from its inception in 1985. He was an associate editor for the ACM Transactions on Mathematical Software and an editorial board member of CONSTRAINTS. He was the Conference Chair of SYMSAC 1981 and the Program Chair of SYMSAC 1976, the 1995 East Coast Computer Algebra Day and ISSAC 1996. ISSAC is the International Symposium for Symbolic and Algebraic Computation and SYMSAC its predecessor symposium. In 2004 Caviness established the ACM-SIGSAM Richard Dimick Jenks Memorial Prize for Excellence in Software Engineering Applied to Computer Algebra in the name of his friend.
Caviness won the Bausch and Lomb Science Medal in 1958 and an NSF Graduate Fellowship 1962-66. He was a member in the Phi Eta Sigma, Phi Beta Kappa and Sigma Xi honor societies.
In his retirement Bobby Caviness was active in residential building projects for the needy by his church and in other charities. He died of pancreatic cancer. He was married to his wife Jane for 56 years. They have a daughter Kristen.