In 1969, the team that developed the automated teller machine in the United Kingdom at IBM Hursley used parts from that project to build an IBM School Computer. It was a community outreach project, and it went on tour. When it came to Marlborough College, Davenport, aged 16, discovered that, although it was ostensibly a six-digit computer, the microcode had access to a 12-digit internal register to do multiply/divide. He used this to implement Draim's algorithm from his father Harold Davenport's book, The Higher Arithmetic, and tested eight-digit numbers for primality.[6]
Between school and university, Davenport worked in a government laboratory for nine months, again writing and using multiword arithmetic, but also using number theory to solve a problem in hashing, which was published. He was at IBM Yorktown Heights for a year, and returned to Cambridge as a Research Fellow. He went to Grenoble for a year, before taking a post at the University of Bath in 1983.[6]
Davenport is an author of a textbook about computer algebra and of many papers.[7][8][9][10] He has been Project Chair of the European OpenMath Project and its successor Thematic Network, with responsibilities for aligning OpenMath and MathML, producing Content Dictionaries and supervised a Reduce-based OpenMath/MathML translator, and was Treasurer of the European Mathematical Trust. He was Founding Editor-in-Chief of the London Mathematical Society's Journal of Computation and Mathematics.[11]
^Davenport, James Harold. On the integration of algebraic functions. Berlin; New York : Springer, 1981. 197 p.; 25 cm. ISBN978-0-387-10290-0 (paperback)
^Computer algebra : systems and algorithms for algebraic computation / J.H. Davenport, Y. Siret, E. Tournier; translated from the French by A. Davenport and J.H. Davenport. London : San Diego : Academic Press, 1988. xix, 267 p. : ill.; 24 cm. ISBN978-0-12-204230-0
^EUROCAL ’87 : European Conference on Computer Algebra, Leipzig, GDR, June 2–5, 1987 : proceedings / J.H. Davenport (ed.). Berlin; New York : Springer-Verlag, c1989. viii, 499 p. : ill.; 25 cm. ISBN978-0-387-51517-5 (New York : acid-free paper) ISBN978-3-540-51517-3 (Berlin : acid-free paper)
^Mathematical knowledge management : second international conference, MKM 2003, Bertinoro, Italy, February 16–18, 2003 : proceedings / Andrea Asperti, Bruno Buchberger, James H. Davenport (eds.).