In 1969, the team that developed the ATM at IBM Hursley (UK) used parts from that project to build an IBM School Computer, as a community outreach project, and it toured the region. When it came to James Davenport’s school, he (at age 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 therefore used this to implement Draim's algorithm from his father's book, The Higher Arithmetic, and was testing eight-digit numbers for primality until the teacher’s patience wore out.

This is typical of Davenport’s lifelong interests: pushing computers to their limits to do mathematical computations. He worked in a government laboratory for nine months, again writing and using multiword arithmetic, but also using his knowledge of number theory to solve a problem in hashing, which earned him his first published paper at 18. He went to Cambridge University (Bachelor’s in 1974, Master’s in 1978, and PhD in 1980), to IBM Yorktown Heights for a year, back to Cambridge as a Research Fellow, to Grenoble for a year, which significantly improved his French, as well as his cooking, before going to the relatively new University of Bath “for a couple of years" in 1983. He is still there, though he has also spent time researching and teaching in many other countries. In 1986 in France, he finished his textbook Calcul Formel with Grenoble colleagues, which his mother translated into English as Computer Algebra.

Computer algebra remains his main research interest: as he says, “You don't really understand a subject until you can program a computer do to it, and that goes for mathematics at least as much as anything else.” He is finishing a new textbook on the subject, and has also edited four volumes of conference proceedings on the subject, as well as writing over 100 refereed papers. He has also produced four new editions of The Higher Arithmetic. He is active in the UK's professional world as a vice-president of the British Computer Society, the representative of the Institute of Mathematics and Its Applications on the London Mathematical Society’s Computer Science Committee, and a member of the Outer Circle of the National Advisory Committee on [School] Mathematics Education. In 2014, he was one of only two computer scientists chosen among the 55 national teaching fellows (and Tom Crick, the other one, had studied at Bath). Internationally, he is on the Committee for Electronic Information and Communication of the International Mathematical Union, and just moderated the panel on mathematical MOOCs at the 2014 International Congress of Mathematicians.

Is he a mathematician or a computer scientist? “Yes, and if that were a conjunction rather than a disjunction, I would still say yes. What attracted me to Bath was that mathematics and computer science were one department, and when colleagues felt that growth made a split necessary, I was made a member of both departments.”

What attracts him most to Computing Reviews is the ability to read books and papers he would not otherwise read. “We examine PhD students, not just on their thesis, but also on the broader area. How do we professors keep up ourselves? Reviewing for Computing Reviews is my way.”