  "I am an industrial mathematician." When asked to identify my profession or
academic field of study, this is the most concise answer I can provide.
However, this seemingly straightforward statement is commonly greeted by a
blank stare or an uncomfortable silence, regardless of whether I am speaking to
a fellow mathematician or a non-mathematician. I usually follow up with the
clarification: "I am an applied mathematician who derives much of my
inspiration from the study of industrial problems that I encounter through
collaborations with companies." This dispels some confusion, but unfortunately
still leaves a great deal open to interpretation owing to the vagueness of the
words mathematics, industry and company, each of which covers an extremely
broad range of scientific or socio-economic activity.
  To those academics who actually work in the field of industrial mathematics
(and whose "perspective" referred to in the title is the focus of this article)
this ambiguity is familiar and untroubling. However, for anyone less acquainted
with the work of industrial mathematicians, some clarification is desirable
especially for anyone who might be considering entering the field. This essay
therefore aims to shed light upon the nature of research being done at the
interface between mathematics and industry, paying particular attention to the
following questions: What is industrial mathematics? Where is industrial
mathematics? How does one do industrial mathematics? Why (or more precisely,
what value is there in doing) industrial mathematics?
  I will attempt to answer these questions by means of several case studies
drawn from my own experience in tackling mathematical problems from industry.

History and Overview