In 1974 he was awarded his PhD degree in "Magnetostatic Field Calculations", under Dennis Gibson, from Teesside University.

[2] Professor Caldwell was awarded his first higher doctorate (DSc) degree by Queen's University of Belfast in 1985 for his research and scholarly work on "Mathematical Solution of Physical Problems Particularly Involving Magnetostatic Fields" and his second DSc by Teesside University in 2007 in recognition of his research and scholarly work in Mathematical Modelling.

[3] He took up various teaching posts in the UK before moving to Australia as Head of Mathematics at the University of Southern Queensland in Toowoomba.

[4] Similar with his academic career, Professor Caldwell worked for a number of large organizations including the role as Head of Modelling with Unilever Research UK.

[8][9] On 27 July 2024, he died peacefully and surrounded by family in Hong Kong at Queen Elizabeth Hospital due to complications arising from prostate cancer.