[1] His research in geometric integration encompasses both pure and applied mathematics, modelling the structure of systems such as liquids, climate cycles, and quantum mechanics.

He received a PhD from Caltech (the California Institute of Technology) in 1990, supervised by Herbert Keller in computational fluid dynamics, with a thesis titled "Separated Viscous Flows via Multigrid".

After meeting Jürgen Moser, who was visiting Boulder at the time, McLachlan spent six months on a postdoctoral fellowship in Switzerland, at the Swiss Federal Institute of Technology in Zurich.

[3] In 2002 he became Professor of Applied Mathematics at Massey, and spent a year's sabbatical at the University of Geneva, working with Gerhard Wanner and Ernst Hairer, and the Norwegian Academy of Sciences in Oslo.

[5] From 2008 to 2012, along with Stephen Marsland and Matt Perlmutter, he worked on a Marsden grant project "Geodesics in diffeomorphism groups: geometry and applications", designing efficient numerical integrators that preserved the geometric properties of systems.