Book Review: How to Think Like a Mathematician by Kevin Houston
I came across Kevin Houston’s How to Think Like a Mathematician a while back and honestly wish someone had put it in my hands much earlier. If you’re teaching maths or advising students who are serious about pursuing it beyond school, this is one of those books worth keeping on your radar, and well worth pointing your students towards.
What Houston does rather well is address something we all know is missing from most curricula: the meta-skills of mathematical thinking. He doesn’t just run through content. He unpacks how mathematicians actually read a problem, construct an argument, and navigate the moments when nothing is obvious. For students making the transition from school maths to university level, that shift in thinking is often the hardest part, and this book tackles it head on.
The structure is sensible and well-paced. It opens with logic, definitions, and proof-reading before moving into more demanding territory, all without ever feeling rushed. Houston writes with a clarity that doesn’t talk down to the reader, which I think is exactly the right register for the audience he’s aiming at. The exercises throughout are genuinely useful rather than just decorative.
I’ve recommended it to several students preparing for their IB final years and heading into mathematics or engineering degrees, and the feedback has been consistently positive. It’s the kind of book that doesn’t replace a good textbook but sits alongside one very naturally, filling in the gaps that formal instruction tends to leave.
If you haven’t come across it yet, it’s well worth a look. I highly recommend it for anyone wishing to pursue mathematics seriously in high school and further into their college years.