THE FOUR-SIDED TRIANGLE Callum Reyes Selkirk Press | 2026 | 486pp
Shortly after announcing the geometry-shattering discovery of a new shape between a triangle and a quadrilateral, a top-ranking Russian topologist is found murdered. With political tensions rising between two nuclear superpowers, it falls, once again, to Federal Algebraic Number Theorist Naomi Kessler to find the true killer before both sides intersect at a single, unrecoverable, non-Euclidean point.
★★★ Sufficient, but not necessary.
This is the seventh Naomi Kessler novel, and Reyes at this point knows precisely what his readers are here for - competent tradecraft and rigorous mathematics, delivered in functional prose. And so, the indefatigable Kessler, part-time Federal Algebraic Number Theorist attached to the Office of Pure Mathematics Threat Assessment, is once again summoned from her Princeton office with the familiar phone call, the familiar unmarked car, the familiar briefing in a windowless room. But as familiar as it might be, the plot setup is handled with professional, unnervingly serene economy. Reyes, I’m pleased to report, has learned valuable lessons from the mistakes he made in last year’s The Fermat Contingency, and the conceit of the isosceles rhombus, and the scramble by two superpowers to reconstruct murdered topologist Andrei Volkov’s lost proof of its existence, never once strains credulity.
The pleasures here are genre pleasures, and they mostly land. Kessler’s methodical investigation and her delightfully fastidious use of lemmas and reductio ad absurdum once again pave the way for a series of brisk set (and set theory!) pieces that propel the plot with the reliability of a well-formed syllogism. Reyes also wisely complicates matters with the second-act arrival of a Beijing metamathematician whose motives remain, appropriately, undecidable until the final act.
Reyes ties things off with the tidiness longtime readers will recognise and mostly forgive. The final confrontation resolves on a piece of geometric reasoning that is almost impossible to follow in prose form, but this is a minor quibble, and one the editor has seen fit to counterbalance with a thirty-page appendix containing a more formal mathematical proof.
It is, in the end, a perfectly competent seventh entry in the Naomi Kessler series. Any given reader’s enjoyment of this book paves the way for the enjoyment of the next and, hence, by a simple inductive proof, the enjoyment of every book in the series.
About the Author
Callum Reyes has written seven Naomi Kessler novels and, by his own account, briefed ‘more than one’ real intelligence agency on their plausibility. He lives in Washington, D.C. with his MacBook Air
Who Is This Book For?
The same readers all the previous Naomi Kessler books were for.