Career
Much of his work concerns the theory of normed spaces and convex geometry. In the theory of Banach spaces and summability, he proved the Dvoretzky–Rogers lemma and the Dvoretzky–Rogers theorem, both with Aryeh Dvoretzky. He constructed a counterexample to a conjecture related to the Busemann–Petty problem.
In the geometry of numbers, the Rogers bound is a bound for dense packings of spheres.
Rogers was married to children"s writer Joan North.}.