His work The invariants of quadratic differential forms (1927) is a systematic treatment of Riemann geometry while his work, written jointly with his student Henry Whitehead, The foundations of differential geometry (1933) gives the first definition of a differentiable manifold .
Kanyang trabaho Ang invariants ng parisukat kaugalian forms (1927) ay isang paraan ng paggamot ng Riemann geometry habang ang kanyang trabaho, nakasulat na sama-sama sa kanyang estudyante Henry Whitehead, Ang pundasyon ng mga kaugalian geometry (1933) ay nagbibigay ng unang kahulugan ng isang differentiable sari-sari.