In addition Poinsot worked on number theory and on this topic he studied Diophantine equations, how to express numbers as the difference of two squares and primitive roots. However he is best known for his dedication to geometry and, together with Monge, he contributed to the topic regaining its leading role in mathematical research in France in the eighteenth century.
Sa karagdagan Poinsot nagtrabaho sa numero ng teorya at sa paksang ito siya-aral ng Diophantine equation, kung paano express numero bilang ang pagkakaiba ng dalawang squares at nauna Pinagmulan. Gayunman siya ay pinakamahusay na kilala para sa kanyang pag-aalay sa geometry, at kasama Monge, siya ambag sa topic regaining nangungunang papel nito sa matematika pananaliksik sa France sa ikalabing-walo siglo.