He entered the École Normale Supérieure in 1843 and received his doctoral degree in 1855 from the Sorbonne.

He was sought by Urbain Le Verrier at the Paris Observatory, but chose instead to return to Thaon to study there.

[1] In 1867 Hoüel produced French translations of two key publications of non-Euclidean geometry: Lobachevski's Geometrical Studies on the Theory of Parallels[2] and Bolyai's Science of Absolute Space.

[3] Hoüel published a four volume work titled Théorie Élémentaire des Quantités Complexes.

Tait wrote:[5] In 1876 Hoüel reviewed a Russian language quaternion textbook written by Romer (1868)[6]