Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a French mathematician. 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. In 1859 he began to teach at Bordeaux. In 1863 Hoüel expressed his doubts about the verifiability of the parallel postulate of Euclid. In 1876 Hoüel reviewed a Russian language quaternion textbook written by Romer (1868)