Peter Ludwig Mejdell Sylow (12 December 1832 – 7 September 1918) was a Norwegian mathematician, who proved foundational results in group theory. He was born and died in Christiania (now Oslo).

Sylow was a high school teacher in Halden, Norway, from 1858 to 1898, and a substitute lecturer at Christiania University in 1862, covering Galois theory. It was then that he posed the question that led to his theorems regarding Sylow subgroups. Sylow published the Sylow theorems in 1872, and subsequently devoted eight years of his life, with Sophus Lie, to the project of editing the mathematical works of his countryman, Niels Henrik Abel.

He was appointed professor of Christiania University in 1898.