Erik Albert Holmgren (7 July 1872 – 18 March 1943) was a Swedish mathematician known for contributions to partial differential equations.

Holmgren enrolled at Uppsala University in the autumn of 1890 and received his Bachelor of Arts degree on January 31, 1893.

Holmgren became a docent in mathematics on March 8, 1898 and received his Doctor of Philosophy degree on May 31, 1898, all at Uppsala University.

At the age of thirty-five when Holmgren's was called to be a professor in Uppsala, he had already conducted research at the universities of Göttingen (1900-01), Paris (1902), and Rome (1905-06), which were the most important centers of mathematics at that time.

He had an interest in French culture since his youth, and often traveled to France and Italy to combine his holidays with his research trips.