He was born at
Farsund in
Vest-Agder, Norway. He was the son of Theodor Birkeland (1834–1913) and Therese Karoline Overwien (1846–1883). He graduated from the Christiania Technical School in 1899. In 1906, he received a scholarship to study mathematics in Paris and
Göttingen. He became a professor at the
Norwegian Institute of Technology from 1910. He was rector of the
Norwegian Institute of Technology and from 1923 professor at the
University of Oslo. He was a co-founder of the
Norwegian Mathematical Society in 1918 and he was its vice chairman in the early years. He was for a time chairman of Trondheim Polytechnic Association. He was decorated Knight of the
Order of St. Olav. ==Selected works==