One of the rare Norwegian mathematicians of renown, I was educated at the University of Christiana in Oslo.

On a visit to Paris, I collaborated with Felix Klein on a series of papers dealing with transformation groups, which eventually were named after me.

I was hooked, as the remainder of my career was focused on the mathematics of continuous transformation groups, especially as they related to symmetry and dynamics.

Basically, I showed how transformation groups can be used to classify partial differential equations and reduce classical methods to a single principle.

I also discovered a special "contact transformation" (now named after me) by which a sphere can be made to correspond to a straight line.

As a Norwegian mathematician, I was made a Honorary Member of the London Mathematical Society and a Fellow of the Royal Society.