Albert Victor Bäcklund was born on January 11th, 1845 in a small village in Malmöhus län in southern Sweden. He received his tertiary education at the University of Lund. In 1864, he was offered a position at the Astronomical Observatory where he became a student of Professor Axel Möller. In 1868, Bäcklund received his PhD for a thesis concerning a method for measuring latitude from astronomical observations. Shortly after, Bäcklund commenced his work on geometry and became aware of the work of the Norwegian mathematician Sophus Lie. (Bäcklund alluded to Lie for the first time in 1872 in his Jugendarbeit.)

In 1874, Bäcklund was awarded a travel grant from the government to pursue his studies on the Continent for six months. He spent most of his time in Leipzig and Erlangen where he met Klein and Lindemann. Ideas he gained in this period inspired his later work in geometry on what have come to be known as Bäcklund transformations.

In 1878, Bäcklund was awarded the title of Associate Professor of Mechanics and Mathematical Physics at the University of Lund. In 1888, he was elected a Fellow of the Swedish Academy of Science but it was not until 1897 that Bäcklund finally obtained a Professorship at Lund. During the period 1907-1909, Bäcklund was the rector of the University of Lund.

Following his retirement in 1910, Bäcklund resumed his studies in Differential Geometry and participated in the debate on the recently introduced Theory of General Relativity. Bäcklund died on February 23rd, 1922. The publications of Bäcklund are listed below.

The historical origin of Bäcklund transformations resides in the attempts to extend the pioneering work of Lie on contact transformations. Lie had raised the question of the existence of transformations for which tangency of higher order is an invariant condition. Bäcklund independently studied this problem.

In a series of papers published in Mathematische Annalen between the years 1875-1882, Bäcklund not only made an important contribution to the theory of tangent transformations but, importantly, was led to introduce a second class of transformations of surfaces which, together with their modern extensions, have become known as Bäcklund transformations. In particular, the celebrated auto-Bäcklund transformation associated with the generation of pseudo-spherical surfaces was set down.

Publications

• Någro satser on plana algebraiska kurvors normaler, Lunds Univ. Årsskr V (1869).
• Ett bidrag till kul-komplernas theori, Lunds Univ. Årsskr IX (1873).
• Einiges über Kurven- und Flächen-Transformationen, Lunds Univ. Årsskr X 1-12 (1874).
• Über Flächentransformationen, Math. Ann. IX 298-320 (1875).
• Über partielle Differentialgleichungen höherer Ordnung, die intermediäre erste Integrale besitzen, Math. Ann. XI 199-241 (1877).
• Über Systeme partieller Differentialgleichungen erster Ordnung, Math. Ann. XI 412-433 (1877).
• Über partielle Differentialgleichungen höherer Ordnung, die intermediäre erste Integrale besitzen. Zweite Abhandlung, Math. Ann. XIII 69-108 (1878).
• Zur Theorie der Charakteristiken der partiellen Differentialgleichungen zweiter Ordnung, Math. Ann. XIII 411-428 (1878).
• Zur Theorie der partiellen Differentialgleichungen zweiter Ordnung, Math. Ann. XV 39-88 (1879).
• Zur Theorie der partiellen Differentialgleichungen erster Ordnung, Math. Ann. XVII 285-328 (1880).
• Zur Theorie der Flächentransformationen, Math. Ann. XIX 387-422 (1882).
• On ytor med konstant negativ krökning, Lunds Univ. Årsskr XIX (1883).
• Einiges über Kugelkomplexe, Annali di Matematica Ser III XX 65-107 (1913).
• Ein Satz von Weingarten über auf einander abwickelbare Flächen, Lunds Univ. Årsskr XIV (1918).
• Zur Transformationstheorie partieller Differentialgleichungen zweiter Ordnung, Lunds Univ. Årsskr XVI (1920).