Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory. He studied for his habilitation at the University of Cologne, receiving it in 1922. He joined the faculty of the University of Zurich in 1927, and was promoted to ordinary professor there in 1944.
Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger, as is the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex. Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox.
- Finsler, Paul (1918), Über Kurven und Flächen in allgemeinen Räumen, Dissertation, Göttingen, JFM 46.1131.02 (Reprinted by Birkhäuser (1951))
- O'Connor, John J.; Robertson, Edmund F., "Paul Finsler", MacTutor History of Mathematics archive, University of St Andrews.
- Paul Finsler at the Mathematics Genealogy Project.
- Finsler, Paul; Hadwiger, Hugo (1937), "Einige Relationen im Dreieck", Commentarii Mathematici Helvetici 10 (1): 316–326, doi:10.1007/BF01214300.
- Breger, Herbert (1992), "A restoration that failed: Paul Finsler's theory of sets", in Gillies, Donald, Revolutions in Mathematics, Oxford University Press, pp. 249–264.
- Busemann, H. (1952). "Review: Über Kurven und Flächen in allgemeinen Räumen, by P. Finsler". Bull. Amer. Math. Soc. 58 (1): 102. doi:10.1090/s0002-9904-1952-09572-0.
- Burckhardt, J. J. (1980), Die Mathematik an der Universität Zurich 1916-1950 unter den Professoren R. Fueter, A. Speiser und P. Finsler, Basel.