**Viktor Vladimirovich Wagner** was a Russian mathematician who worked in differential geometry and on semigroups.

- Vagner took a job teaching in high schools but these were not schools with high educational aspirations, with one of the schools he taught at being a school for juvenile delinquents.
- It is amazing that, given his background and the environment in which he worked, Vagner was able to pursue the study of mathematics and physics in his own time.
- Vagner's interests were, at this time, mainly in theoretical physics.
- Tamm had to supervise students on the physics of metals but after having discussions with Vagner he clearly saw how the young student had his heart set on studying relativity.
- So Vagner tool Tamm's advice and approached Benjamin Fedorovich Kagan.
- Vagner became his student in 1932 and wrote a thesis on the differential geometry of non-holonomic manifolds for his Candidate's Degree (equivalent to a Ph.D.).
- Vagner's first paper Sur la géométrie différentielle des multiplicités anholonomes Ⓣ(On the differential geometry of anholonomic multiplicities) was published in 1935 followed, remarkably, by eight papers in 1938 including A generalization of non-holonomic manifolds in Finslerian space.
- Vagner was appointed to the Chair of Geometry at Saratov University after the award of the degree of Doctor of Science and he continued to work there until he retired in 1978.
- All Vagner's research is connected with differential geometry and algebraization of its foundations.
- Algebraic systems considered by Vagner were usually related to differential geometric structures.
- Among Vagner's early papers we mention Differential geometry of non-linear non-holonomic manifolds in the three-dimensional Euclidean space (1940), The geometry of an (n-1)-dimensional non-holonomic manifold in an n-dimensional space (Russian) (1941), Geometric interpretation of the motion of non-holonomic dynamical systems (Russian) (1941), On the problem of determining the invariant characteristics of Liouville surfaces (Russian) (1941), and On the Cartan group of holonomicity for surfaces (1942).
- Vagner published the book Geometria del calcolo delle variazioni Ⓣ(Geometry of the calculus of variations) in Italian in 1965 in which he gave a systematic treatment of his own approach to the geometry of the calculus of variations, which he developed during the years 1942-1952.
- The quote by Schein above indicates how geometry led Vagner to study algebraic systems.
- This led Vagner to investigate inverse semigroups which he was the first to introduce (although he did not use that name) in the paper Generalised groups (Russian) paper in 1952.
- Even specialists sought Vagner's advice in various questions of philosophy, history, linguistics, literature.
- And also Vagner was a very decent man.

Born 4 November 1908, Saratov, Russia. Died 16 August 1981, Brest, Belarus, USSR.

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Origin Russia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive