Veniamin Fedorovich Kagan

Background

Veniamin Kagan was born on March 10, 1869, in Siauliai, Kovno Governorate, Russian Empire (now Siauliai, Lithuania). His father Fedor Kagan was a clerk, and his mother was a housewife. He also had an elder sister Maria.

In 1871 his family moved to Yekaterinoslav (now Dnipro), where Kagan grew up.

Education

Kagan entered Novorossysky University, Odessa, in 1887, but was expelled in 1889 for participating in the democratic students’ movement and was sent to Ekatcrinoslav (now Dnepropetrovsk). In 1892 he passed the examinations in the department of physics and mathematics of Kyiv University. He passed the examinations for the master’s degree at St. Petersburg in 1895.

Career

Kagan became a lecturer at Novorossysky in 1897 and professor in 1917. Besides teaching at Novorossysky, Kagan gave higher education classes for women and presented courses at a Jewish high school. He edited Vestnik opytnoi fiziki i elementarnoi matematiki (“Journal of Experimental Physics and Elementary Mathematics”) in 1902-1917 and was a director of a large scientific publishing house, Mathesis.

Kagan’s first important work was devoted to a very original and ingenious exposition of Lobachevsky’s geometry. Next, he considered problems of the foundations of geometry, proposing in 1902 a system of axioms and definitions considerably different from all previously suggested, and particularly different from that of Hilbert. This system was based on the notion of space as a set of points in which to every two points there corresponds a nonnegative number - distance - invariant in respect to a system of point transformations (movements) in this space; the point, the principal element from which other figures are generated, is not defined. Very complete construction of Euclid’s geometry on such a basis is in the first volume of Kagan’s master’s thesis, defended in 1907; the second volume contains a detailed history of the doctrines of the foundations of geometry. In 1903 Kagan presented a new demonstration, remarkable in its simplicity, of Dehn’s well-known theorem on equal polyhedrons (1900). Since he was interested in Einstein’s theory of relativity, Kagan also began studies in tensor differential geometry which he pursued intensively in Moscow, to which he moved in 1922.

For almost ten years Kagan was in charge of the science department of the state publishing house, and for many years he supervised the department of mathematical and natural sciences of the Great Soviet Encyclopedia. But his principal efforts were directed to Moscow University, where he was elected professor in 1922; in 1927 he organized a seminar on vector and tensor analysis, and from 1934 he held the chair of differential geometry. At Moscow, Kagan created a large scientific school with considerable influence on the development of contemporary geometrical thought; his disciples include Y. S. Dubnov, P. K. Rashevsky, A. P. Norden, and V. V. Wagner. Kagan himself was concerned mainly with the theory of subprojective spaces, a generalization of Riemannian spaces of constant curvature.

Kagan also wrote studies on the history of non-Euclidean geometry and published a detailed biography of Lobachevsky. He was the general editor of the five-volume edition of Lobachevsky’s complete works (1946-1951).

Achievements

• Veniamin Kagan went down in history as a noted Soviet mathematician. He published over 100 mathematical papers in different parts of geometry, particularly on hyperbolic geometry and Euclidean and non-Euclidean geometry and the theory of subprojective spaces.
  
  In 1929 he was named Honored Scientist of the RSFSR. In 1940 he was awarded the Order of the Red Banner of Labour. In 1943 he was awarded the U.S.S.R. State Prize. In 1946 he was awarded the Soviet medal of Stalin for valiant work in the Great Patriotic War of 1941-1945.

Works

More photos

• book

  • Jahresbericht der Deutschen Mathematiker-Vereinigung, Volume 11

    (The book contains Kagan's work Ein System von Postulaten,...)

    1902
  • Mathematische Annalen, Volume 57

    (The book contains Kagan's work Über die Transformation de...)

    1903
  • N. Lobachevsky and His Contribution to Science 1957

Connections

Kagan was married twice. His first wife was Elena Kagan; together they had two daughters, Nadezhda and Lidiya. She died in 1918. He married Maria Kagan in 1920, together they raised her two children from her first marriage, Ernestina and Joseph.

Father:

Fedor Kagan

Spouse:

Maria Kagan

late spouse:

Elena Kagan

Daughter:

Nadezhda Kagan

Daughter:

Lidiya Kagan

step-daughter:

Ernestina Kagan

Step-son:

Joseph Kagan

Student:

Y. S. Dubnov

Student:

P. K. Rashevsky

Student:

A. P. Norden

Student:

V. V. Wagner

References

• Dictionary of Scientific Biography, Volume 7
  1973