Pavel Aleksandrov

Pavel Aleksandrov authored approximately three hundred academic papers throughout a career defined by foundational contributions to topology, set theory, and function theory. Emerging from the Moscow school of mathematics, he bridged the gap between combinatorial and general topology, establishing frameworks that remain central to modern algebraic topology and the study of abstract mathematical spaces.

Early Career and Education

Born in 1896 in Noginsk, Aleksandrov attended the Smolensk gymnasium before enrolling at Lomonosov Moscow State University in 1913. Under the mentorship of Nikolai Luzin and Dmitri Egorov, he engaged with the rigorous challenges of set theory. A 1917 crisis regarding the continuum hypothesis interrupted his progression, leading him to work in Chernihiv where he helped organize a drama theater and contracted typhus. He completed his studies by 1921 and held faculty positions at Moscow State University until 1982, as well as at the Steklov Institute of Mathematics starting in 1939.

Mathematical Innovations

Aleksandrov was a key figure in the Moscow topological school, collaborating extensively with Pavel Urysohn during visits to the University of Göttingen. Together, they formulated the metrization theorem and the compactification theorem for locally compact Hausdorff spaces. His independent work introduced the concept of the exact sequence and the nerve of a covering, which facilitated the development of Alexandrov-Čech cohomology. He additionally formalized the homological theory of dimension in 1932, expanding the methods used for combinatorial research into general topological spaces.

Professional Conduct and Recognition

In 1936, Aleksandrov took a prominent role in the political criticism of his former mentor, Luzin, during the Luzin affair. His academic standing flourished regardless, leading to his admission into various international societies including the American Philosophical Society and the German Academy of Sciences Leopoldina. He received numerous distinctions throughout his life, including the Stalin Prize in 1942 and seven awards of the Order of Lenin, spanning from 1946 to 1975.

Personal Life and Relationships

Aleksandrov maintained a brief marriage to Ekaterina Romanovna Eiges in 1921. Following their divorce, he entered a close partnership with Pavel Urysohn, which ended upon Urysohn's drowning in the Atlantic Ocean in 1924. In the latter half of his life, he shared a long-term, stable relationship with the mathematician Andrey Kolmogorov. Aleksandrov remained a dedicated teacher, mentoring generations of students including Lev Pontryagin and Andrey Tychonoff. He died in 1982 in Moscow and is buried at the Kavezinski cemetery.

Fast facts

• Born: 1896, Noginsk
• Died: 1982, Moscow
• Primary Field: Topology
• Academic Home: Lomonosov Moscow State University
• Notable Contribution: Alexandrov compactification
• Stalin Prize recipient: 1942
• Language proficiency: Russian, German, French
• Burial location: Kavezinski cemetery

Questions readers ask

What is the Alexandroff extension?

It is a mathematical construction that allows for the compactification of any locally compact Hausdorff space by the addition of a single point.

Did Aleksandrov hold international academic roles?

Yes, he worked at the Institute for Advanced Study between 1927 and 1928 and held memberships in organizations like the American Philosophical Society and the German Academy of Sciences at Berlin.

Who was his long-term partner?

He maintained a lifelong relationship with the mathematician Andrey Kolmogorov, which lasted over fifty years.

Achievements

• Order of Lenin — 1946
• Order of the October Revolution — 1980
• Order of the Badge of Honour — 1940
• Order of the Red Banner of Labour — 1945
• Stalin Prize — 1942
• Notable work: Čech cohomology
• Notable work: Alexandroff extension
• Notable work: Alexandroff plank
• Notable work: long line
• Held posts at Lomonosov Moscow State University, Steklov Institute of Mathematics and Institute for Advanced Study