Pavel Alexandrov facts for kids
Quick facts for kids
Pavel Alexandrov
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| Born |
Pavel Sergeyevich Alexandrov
7 May 1896 Bogorodsk, Moscow Governorate, Russian Empire
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| Died | 16 November 1982 (aged 86) |
| Nationality | Soviet Union |
| Alma mater | Moscow State University |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Dmitri Egorov Nikolai Luzin |
| Doctoral students | Aleksandr Kurosh Lev Pontryagin Yu. M. Smirnov Petru Soltan Andrey Tikhonov Lev Tumarkin |
Pavel Sergeyevich Alexandrov (Russian: Па́вел Серге́евич Алекса́ндров), also known as Paul Alexandroff, was an important Soviet mathematician. He was born on May 7, 1896, and passed away on November 16, 1982. He wrote around 300 papers, making big contributions to areas of math called set theory and topology. In topology, some ideas like the Alexandroff compactification and the Alexandrov topology are named after him.
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A Life in Mathematics
Pavel Alexandrov studied at Moscow State University. There, his teachers were famous mathematicians Dmitri Egorov and Nikolai Luzin. He also spent time at the University of Göttingen in Germany in 1923 and 1924 with another mathematician, Pavel Urysohn.
After earning his Ph.D. in 1927, he continued to work at Moscow State University. He also joined the Steklov Institute of Mathematics, a major research center. In 1953, he became a member of the Russian Academy of Sciences, which is a great honor for a scientist.
Early Challenges
Early in his career, Alexandrov faced a difficult math problem. His teacher, Luzin, challenged him to figure out if the continuum hypothesis was true. This problem was very hard, and it made Alexandrov feel stuck in his work around 1917. He felt like he couldn't move forward in mathematics for a while.
During this time, he even helped organize a drama theater in Chernihiv. He also became ill with typhus.
Family and Friendships
In 1921, Pavel Alexandrov married Ekaterina Romanovna Eiges. She was a poet and also worked with libraries and mathematics.
Alexandrov also became very close friends with another famous mathematician, Andrey Kolmogorov. Their friendship lasted for 50 years. Alexandrov said they never had a disagreement or misunderstanding.
In 1955, Alexandrov signed a letter called the "Letter of Three Hundred." This letter criticized a controversial idea in biology called Lysenkoism, which was not based on good science. This showed his commitment to scientific truth.
Pavel Alexandrov was buried at the Kavezinsky cemetery near Moscow.
His Work in Science
Alexandrov's main work was in topology, which is a branch of mathematics that studies shapes and spaces. He also worked on set theory, which deals with collections of objects, and other areas of math.
He introduced a new idea called "compactness" in topology. He and P. S. Urysohn showed how important this idea was. They proved a key theorem about how to "compactify" a space by adding just one point.
From 1923, Alexandrov started studying combinatorial topology. This area combines ideas from general topology with ways to count and arrange things. He helped connect these two fields, which became important for modern algebraic topology. He also introduced the idea of an exact sequence, which is a basic concept in algebraic topology.
He also came up with the idea of a "nerve of a covering." This led him to discover something called Alexandrov-Cech Cohomology, which helps mathematicians understand the structure of spaces.
In 1924, Alexandrov proved that in any open cover of a certain type of space, you can find a "locally finite open cover." He was the first to introduce this important concept in topology.
He also made big steps in the "theory of dimension," which helps describe how many directions you can move in a space. He developed ways to study general topological spaces using combinatorial methods.
Moscow Topological School
Pavel Alexandrov and P. S. Urysohn started the Moscow topological school. This group of mathematicians became known worldwide for their work in topology. Many ideas and theorems in topology are named after Alexandrov, like the Alexandrov compactification and the Alexandrov topology.
Important Books
Alexandrov wrote several important books that helped develop science and mathematics education in Russia. These include:
- Introduction to the General Theory of Sets and Functions
- Combinatorial Topology
- Lectures on Analytical Geometry
- Dimension Theory (with B. A. Pasynkov)
- Introduction to Homological Dimension Theory
He also wrote a classic textbook called Topologie I with Heinz Hopf in German.
The Luzin Affair
In 1936, there was a difficult situation involving Alexandrov's former teacher, Nikolai Luzin. This event is known as the Luzin affair. Even though Alexandrov had been Luzin's student, he was involved in the criticism against Luzin during this time. Their relationship remained strained afterward.
His Students
Pavel Alexandrov taught many students who became famous mathematicians themselves. Some of his most well-known students include Lev Pontryagin, Andrey Tychonoff, and Aleksandr Kurosh. He guided many generations of mathematicians, helping them become leaders in the field.
Awards and Recognition
Pavel Alexandrov received many honors and awards for his important contributions to mathematics:
- Hero of Socialist Labour
- Stalin Prize
- Order of Lenin, six times (1946, 1953, 1961, 1966, 1969 and 1975)
- Order of the October Revolution
- Order of the Red Banner of Labour
- Order of the Badge of Honour
- Member of the American Philosophical Society (1946)
- Member of the United States National Academy of Sciences (1947)
Books
- Alexandroff P., Hopf H. Topologie Bd.1 — B: , 1935
Books In Russian
