Vladimir Arnold facts for kids
Quick facts for kids
Vladimir Arnold
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Vladimir Arnold in 2008
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| Born | 12 June 1937 |
| Died | 3 June 2010 (aged 72) Paris, France
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| Nationality | Soviet Union, Russian |
| Alma mater | Moscow State University |
| Known for | ADE classification Arnold's cat map Arnold conjecture Arnold diffusion Arnold's rouble problem Arnold's spectral sequence Arnold tongue ABC flow Arnold–Givental conjecture Gömböc Gudkov's conjecture Hilbert's thirteenth problem KAM theorem Kolmogorov–Arnold theorem Liouville–Arnold theorem Topological Galois theory Mathematical Methods of Classical Mechanics |
| Awards | Shaw Prize (2008) State Prize of the Russian Federation (2007) Wolf Prize (2001) Dannie Heineman Prize for Mathematical Physics (2001) Harvey Prize (1994) RAS Lobachevsky Prize (1992) Crafoord Prize (1982) Lenin Prize (1965) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Paris Dauphine University Steklov Institute of Mathematics Independent University of Moscow Moscow State University |
| Doctoral advisor | Andrey Kolmogorov |
| Doctoral students |
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Vladimir Igorevich Arnold (sometimes spelled Arnol'd, Russian: Влади́мир И́горевич Арно́льд) was a very important Soviet and Russian mathematician. He was born on June 12, 1937, and passed away on June 3, 2010.
Arnold is famous for his work on the Kolmogorov–Arnold–Moser theorem. This theorem helps us understand how stable certain systems are, like planets orbiting the sun. He also made big discoveries in many other areas of mathematics. These include the study of dynamical systems theory (how things change over time), topology (the study of shapes), and classical mechanics (how objects move).
He helped start two new parts of mathematics: KAM theory and topological Galois theory. Many people think he was one of the greatest mathematicians ever.
Arnold also loved to share his knowledge. He taught many students and wrote several textbooks, like the well-known Mathematical Methods of Classical Mechanics. His books and lectures inspired many other mathematicians and scientists. He believed that math should be taught in a clear, easy-to-understand way.
About Vladimir Arnold
Vladimir Igorevich Arnold was born in Odessa, Soviet Union (which is now Odesa, Ukraine). His father, Igor Vladimirovich Arnold, was also a mathematician. His mother, Nina Alexandrovna Arnold, was an art historian.
When Vladimir was a school student, he asked his father why multiplying two negative numbers gives a positive number. He was not happy with the complex answer he got. This made him dislike teaching methods that were too abstract.
When he was thirteen, his uncle, an engineer, told him about calculus. This is a type of math used to understand how things change. This sparked Vladimir's interest in mathematics. He started to read his father's math books, including works by famous mathematicians like Leonhard Euler.
Early Discoveries
While still a teenager, in 1957, Arnold was a student of Andrey Kolmogorov at Moscow State University. At just 19 years old, he solved Hilbert's thirteenth problem. This problem asked if complex functions could be built from simpler two-variable functions. Arnold showed that they could, which was a huge achievement. This discovery is known as the Kolmogorov–Arnold representation theorem.
After finishing university in 1959, he worked at Moscow State University until 1986. He then moved to the Steklov Mathematical Institute. In 1990, he became a member of the Academy of Sciences of the Soviet Union.
In 1999, Arnold had a serious bike accident in Paris. He suffered a brain injury and lost his memory for a while. But he made a good recovery and continued his work. He worked at the Steklov Institute of Mathematics in Moscow and at Paris Dauphine University until he passed away.
Arnold was also known for his good sense of humor among his students and friends.
His Passing
Vladimir Arnold passed away on June 3, 2010, in Paris, just nine days before his 73rd birthday. He was buried in Moscow.
Sharing Mathematical Ideas
Arnold was famous for his clear and easy-to-understand writing style. He combined strict mathematical rules with real-world ideas. His textbooks often showed new, visual ways to look at math topics. These books helped develop new areas of mathematics.
Some people said his books were so good that only experts could fully appreciate them. They felt that students might find some details missing. But Arnold said his books were for "those who truly wish to understand it."
Arnold did not like the trend in the mid-20th century where mathematics became very abstract. He believed this made math harder to learn. He was also very interested in the history of mathematics. He often told his students to read books about the history of math. He studied the works of old masters like Isaac Newton and Henri Poincaré. He often found new ideas in their old writings.
Arnold's Key Work
Arnold worked on many different math topics. These included dynamical systems theory, topology, algebraic geometry, and differential equations. A mathematician named Michèle Audin called him "a geometer in the widest possible sense." She said he was very quick to connect different areas of math.
Solving Hilbert's Thirteenth Problem
This problem asked if any continuous function with three variables could be made by combining a limited number of continuous functions with only two variables. Vladimir Arnold, at 19 years old, gave a positive answer in 1957. His teacher, Andrey Kolmogorov, had shown the year before that functions of many variables could be built from three-variable functions. Arnold then showed that only two-variable functions were needed.
Understanding Dynamical Systems
Arnold, along with Jürgen Moser, built on the ideas of Andrey Kolmogorov. This led to the Kolmogorov–Arnold–Moser theorem, often called "KAM theory." This theory helps explain how some repeating motions, like planets orbiting, can stay stable even when they are slightly disturbed. KAM theory shows that these systems can remain stable for a very long time under certain conditions.
Studying Singularities
In 1965, Arnold attended a seminar on catastrophe theory. He said this event "profoundly changed my mathematical universe." After this, the study of singularity theory became a major focus for Arnold and his students. Singularities are points where mathematical functions behave in unusual ways.
Fluid Dynamics Discoveries
In 1966, Arnold published a paper that connected the math for rotating rigid bodies with the math for how fluids flow. This linked topics that were thought to be separate. It helped solve many questions about fluid flows and their turbulence.
Geometry of Curves
According to another mathematician, Marcel Berger, Arnold changed how people understood the theory of plane curves. He introduced new ways to describe these curves, known as the Arnold invariants.
Other Contributions
Arnold also suggested the idea of the gömböc, a special 3D shape that always returns to a stable position when placed on a flat surface.
Awards and Recognition
Vladimir Arnold received many important awards for his work:
- Lenin Prize (1965), for his work on how celestial bodies move.
- Crafoord Prize (1982), for his contributions to the study of non-linear differential equations.
- He was elected as a member of the United States National Academy of Sciences in 1983.
- He became a Foreign Member of the Royal Society of London in 1988.
- Lobachevsky Prize of the Russian Academy of Sciences (1992).
- Harvey Prize (1994), for his work on the stability of dynamical systems and singularity theory.
- Dannie Heineman Prize for Mathematical Physics (2001), for his work on dynamics and singularities.
- Wolf Prize in Mathematics (2001), for his important work in many areas of mathematics.
- State Prize of the Russian Federation (2007), for his amazing achievements in mathematics.
- Shaw Prize in mathematical sciences (2008), for his contributions to mathematical physics.
A small planet, 10031 Vladarnolda, was named after him in 1981. The Arnold Mathematical Journal, which started in 2015, is also named in his honor.
Fields Medal Situation
Arnold was nominated for the Fields Medal in 1974, which is one of the highest honors for a mathematician. However, due to problems with the Soviet government at the time, the award was withdrawn. Arnold had openly disagreed with some government actions, which caused him difficulties, including not being allowed to leave the Soviet Union for many years.
