Arnold Vladimir Igorevich is a Soviet and Russian mathematician who developed theories concerning differential equations, singularities of smooth mappings, and also wrote many works on theoretical mechanics and topology.
Biography
Arnold Vladimir Igorevich (photo posted in the article) was born on 06/12/1937 in Ukraine, in the city of Odessa.
However, his family soon moved to Moscow, where the future mathematician spent his childhood. After graduating from the capital's school No. 59, Vladimir Arnold became a student at the Faculty of Mechanics and Mathematics of Moscow State University, who successfully graduated in 1959.
The future scientist was lucky. His teacher was the famous mathematician Andrei Nikolaevich Kolgomorov. Already in his 20s, Vladimir Arnold expressed the opinion that any continuous function consisting of several variables can be represented as a combination of a certain number of functions. This allowed us to solve the 13th Hilbert problem.
Having received a diploma from Moscow State University, Arnold Vladimir Igorevich stayed to work at his native university. In the period from 1965 to 1986, he served as professor. As a wonderful teacher, Vladimir Igorevich conducted his classes, focusing on the comprehensibility of presentation and visualization. At the same time, he considered the formal style, providing for an accurate presentation of axioms, to be extremely ineffective. The mathematician considered this approach to teaching even harmful. Moreover, he recommended explaining exact science by his method to both students and schoolchildren.
The next place of his work was the Steklov Institute of Mathematics. Here Arnold Vladimir Igorevich worked from 1986 until the last days of his life. In those same years, he was an employee of the University of Paris-Dauphin.
Died mathematician Arnold Vladimir Igorevich 06/03/2010 in the capital of France. In Paris, a 72-year-old scientist was undergoing treatment. Vladimir Igorevich entered the hospital of St. Antoine on the eve of his death. Here he underwent an operation that he could not bear.
The mathematician Arnold Vladimir Igorevich was buried on June 15, 2010 at the Novodevichy Cemetery in Moscow. Academician Vitaly Ginzburg is resting next to him .
A family
Thanks to what, so interesting was the development of a famous Russian scientist, who was Vladimir Igorevich Arnold, a biography? The family of mathematicians played not the last role in his life.
The scientist's father, Igor Vladimirovich Arnold, was a doctor of pedagogical sciences. He was also a corresponding member of the APN of the RSFSR, professor, mathematician and methodologist. Vladimir Igorevich’s grandfather - Arnold Vladimir Fedorovich - was an extras and economist. He wrote several works studying the costs of peasant farms and agronomic technology. The paternal side of Vladimir Igorevich’s grandmother is the writer B. S. Zhitkov.
The mother of the famous Russian mathematician, Arnold Nina Alexandrovna, was an art critic. Her place of work was the Pushkin Museum. Vladimir Igorevich’s maternal grandfather is Isakovich Alexander Solomonovich. He was a lawyer, as well as a researcher and head of the educational unit at the Odessa Research Institute of Refrigeration Industry.
On the maternal side, Vladimir Igorevich was the nephew of physicists: Isakovich Mikhail Alexandrovich (head of the theoretical department at the Acoustic Institute of the Academy of Sciences of the USSR) and Paradise Natalia Alexandrovna, who worked as editor of the department of physics, located in the All-Union State Library of Scientific Literature.
The maternal brother of Arnold V.I.'s grandmother is the famous physicist L.I. Mandelstam. The mathematician’s brother, Arnold Dmitry Igorevich, devoted his life to the same science.
Academic career at home
How successful was the activity carried out by Vladimir Igorevich Arnold? His biography as a mathematician was the most brilliant at first in the USSR, and after - in Russia. His achievements in this field have been widely recognized in the circles of domestic and foreign scientists.
Already in 1965, he could become a full member of the USSR Academy of Sciences, but the voting results revealed a lack of just one vote. His election took place only 25 years later. The main reason for such a long break lies, most likely, in the independence of the scientist's views. Vladimir Igorevich expressed his views on the content of mathematical works, regardless of the personality of the author. Sometimes even academics came under fire from his critics.
A serious barrier to his career was the signing by him in 1968 of the "Letters of Ninety-Nine." This was a message compiled in defense of the Soviet logician A.S. Yesenin-Volpin, who was subjected to compulsory psychiatric treatment. Arnold was forbidden to travel abroad for this dissident act. And until the end of the 1980s, the scientist was limited in communication with foreign mathematicians. This fact, as Vladimir Igorevich himself believed, negatively affected his scientific achievements.
Academic career abroad
The surge in prices caused by the change in state structure forced Vladimir Igorevich to look for other sources of income. And, recalling his trip to France in 1964-1965, he accepted the offer of cooperation with the Dauphin University of Paris.
Since 1976, the scientist was elected an Honorary Member of the Mathematical Society in London, which was very flattering. According to Arnold himself, participation in this club was much more prestigious than getting the Fields medal. The famous mathematician was offered membership in the Papal Academy. But he refused it, explaining this by disagreeing with the still-not-overturned sentence, which in 1600 was passed by the Inquisition to Giordano Bruno.
In 1987, V.I. Arnold was chosen as an Honorary Foreign Member of the Academy of Arts and Sciences of America. And a year later he was accepted into the Royal Society of London.
In 1990, Vladimir Igorevich was elected an academician of the USSR Academy of Sciences, and from 1996 to 2010 he was President of the Moscow Mathematical Society. Similar activities were carried out by Arnold and abroad. So, from 1996 to 2002, the scientist was vice president and member of the Executive Committee of the International Mathematical Union.
Key Achievements
Throughout his scientific career, mathematician Arnold Vladimir Igorevich had a significant influence on various theories. At the same time, he made the main contribution:
- In the solution of one of the possible interpretations of the thirteenth Hilbert problem.
- In a theory considering perturbations of Hamiltonian systems. The totality of the methods, results and ideas received has its own name. Today it is the Kolmogorov-Arnold-Moser theorem (KAM theory).
- Into application for hydrodynamics of topological methods.
- In the theory of features. This development allowed to revolutionize the classification of features. The theory has become much richer and overgrown with numerous applications.
- Into the topology of algebraic real varieties. Arnold was one of the first to use complex technology in the study of this topology.
- A critical rethinking of the basic concept regarding the integrability of such common dynamic systems. Now this concept has a different name. Today it is Arnold-Liouville integrability.
- In constructing the form of families of matrices. This work resulted in a generalization of the understanding of the Jordan form of matrices.
- In the idea of constructing the so-called symplectic topology as one of the sources of quantum cohomology.
It is impossible not to mention the peculiar record that Vladimir Igorevich broke Arnold. Quotes from this scientist have been voiced by mathematicians more than 22,000 times.
Activities
Since the beginning of the 1960s, Vladimir Igorevich Arnold directed all his potential to comprehend the structure of the world, resorting to mathematical methods. At the same time, the scientist investigated those objects that few people paid attention to using their encyclopedic knowledge.
Vladimir Igorevich Arnold, whose achievements in the field of mathematics is difficult to overestimate, laid the foundations of many theories. However, when his ideas took a clear outline, and revealed their main direction of development, the scientist stepped aside. Having formulated the main task, Vladimir Igorevich left the development of details to his many students who loved the mentor and believed in him.
Feature theory
There is only one area in which Vladimir Igorevich Arnold (his biography is inextricably linked with mathematics) worked out all the questions from beginning to end. This is a theory of features. Its foundations and developments appeared thanks to Arnold, his school and the participation of researchers from the Soviet Union and their foreign colleagues.
In some Western publications, these works are called "catastrophe theory." This is a section of mathematics that describes any sudden change that occurs in an arbitrary system with small deviations from the initial states.
Take, for example, Ziman's car. This device is easy to assemble at home from fairly simple parts - a piece of paper, cardboard, pencil and two erasers.
Ziman's car is an example of a system in which disasters are possible. In such a device, a pencil is connected with elastic bands to a rotating disk made of cardboard. Sometimes its movement occurs smoothly, and sometimes, in response to a small change, in jerks. Such instability can be observed in many systems.
This field of knowledge occupies the minds of many researchers. System stability and instability can be applied to equations describing market evolution and heat transfer processes. The solution of such problems will make it possible to predict any direction in the behavior of nuclear reactors, and not only in a stable, but also in a catastrophic mode.
Arnold Vladimir Igorevich is not the founder of this section of mathematical science. The father of the "theory of disasters" is considered R. Tom. However, it was the Russian scientists who wrote the classic book dedicated to this area. Its name is Disaster Theory.
Ranks and awards
The bright rise of the young mathematician was appreciated by the state. Back in 1960, he was awarded the prize of the Moscow Mathematical Society. And five years later, V.I. Arnold and A.M. Kolmogorov were noted for their work on the KAM theory. Scientists were awarded the prestigious Lenin Prize. It was simply impossible to get a higher award in the USSR.
The scientist also received recognition of his merits from the world mathematical community. In 1974 in Vancouver, and also in 1983 in Warsaw, he read papers at the International Mathematical Congresses. A special half-hour performance by V.I. Arnold took place in 1966 in Moscow.
In 1982, Arnold shared with L. Nirenberg (USA) the newly established Swedish Academy of Sciences, but immediately became the prestigious Krafford Prize. However, the party leadership of the USSR did not release him to Stockholm to receive it.
In 2001, Vladimir Igorevich was awarded the Wolf Prize. Her scientist was awarded for active and fruitful work in various areas of mathematics.
In 2007, Arnold was among the first winners of the Russian State Prize. And a year later he was awarded the "Asian Nobel." This was the Schau prize, which the scientist shared with L.D. Faddeev, which was the next world recognition of Arnold's achievements.
Publications
Along with scientific works, Arnold Vladimir Igorevich wrote articles. Published in newspapers, as well as magazines and interviews with the famous mathematician.
Many of Arnold's articles touched on school education. The scientist criticized the educational system in foreign countries. At the same time, the problems of mathematical education in domestic schools were raised. The scientist expressed his negative opinion about the "dragging" of children for certain tasks.
Arnold Vladimir Igorevich also wrote books. These works, as a rule, concerned his scientific activity. However, here he did not forget about the younger generation. So, one of the books written by Arnold Vladimir Igorevich is “Tasks for children from 5 to 15 years old”. Let's consider it in more detail.
A fascinating journey into exact science
Surprising in its content is the book written by Vladimir Arnold - “Tasks for children from 5 to 15 years.” The answers to many of the questions contained in it are easiest to find for five-year-olds than for “trained” schoolchildren or students. It is difficult for professors, as well as Fields and Nobel laureates to solve such problems.
The idea of writing this book arose in the spring of 2004 in Paris. It was then that representatives of the Russian intelligentsia living in France asked Arnold to help their children in acquiring a culture of thinking so traditional for Russia. According to the scientist, this is precisely what should raise early independent thoughts in a person about simple, but at the same time difficult questions.
The brochure includes 77 tasks, composed or selected by the author. The solution to most of them does not need to receive special knowledge that would go beyond school education. Vladimir Igorevich addressed his book to preschoolers and schoolchildren, students and teachers. It is worth adopting for those parents who consider the upbringing of the culture of their child’s thinking to be a necessary part of personality development.
Here is one example of a task requiring a small discovery. On the bookshelf are two volumes of Pushkin's works. The thickness of the pages of each of them is 2 cm. In addition, the covers of these books are 2 mm each. On the first page of volume 1 was a bookworm. Then he gnawed his way along the shortest distance and ended up on the last page of Volume 2. What is the distance he has traveled?
This is a wonderful topological (geometric) problem, the answer of which is very unexpected for many - 4 mm. He is able to confuse many Nobel laureates, but preschoolers who still know how to make discoveries cope with it, as a rule, perfectly.