Vladimir Arnold

His father was Igor Vladimirovich Arnold (1900–1948), a mathematician.

His mother was Nina Alexandrovna Arnold (1909–1986, née Isakovich), a Jewish art historian.

While a school student, Arnold once asked his father on the reason why the multiplication of two negative numbers yielded a positive number, and his father provided an answer involving the field properties of real numbers and the preservation of the distributive property.

Arnold was deeply disappointed with this answer, and developed an aversion to the axiomatic method that lasted through his life.

When Arnold was thirteen, his uncle Nikolai B. Zhitkov, who was an engineer, told him about calculus and how it could be used to understand some physical phenomena, this contributed to sparking his interest for mathematics, and he started to study by himself the mathematical books his father had left to him, which included some works of Leonhard Euler and Charles Hermite.

Vladimir Igorevich Arnold (alternative spelling Arnol'd, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician.

He is known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, symplectic topology, differential equations, classical mechanics, differential geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem.

Vladimir Igorevich Arnold was born on 12 June 1937 in Odesa, Soviet Union (now Odesa, Ukraine).

His first main result was the solution of Hilbert's thirteenth problem in 1957 at the age of 19.

He co-founded two new branches of mathematics: topological Galois theory (with his student Askold Khovanskii) and KAM theory.

Arnold was also known as a popularizer of mathematics.

Through his lectures, seminars, and as the author of several textbooks (such as Mathematical Methods of Classical Mechanics) and popular mathematics books, he influenced many mathematicians and physicists.

Many of his books were translated into English.

His views on education were particularly opposed to those of Bourbaki.

While a student of Andrey Kolmogorov at Moscow State University and still a teenager, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby solving Hilbert's thirteenth problem.

This is the Kolmogorov–Arnold representation theorem.

After graduating from Moscow State University in 1959, he worked there until 1986 (a professor since 1965), and then at Steklov Mathematical Institute.

He became an academician of the Academy of Sciences of the Soviet Union (Russian Academy of Science since 1991) in 1990.

Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline.

The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections was also a motivation in the development of Floer homology.

In 1999 he suffered a serious bicycle accident in Paris, resulting in traumatic brain injury.

He regained consciousness after a few weeks but had amnesia and for some time could not even recognize his own wife at the hospital, He went on to make a good recovery.

Arnold worked at the Steklov Mathematical Institute in Moscow and at Paris Dauphine University up until his death.

he was reported to have the highest citation index among Russian scientists, and h-index of 40.

His students include Alexander Givental, Victor Goryunov, Sabir Gusein-Zade, Emil Horozov, Boris Khesin, Askold Khovanskii, Nikolay Nekhoroshev, Boris Shapiro, Alexander Varchenko, Victor Vassiliev and Vladimir Zakalyukin.

To his students and colleagues Arnold was known also for his sense of humour.

For example, once at his seminar in Moscow, at the beginning of the school year, when he usually was formulating new problems, he said:

"There is a general principle that a stupid man can ask such questions to which one hundred wise men would not be able to answer. In accordance with this principle I shall formulate some problems."

His defense was that his books are meant to teach the subject to "those who truly wish to understand it" (Chicone, 2007).

Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century.

He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French mathematical education, and then later on that of other countries as well.

Arnold died of acute pancreatitis on 3 June 2010 in Paris, nine days before his 73rd birthday.

He was buried on 15 June in Moscow, at the Novodevichy Monastery.

In a telegram to Arnold's family, Russian President Dmitry Medvedev stated:

"The death of Vladimir Arnold, one of the greatest mathematicians of our time, is an irretrievable loss for world science. It is difficult to overestimate the contribution made by academician Arnold to modern mathematics and the prestige of Russian science.

Teaching had a special place in Vladimir Arnold's life and he had great influence as an enlightened mentor who taught several generations of talented scientists.

The memory of Vladimir Arnold will forever remain in the hearts of his colleagues, friends and students, as well as everyone who knew and admired this brilliant man."

Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching and education.

His writings present a fresh, often geometric approach to traditional mathematical topics like ordinary differential equations, and his many textbooks have proved influential in the development of new areas of mathematics.

The standard criticism about Arnold's pedagogy is that his books "are beautiful treatments of their subjects that are appreciated by experts, but too many details are omitted for students to learn the mathematics required to prove the statements that he so effortlessly justifies."