Igor Shafarevich facts for kids
Quick facts for kids
Igor Shafarevich
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| Born |
Igor Rostislavovich Shafarevich
3 June 1923 |
| Died | 19 February 2017 (aged 93) Moscow, Russia
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| Nationality | Russian |
| Alma mater | Steklov Institute of Mathematics |
| Known for | Shafarevich–Weil theorem, Golod–Shafarevich theorem, Shafarevich's theorem on solvable Galois groups, Grothendieck–Ogg–Shafarevich formula, Néron–Ogg–Shafarevich criterion |
| Awards | Leonard Euler Gold Medal (2017) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Lomonosov Moscow State University |
| Doctoral advisor | Boris Delaunay |
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Igor Rostislavovich Shafarevich (Russian: И́горь Ростисла́вович Шафаре́вич; June 3, 1923 – February 19, 2017) was a Soviet and Russian mathematician. He made important discoveries in areas like algebraic number theory and algebraic geometry. Outside of math, he wrote books and articles that discussed his views on society and history.
Contents
Amazing Math Discoveries
From a young age, Igor Shafarevich made big contributions to many parts of mathematics. These included algebraic number theory, algebraic geometry, and arithmetic algebraic geometry.
Number Theory Breakthroughs
In algebraic number theory, Shafarevich helped create the Shafarevich–Weil theorem. This theorem is about special mathematical groups called Galois groups. He was also the first to create a full formula for something called the Hilbert pairing, which is important in number theory.
Another famous result is Shafarevich's theorem on solvable Galois groups. This theorem shows how to connect every finite solvable group to Galois groups over rational numbers. He also worked on the Golod–Shafarevich theorem, which is about towers of number fields.
Exploring Algebraic Geometry
Shafarevich and his students greatly helped in studying the algebraic geometry of surfaces. He started a famous seminar in Moscow about classifying algebraic surfaces. This seminar helped introduce new ways of thinking about algebraic geometry in the Soviet Union.
His research into elliptic curves led him to discover a special group related to these curves. This group is now called the Tate–Shafarevich group, often shortened to 'Sha' (Ш). He also contributed to the Grothendieck–Ogg–Shafarevich formula and the Néron–Ogg–Shafarevich criterion.
With his former student Ilya Piatetski-Shapiro, he proved a version of the Torelli theorem for K3 surfaces.
The Shafarevich Conjecture
He also came up with the Shafarevich conjecture. This idea suggested that there are only a limited number of certain mathematical objects (called Abelian varieties) with specific properties. This conjecture was later proven by another mathematician, Gerd Faltings.
His Students and Awards
Many of Shafarevich's students became famous mathematicians themselves, including Yuri Manin and Alexey Parshin.
He was a member of important scientific groups like the Serbian Academy of Sciences and Arts and the German Academy of Sciences Leopoldina. In 1981, he became a foreign member of the Royal Society in the UK. In 2017, he received the Leonhard Euler Gold Medal from the Russian Academy of Sciences, which is a very high honor in mathematics.
His Life and Ideas
Igor Shafarevich sometimes had disagreements with the Soviet government in the 1950s. However, he was protected by Ivan Petrovsky, who was the head of Moscow University. Shafarevich was part of a group of thinkers who supported the traditions of the Eastern Orthodox Church.
Standing Up for Rights
In the 1970s, Shafarevich became one of Andrei Sakharov's helpers. Sakharov was a famous scientist and human rights activist. Shafarevich helped investigate human rights issues, and because of this, he was removed from his job at Moscow University. He believed that politics should not interfere with universities.
His Book: The Socialist Phenomenon
Shafarevich wrote a book called The Socialist Phenomenon, which was published in 1980. In this book, he looked at many examples of socialism throughout history, from ancient times to modern states. He suggested that the main ideas of socialism come from a desire to limit individualism.
The book has three main parts:
- Ancient and Medieval Ideas: This part looks at socialist ideas from ancient Greeks like Plato, and from different religious groups in the Middle Ages. It also covers modern writers like Thomas More.
- State-Controlled Societies: This section describes how socialism appeared in places like the Inca Empire, the Jesuit state in Paraguay, and ancient societies in Mesopotamia, Egypt, and China.
- His Analysis: In this part, Shafarevich pointed out three common themes in socialism: getting rid of private property, changing the idea of the family, and removing religion (especially Christianity).
Shafarevich believed that ancient forms of socialism were not based on a specific idea, but that socialism as an idea grew as people started to focus more on individuals. He suggested that socialism is linked to a desire to remove individual differences.
Thoughts on Math and Faith
Igor Shafarevich was a Russian Orthodox Christian. He connected his religious beliefs with his understanding of mathematics.
When he received a prize from the Göttingen Academy of Sciences, Shafarevich talked about how mathematics and religion are related. He noted that discoveries in pure mathematics, like non-Euclidean geometry, show that math reflects a real, objective world. He felt that for mathematics to have a clear direction, it needs a goal. He believed this goal could be practical uses or God as the source of its development. Shafarevich chose the latter, as pure mathematics is not always driven by practical needs.
Later Political Involvement
After the Soviet Union ended, Shafarevich became involved in Russian politics. In 1991, he joined the first meeting of the Russian All-People's Union. In 1992, he became a member of the founding committee for the National Salvation Front. In 1993, he ran for a position in the State Duma but was not elected.
He was also part of the editorial boards for magazines like Nash Sovremennik and Den (which later became Zavtra). In 1994, he joined the "All-Russian National Right Wing Centre."
A Historical Discussion
Igor Shafarevich wrote an essay called Russophobia, which later became part of his book Three Thousand-Year-Old Mystery. This work led to some discussions and different opinions about his views. The essay was first shared secretly in the Soviet Union and then officially published in 1989. At the same time, Shafarevich spoke out against unfair practices that prevented students of Jewish background from entering top Moscow universities in the 1970s and early 1980s.
In Russophobia, he suggested that sometimes in history, small groups of educated people might have ideas that are very different from most people in a country. He believed that in Russia, a group of intellectuals, which he said included many Jews, had negative feelings towards traditional Russian life. He also claimed they played a role in the strict governments of Vladimir Lenin and Joseph Stalin.
Because of this essay, the United States National Academy of Sciences (NAS) asked him to resign his membership. Shafarevich stated that his essay was not against any group of people. He also pointed out that the NAS had made him a member without his asking. Later, when the United States took military action in Iraq, Shafarevich sent in his resignation.
Some people continued to discuss his views, saying that his work contained factual errors. For example, some argued he incorrectly identified certain people involved in the execution of Nicholas II as Jewish. Shafarevich's book Three Thousand-Year-Old Mystery further explored his ideas.
In 2005, Shafarevich was one of many people who signed the Letter of 5000. A doctoral study in 2009 by Krista Berglund concluded that Shafarevich's views had been misunderstood.
See also
In Spanish: Ígor Shafarévich para niños
