Grigori Perelman facts for kids
Quick facts for kids
Grigori Perelman
|
|
|---|---|
| Григорий Перельман | |
_(cropped).jpg)
Perelman in 1993
|
|
| Born |
Grigori Yakovlevich Perelman
13 June 1966 Leningrad, Soviet Union
(now Saint Petersburg, Russia) |
| Education | Leningrad State University (PhD) |
| Known for |
|
| Awards |
|
| Scientific career | |
| Fields |
|
| Institutions | POMI New York University University of California, Berkeley |
| Thesis | Saddle Surfaces in Euclidean Spaces (1990) |
| Doctoral advisor |
|
Grigori Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман, IPA: [ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman]; born June 13, 1966) is a Russian mathematician. He is famous for his important work in areas of math like geometric analysis and geometric topology.
Perelman is best known for solving the Poincaré conjecture, a very difficult math problem that had been unsolved for 100 years. He also proved Thurston's geometrization conjecture. Despite his amazing achievements, he has turned down major awards, including the prestigious Fields Medal and the Millennium Prize (which came with a million dollars!). Since 2005, he has lived a quiet life in Saint Petersburg, Russia, and avoids interviews.
Contents
Early Life and Schooling
Grigori Perelman was born in Leningrad, which is now Saint Petersburg, Russia, on June 13, 1966. His parents were Jewish. His mother, Lyubov, who was also a mathematician, stopped her studies to raise him.
Grigori showed a special talent for math when he was only 10 years old. His mother enrolled him in a special after-school math program. He later attended a special school for math and physics, where he was excellent in all subjects except physical education.
In 1982, just after his 16th birthday, he won a gold medal at the International Mathematical Olympiad. He got a perfect score! After high school, he went to Saint Petersburg State University to study math.
After earning his PhD in 1990, Perelman started working at the Steklov Institute of Mathematics in Saint Petersburg. He also spent time doing research at universities in the United States, like New York University and the University of California, Berkeley. In 1994, he solved the soul conjecture, another big problem in math. He was offered jobs at top universities, but he chose to return to the Steklov Institute in 1995.
Major Math Discoveries
Perelman made very important contributions to math, especially in understanding shapes and spaces.
Understanding Alexandrov Spaces
Perelman did early work on something called Alexandrov spaces. These are special kinds of spaces that can be curved, but not necessarily smooth like a perfect ball. He helped set up the modern ideas for studying these spaces. He also showed that if these spaces are similar enough, they are also topologically the same.
Solving the Soul Conjecture
In 1994, Perelman proved the soul conjecture. Imagine a curved surface that stretches out forever. The soul conjecture is about finding a smaller, compact part of that surface (called the "soul") that can represent the whole shape. Perelman's proof was a big step forward in understanding these complex shapes.
The Poincaré and Geometrization Conjectures
The Poincaré conjecture was one of the most famous unsolved problems in math for 100 years. It's about understanding the shape of a three-dimensional space. Imagine a rubber band on the surface of a ball. You can always shrink that rubber band to a single point. The Poincaré conjecture asks: if you have a three-dimensional shape where every "loop" can be shrunk to a point, is that shape always like a 3-sphere (the 3D version of a ball's surface)?
William Thurston later came up with the Thurston geometrization conjecture. This idea said that all three-dimensional shapes could be broken down into simpler pieces, each with a specific geometric structure. The Poincaré conjecture was just a small part of this bigger idea.
Richard S. Hamilton developed a tool called "Ricci flow." Think of it like heat spreading out in an object until the temperature is even. Ricci flow tries to smooth out the curvature of a shape. Hamilton made a lot of progress, but he couldn't fully solve the problem because of "singularities" (points where the curvature becomes infinite).
Perelman's Breakthrough
In 2002 and 2003, Perelman posted his ideas online. He showed how to deal with the singularities in Ricci flow. He developed new techniques, including the "noncollapsing theorem" and the "canonical neighborhoods theorem." These ideas helped him understand how the shapes would change and where problems (singularities) would appear.
He then used a method called "Ricci flow with surgery." This is like letting the shape deform, and when a singularity starts to form, you "cut out" the problematic part and "glue" it back together in a simpler way. By doing this, Perelman was able to show that the Ricci flow process would eventually lead to a simpler, understandable shape. This allowed him to prove both the Poincaré conjecture and the geometrization conjecture.
Checking the Proof
Perelman's work was very complex and hard to read, but mathematicians around the world quickly started to study it. Several teams of mathematicians, including Bruce Kleiner and John Lott, Huai-Dong Cao and Zhu Xiping, and John Morgan and Gang Tian, wrote detailed explanations of his proof. After years of careful checking, they all agreed that Perelman's arguments were correct.
Awards and Refusals
In 2006, Perelman was offered the Fields Medal, which is like the Nobel Prize for mathematicians. He turned it down. He told the president of the International Mathematical Union: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo." He felt that if his proof was correct, no other award was needed.
In 2010, he was awarded the first Millennium Prize for solving the Poincaré conjecture, which came with a one-million-dollar award. He also refused this prize. He said he felt the decision was unfair because he believed his contribution was no greater than that of Richard S. Hamilton, who had started the Ricci flow method.
Life Away from Math
Perelman left his job at the Steklov Institute of Mathematics in 2005. He has since lived a very private life in Saint Petersburg. He has said that he was disappointed with the ethical standards in the field of mathematics. He felt that some mathematicians were not honest and that others tolerated this behavior.
He has avoided journalists and the media. In 2012, a reporter called him, and he simply said, "You are disturbing me. I am picking mushrooms." It is unclear if he still works on math problems, but some reports suggest he might be interested in other areas, like nanotechnology.
Images for kids
-
Perelman in 1993
See also
In Spanish: Grigori Perelmán para niños
- Ancient solution
- Asteroid 50033 Perelman
- Homology sphere
- Hyperbolic manifold
- "Manifold Destiny" (On The New Yorker article)
- Spherical space form conjecture
- Thurston elliptization conjecture
- Uniformization theorem
