Stephen Smale facts for kids
Quick facts for kids
Stephen Smale
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Smale in 2008
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Stephen Smale
July 15, 1930 Flint, Michigan, U.S.
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| Nationality | American |
| Education | University of Michigan (BS, PhD) |
| Known for | Generalized Poincaré conjecture Handle decomposition h-cobordism theorem Homoclinic orbit Horseshoe map Smale conjecture Smale's problems Morse–Smale system Morse–Smale diffeomorphism Palais–Smale compactness condition Blum–Shub–Smale machine Smale–Williams attractor Morse–Palais lemma Regular homotopy Sard's theorem Sphere eversion Structural stability Whitehead torsion Diffeomorphism |
| Awards | Wolf Prize (2007) National Medal of Science (1996) Chauvenet Prize (1988) Fields Medal (1966) Oswald Veblen Prize in Geometry (1966) Sloan Fellowship (1960) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Toyota Technological Institute at Chicago City University of Hong Kong University of Chicago Columbia University University of California, Berkeley |
| Thesis | Regular Curves on Riemannian Manifolds (1957) |
| Doctoral advisor | Raoul Bott |
| Doctoral students | Rufus Bowen César Camacho Robert L. Devaney John Guckenheimer Morris Hirsch Nancy Kopell Jacob Palis Themistocles M. Rassias James Renegar Siavash Shahshahani Mike Shub |
Stephen Smale (born July 15, 1930) is an American mathematician. He is famous for his work in topology, which studies shapes and spaces. He also researched dynamical systems (how things change over time) and mathematical economics (using math in economics).
Smale received the Fields Medal in 1966. This is one of the highest honors in mathematics. He taught at the University of California, Berkeley for over 30 years. Today, he is a Professor Emeritus there. He is interested in algorithms, numerical analysis, and global analysis.
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Stephen Smale's Early Life and Career
Smale was born in Flint, Michigan. He started at the University of Michigan in 1948. At first, he was a good student. He even took an advanced calculus class.
However, his grades dropped in his second and third years. He got many Bs, Cs, and even an F in nuclear physics. Despite this, he earned his Bachelor of Science degree in 1952.
Luckily, Smale was accepted into the math graduate program at the University of Michigan. His grades were still low at first. But when the department chair threatened to remove him, he started working harder. Smale earned his PhD in 1957. His advisor was Raoul Bott. After graduating, he began teaching at the University of Chicago.
Speaking Out and Challenges
Early in his career, Smale was known for his strong opinions. He once joked that he did his best work "on the beaches of Rio." He was also involved in social movements. For example, he supported the Free Speech movement.
In 1966, he traveled to Moscow to accept the Fields Medal. There, he held a press conference. He spoke out about world events and human rights. After returning to the U.S., his funding was not renewed. His strong opinions sometimes caused challenges.
Teaching and Research Positions
In 1960, Smale received a special fellowship. He joined the math faculty at Berkeley. The next year, he became a professor at Columbia.
In 1964, he returned to Berkeley. He spent most of his career there. He became a professor emeritus in 1995. Then, he took a new job at the City University of Hong Kong.
Smale also collected minerals. He built one of the best private collections. Many of his minerals are shown in the book The Smale Collection: Beauty in Natural Crystals.
From 2003 to 2012, Smale taught at the Toyota Technological Institute at Chicago. In 2009, he became a Distinguished University Professor at the City University of Hong Kong.
Awards and Recognition
Smale has received many important awards:
- In 1988, he won the Chauvenet Prize. This award is for excellent math writing.
- In 2007, he received the Wolf Prize in mathematics.
- He also won the National Medal of Science in 1996.
- As mentioned, he was awarded the Fields Medal in 1966.
Stephen Smale's Mathematical Discoveries
Smale made many important contributions to mathematics.
Understanding Shapes and Spaces
One of his early works looked at how a two-dimensional sphere (like a ball) can be placed into a larger space. He helped explain when two different ways of placing a sphere can be smoothly changed into each other. His work showed that a sphere can be turned inside out without tearing it. This is known as sphere eversion.
His student, Morris Hirsch, extended this work. Their ideas were very important for other mathematicians.
Studying Changing Systems
In the study of dynamical systems, Smale introduced what is called a Morse–Smale system. These systems help understand how things move and change over time.
Using these ideas, Smale solved a big problem in math called the generalized Poincaré conjecture. He solved it for dimensions greater than four. This was a major breakthrough. He also developed the h-cobordism theorem the next year. This helped classify certain types of five-dimensional shapes.
Smale also created the horseshoe map. This map helped inspire a lot of research in how complex systems behave. He also brought Morse theory into mathematical economics.
Smale's Problems for the Future
In 1998, Smale created a list of 18 important math problems. These problems were for mathematicians to solve in the 21st century. This list was inspired by Hilbert's famous list from 1900.
Smale's list includes some of Hilbert's original problems, like the Riemann hypothesis. This problem is still unsolved today. Other famous problems on his list include the P = NP problem and the Navier–Stokes equations. These are also known as Millennium Prize Problems.
See also
In Spanish: Stephen Smale para niños
- 5-manifold
- Axiom A
- Geometric mechanics
- Homotopy principle
- Mean value problem
