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 |
List
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 important work in areas like topology (the study of shapes), dynamical systems (how things change over time), and mathematical economics (using math to understand money and markets).
In 1966, he received the Fields Medal, which is like the Nobel Prize for mathematicians. He taught mathematics at the University of California, Berkeley for over 30 years. Today, he is a Professor Emeritus there, meaning he is a retired professor who still has a connection to the university. He continues to be interested in algorithms (steps for solving problems), numerical analysis (using numbers to solve math problems), and global analysis (studying math on large scales).
Contents
Stephen Smale's Journey in Education and Career
Stephen Smale was born in Flint, Michigan. He started college at the University of Michigan in 1948. At first, he was a very good student, especially in calculus.
Overcoming Academic Challenges
However, during his second and third years, his grades were not as good. He even failed a class in nuclear physics. Despite these struggles, he earned his Bachelor of Science degree in 1952. Luckily, he was still accepted into the graduate program for mathematics at the University of Michigan.
His grades were still low during his first years as a graduate student. The head of the department, Theophil Henry Hildebrandt, told Smale he might have to leave. This made Smale take his studies much more seriously. He finally earned his PhD in 1957, with help from his advisor, Raoul Bott. After that, he started his career teaching at the University of Chicago.
Smale's Public Actions and Views
Early in his career, Stephen Smale was known for his strong opinions. He once joked that he did his best work "on the beaches of Rio." He was also active in different social movements. For example, he supported the Free Speech movement and was part of a group called the Fair Play for Cuba Committee.
In 1966, he traveled to Moscow to receive the Fields Medal. While there, he held a press conference. He used this chance to speak out against the Vietnam War and how the Soviet Union treated its thinkers. When he returned to the U.S., he lost his funding for research. He was even called to testify before a government committee called the House Un-American Activities Committee.
Teaching and Research Positions
In 1960, Smale received a special research award called a Sloan Research Fellowship. He joined the math faculty at University of California, Berkeley. The next year, he became a professor at Columbia University. In 1964, he returned to Berkeley, where he spent most of his career.
He became a professor emeritus at Berkeley in 1995. After that, he became a professor at the City University of Hong Kong. He also collected many beautiful minerals over the years. Some of his mineral collection can be seen 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 also became a special professor at the City University of Hong Kong.
Awards and Recognition
Stephen Smale has received many important awards for his work.
- In 1988, he won the Chauvenet Prize from the Mathematical Association of America.
- In 2007, he was given the Wolf Prize in mathematics.
Stephen Smale's Mathematical Discoveries
Stephen Smale made many important discoveries in mathematics. His work often involved understanding shapes and how they change.
Understanding Shapes and Transformations
One of his early discoveries was about how a two-dimensional sphere (like the surface of a ball) can be transformed. He showed that if you can smoothly change one shape into another, they are similar in a mathematical way.
He also studied how to "immerse" a sphere into a larger space. Imagine pushing a balloon into a room without tearing it. He figured out when two different ways of doing this could be smoothly changed into each other. His work even showed how a sphere could be turned inside out, which is called sphere eversion. This means you can flip a sphere inside out without making any creases or tears!
Dynamical Systems and How Things Change
In the study of dynamical systems, which are systems that change over time, Smale introduced something called a Morse–Smale system. These systems are very stable and predictable. He showed how to connect these systems to the shape of the space they are in.
He also helped solve a very famous math problem called the generalized Poincaré conjecture. This problem was about understanding the shape of spaces in higher dimensions. Smale's work helped prove this for dimensions greater than four. He also developed the h-cobordism theorem, which helped classify certain five-dimensional shapes.
The Horseshoe Map and Smale's Problems
Smale also created the horseshoe map. This is a mathematical idea that helped explain how complex and chaotic behavior can appear in simple systems. It inspired a lot of future research in this area. He also brought ideas from Morse theory (a way to study shapes using functions) into mathematical economics.
In 1998, Stephen Smale created a list of 18 important math problems for mathematicians to solve in the 21st century. This list is known as Smale's problems. It was inspired by David Hilbert's famous list of problems from 1900. Smale's list included some of Hilbert's original problems, like the Riemann hypothesis, which is still unsolved. Other famous problems on his list, like the Poincaré conjecture (which has since been proven by Grigori Perelman) and the P = NP problem, are also part of the Millennium Prize Problems.
Images for kids
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Stephen Smale in 2008
See also
In Spanish: Stephen Smale para niños
- 5-manifold
- Axiom A
- Geometric mechanics
- Homotopy principle
- Mean value problem
