Raoul Bott facts for kids
Quick facts for kids
Raoul Bott
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Raoul Bott in 1986
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| Born | September 24, 1923 Budapest, Hungary
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| Died | December 20, 2005 (aged 82) |
| Nationality | Hungarian American |
| Alma mater | McGill University< Carnegie Mellon University |
| Known for | Bott cannibalistic class Bott periodicity theorem Bott residue formula Bott–Duffin synthesis Bott–Samelson resolution Bott–Taubes polytope Bott–Virasoro group Atiyah–Bott formula Atiyah–Bott fixed-point theorem Borel–Weil–Bott theorem Morse–Bott theory |
| Awards | Veblen Prize (1964) Jeffery–Williams Prize (1983) National Medal of Science (1987) Steele Prize (1990) Wolf Prize (2000) ForMemRS (2005) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Michigan in Ann Arbor Harvard University |
| Doctoral advisor | Richard Duffin |
| Doctoral students |
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Raoul Bott (September 24, 1923 – December 20, 2005) was a brilliant mathematician from Hungary who later became an American citizen. He made many important discoveries in a field of math called geometry. Geometry is the study of shapes, sizes, positions, and properties of space.
Bott is especially famous for his Bott periodicity theorem. This theorem helps us understand how certain complex mathematical shapes repeat in a pattern. He also developed Morse–Bott functions, which are tools used in geometry. Another key achievement was the Borel–Bott–Weil theorem, which is important in understanding groups of numbers and shapes.
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Early Life and Moving to Canada
Raoul Bott was born in Budapest, Hungary, on September 24, 1923. His father was from Austria, and his mother was from a Hungarian Jewish family. Raoul was raised as a Catholic by his mother and stepfather.
He spent his childhood in Czechoslovakia. In 1938, when he was 15, his family moved to Canada. During World War II, Raoul served in the Canadian Army in Europe.
Education and Early Career
After the war, Bott went to McGill University in Montreal, Canada. He first studied electrical engineering. This field deals with electricity, electronics, and electromagnetism.
Later, he decided to study mathematics. He earned his PhD in math from Carnegie Mellon University in Pittsburgh in 1949. His main teacher was Richard Duffin. Bott's PhD paper was about "Electrical Network Theory."
After finishing his studies, Bott started teaching at the University of Michigan in Ann Arbor. He also continued his research at the Institute for Advanced Study in Princeton. From 1959 to 1999, he was a professor at Harvard University, a very famous school. Raoul Bott passed away in San Diego in 2005 after battling cancer.
Discoveries in Mathematics
Raoul Bott made many important contributions to mathematics. His work often connected different areas of math, like geometry and physics.
Understanding Electronic Filters
Early in his career, Bott worked with Richard Duffin. They studied how to design electronic filters. Filters are devices that let certain signals pass through while blocking others. Think of a radio that filters out static so you can hear the music clearly.
In 1949, they proved a major theorem about designing these filters. Their work helped engineers create better electronic devices. Bott later said that studying these networks helped him understand algebraic topology. This is a branch of math that studies shapes and spaces.
The Bott Periodicity Theorem
One of Bott's most famous discoveries is the Bott periodicity theorem in 1957. This theorem describes a repeating pattern in the world of complex shapes called Lie groups. Imagine a pattern that repeats itself perfectly, but in a very abstract mathematical way. This theorem is very important in a field called K-theory, which helps mathematicians classify and understand different kinds of spaces.
To prove this theorem, Bott created something called Morse–Bott functions. These are special mathematical tools that help study the shapes of spaces.
Working with Michael Atiyah
Bott worked closely with another famous mathematician, Michael Atiyah, for many years. They used Bott's periodicity theorem to help with a big problem called the Atiyah–Singer index theorem. This theorem connects geometry, analysis, and topology.
They also worked on "fixed-point theorems." These theorems help find points that stay in the same place after a mathematical operation. One of their important results was called the "Woods Hole fixed-point theorem."
Atiyah and Bott also studied gauge theory, which is used in physics to describe forces like electromagnetism. They used math to understand the properties of "stable bundles" on surfaces. In 1983, Bott gave a talk where he said he "marvels at Physics," showing how much he enjoyed connecting math with the physical world.
Other Key Contributions
Bott also contributed to the Borel–Bott–Weil theorem, which is about understanding how groups of numbers behave. He worked on foliations, which are ways to divide a space into smaller, smooth slices.
With another mathematician named Chern, he worked on "Bott-Chern classes." These are special mathematical objects that help study complex shapes. He also introduced Bott–Samelson varieties and the Bott residue formula, which are important tools for mathematicians.
Awards and Recognition
Raoul Bott received many awards for his amazing work in mathematics:
- In 1964, he won the Oswald Veblen Prize in Geometry from the American Mathematical Society.
- In 1983, he was awarded the Jeffery–Williams Prize by the Canadian Mathematical Society.
- In 1987, he received the National Medal of Science, one of the highest honors for scientists in the United States.
- In 2000, he was given the Wolf Prize in Mathematics, another very prestigious award.
- In 2005, he was chosen as an Overseas Fellow of the Royal Society of London, a very old and respected scientific group.
Inspiring Future Mathematicians
Raoul Bott was also a dedicated teacher and mentor. He guided 35 students who were working on their PhDs. Some of his students became very famous mathematicians themselves.
For example, Stephen Smale and Daniel Quillen both won the Fields Medal. This is often called the "Nobel Prize of mathematics." Other notable students include Peter Landweber, Robert MacPherson, and Eric Weinstein. Bott's influence helped shape many future generations of mathematicians.
See also
- Bott–Duffin inverse
- Parallelizable manifold
- Thom's and Bott's proofs of the Lefschetz hyperplane theorem
