Per Enflo facts for kids
Quick facts for kids
Per Enflo
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Enflo in 1972
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| Born | 20 May 1944 |
| Alma mater | Stockholm University |
| Known for | Approximation problem Schauder basis Hilbert's fifth problem (infinite-dimensional) uniformly convex renorms of super-reflexive Banach spaces embedding metric spaces (unbounded distortion of cube) "Concentration" of polynomials at low degree< Invariant subspace problem |
| Awards | Mazur's "live goose" for solving "Scottish Book" Problem 153 |
| Scientific career | |
| Fields | Functional analysis Operator theory Analytic number theory |
| Institutions | University of California, Berkeley Stanford University École Polytechnique, Paris The Royal Institute of Technology, Stockholm Kent State University |
| Doctoral advisor | Hans Rådström |
| Doctoral students | Angela Spalsbury Bruce Reznick |
Per H. Enflo (born May 20, 1944) is a famous Swedish mathematician. He works mainly in a field called functional analysis. In this area, he solved some very important math problems.
Three of these problems had been unsolved for more than 40 years! These were:
- The basis problem
- The approximation problem
- The invariant subspace problem for Banach spaces
To solve these, Enflo created new ways of thinking about math. Other researchers then used his methods for many years. Some of his work has also been important in other math areas, like number theory. It has also helped in computer science, especially with computer algebra and approximation algorithms.
Today, Per Enflo is a University Professor at Kent State University. He has also worked at other famous places. These include the University of California, Berkeley and Stanford University. He also taught at École Polytechnique in Paris and the Royal Institute of Technology in Stockholm.
Besides being a mathematician, Per Enflo is also a talented concert pianist.
Math and Living Things
Per Enflo has also used math to study living things. This field is called mathematical biology. He has written papers about how populations of animals and plants change over time. This is known as population dynamics.
Human History and Populations
Enflo has also studied how human populations have changed. This includes population genetics and paleoanthropology.
Today, all humans belong to one group called Homo sapiens sapiens. But long ago, there were other human-like species. For example, Homo habilis first appeared in East Africa about 2 million years ago. Later, Homo erectus spread across the Old World (Africa, Asia, and Europe).
Scientists have debated how modern humans developed. One idea is the "Out of Africa" model. This suggests that modern humans first appeared in East Africa. Then, they moved out of Africa and replaced other human groups. Another idea is the "Multiregional Evolution" hypothesis. This suggests that humans evolved in different parts of the world at the same time.
Neanderthals and modern humans lived in Europe at the same time for thousands of years. Scientists are still trying to figure out exactly how long this period lasted. Modern humans might have arrived in Europe about 40,000 to 43,000 years ago. Neanderthals might have lived as recently as 24,000 years ago. They lived in places like Gorham's Cave in Spain.
Per Enflo, along with other scientists, studied DNA from Neanderthals and modern humans. They tried to explain how Neanderthals might have disappeared. One idea is that modern humans kept moving into Europe. This might have led to modern human DNA mixing with Neanderthal DNA. Eventually, this could have caused Neanderthals to die out.
Enflo has also studied how zebra mussels spread in Lake Erie.
Piano Music
Per Enflo is also a very skilled concert pianist. He was a child prodigy in both music and math.
In 1956, when he was 11, Enflo won a Swedish competition for young pianists. He won it again in 1961. At age 12, he played as a soloist with the Royal Opera Orchestra of Sweden. He played his first big concert at the Stockholm Concert Hall in 1963. Some of his piano teachers were famous musicians like Bruno Seidlhofer and Géza Anda.
In 1999, Enflo took part in a piano competition for talented amateur pianists. This was the first annual Van Cliburn Foundation's International Piano Competition for Amateurs.
Enflo often performs piano concerts. He plays in and around Kent, Ohio. He also performs in a Mozart music series in Columbus, Ohio. His solo piano concerts have been played on the radio station WOSU-FM.
External sources
- Biography of Per Enflo at Canisius College
- Homepage of Per Enflo at Kent State University
- Per Enflo at the Mathematics Genealogy Project
