Person: Feigenbaum, Mitchell Jay
Mitchell Feigenbaum was an American mathematical physicist who discovered the so-called Feigenbaum constant in chaos theory.
Mathematical Profile (Excerpt):
- Up until the time he went to university Mitchell would not enjoy the company of his fellow pupils.
- The school system seemed unable to provide Feigenbaum with the right stimulus for he tried as hard as he could to avoid classes despite making remarkable academic progress and scoring full marks in mathematics and science in the examinations covering the State.
- Even when he went to Tilden High School in Brooklyn, a school with a fine reputation, Feigenbaum found the education there no more enjoyable, despite once again excelling in examinations.
- While at school Feigenbaum had usually learnt more in studying by himself than in the formal lessons.
- The machine came with a paper by Shannon on Boolean logic which fascinated Feigenbaum with his self-learning attitude.
- In February 1960, at the age of sixteen, Feigenbaum entered the City College of New York.
- It was while he was at MIT that Feigenbaum first used a computer but not as part of his studies there.
- At MIT Feigenbaum's doctoral studies were supervised by Francis Low and he was awarded a doctorate in 1970 for a dissertation on dispersion relations.
- After the two years at Cornell, Feigenbaum went to Virginia Polytechnic Institute as a postdoctoral worker, again with a two year position.
- After the two years at Virginia Polytechnic Institute, Feigenbaum was offered a long term position on the staff of the theory division at Los Alamos.
- The 'wonderful directions' that Feigenbaum refers to here involve the study of chaos where he was to make a remarkable discovery.
- It was made since data was available from computing and, as Feigenbaum himself has noted, only became obvious because the computers he used calculated so slowly that he could see the intermediate steps of the calculation.
- Feigenbaum's involvement with computers moved forward in December 1974 when he got his own programmable calculator for the first time, the HP65.
- The remarkable result obtained by Feigenbaum was to show that not only was the behaviour qualitatively similar but there was a very precise mathematical result which held for all such logistic equations.
- Feigenbaum did not actually work with the precise logistic equation which May studied and in fact his work was independent of that by May.
- When Feigenbaum first found 4.669 in August 1975, which he only found to three places due to the limit of the accuracy of his HP65, he spend some time trying to see if it was a simple combination of 'well-known' numbers.
- Of course, now the number is 'well-known' and called the Feigenbaum number.
- This in itself was surprising but in October 1975 Feigenbaum found that this number is the same for a large class of period doubling mappings.
- By April 1976 Feigenbaum had completed his first paper on the topic.
- Feigenbaum has made other contributions to the theory of chaos and he has also written two papers on the mathematics of making maps.
- Dr Feigenbaum also created a new computerised type placement program which places thousands of map labels in minutes, a task which previously required days of tedious labour.
- It might at this point be reasonable to wonder whether Feigenbaum considers himself a mathematician or a physicist.
- In 1982 Feigenbaum left Los Alamos when he was appointed to a professorship at Cornell.
Born 19 December 1944, Philadelphia, USA. Died 30 June 2019, New York City, New York, USA.
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Thank you to the contributors under CC BY-SA 4.0!
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive