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The Unreasonable Effectiveness of Mathematics
Hamming's response to Eugene Wigner's article entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", published in 1960. This response was originally published as part of the American Mathematical Monthly, Vol. 87, No. 2, Feb., 1980. Hamming expands on Wigner's ideas, tackling on the question implied on the title of the response, although doing so loosely as to leave the question open.
- GenresMathematicsPhilosophy
10 pages, Unknown Binding
First published February 1, 1980
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About the author
Richard Hamming
13 books129 followersProfessor Richard Wesley Hamming, Ph.D. (University of Illinois at Urbana-Champaign, 1942; M.S., University of Nebraska, 1939; B.S., University of Chicago in 1937), was a mathematician whose work had many implications for computer science and telecommunications. His contributions include the Hamming code (which makes use of a Hamming matrix), the Hamming window (described in Section 5.8 of his book Digital Filters), Hamming numbers, sphere-packing (or hamming bound) and the Hamming distance.
Hamming was a professor at the University of Louisville during World War II, and left to work on the Manhattan Project in 1945, programming one of the earliest electronic digital computers to calculate the solution to equations provided by the project's physicists. The objective of the program was to discover if the detonation of an atomic bomb would ignite the atmosphere. The result of the computation was that this would not occur, and so the United States used the bomb, first in a test in New Mexico, and then twice against Japan. Later, from 1946 to 1976, he worked at the Bell Telephone Laboratories, where he collaborated with Claude Shannon. During this period, he was an Adjunct Professor at the City College of New York, School of Engineering. On July 23, 1976 he moved to the Naval Postgraduate School, where he worked as an Adjunct Professor until 1997, when he became Professor Emeritus. He died a year later in 1998.
He was a founder and president of the Association for Computing Machinery. His philosophy on scientific computing appears as preface to his 1962 book on numerical methods: The purpose of computing is insight, not numbers.
Awards:
Turing Award, Association for Computing Machinery, 1968.
Fellow of the IEEE, 1968.
IEEE Emanuel R. Piore Award, 1979.
Member of the National Academy of Engineering, 1980.
Harold Pender Award, University of Pennsylvania, 1981.
IEEE Richard W. Hamming Medal, 1988.
Fellow of the Association for Computing Machinery, 1994.
Basic Research Award, Eduard Rhein Foundation, 1996.
Certificate of Merit, Franklin Institute, 1996
The IEEE Richard W. Hamming Medal, named after him, is an award given annually by Institute of Electrical and Electronics Engineers (IEEE), for "exceptional contributions to information sciences, systems and technology", and he was the first recipient of this medal.
Hamming discusses the use and potential of computers in the 1965 film Logic By Machine.
Hamming was a professor at the University of Louisville during World War II, and left to work on the Manhattan Project in 1945, programming one of the earliest electronic digital computers to calculate the solution to equations provided by the project's physicists. The objective of the program was to discover if the detonation of an atomic bomb would ignite the atmosphere. The result of the computation was that this would not occur, and so the United States used the bomb, first in a test in New Mexico, and then twice against Japan. Later, from 1946 to 1976, he worked at the Bell Telephone Laboratories, where he collaborated with Claude Shannon. During this period, he was an Adjunct Professor at the City College of New York, School of Engineering. On July 23, 1976 he moved to the Naval Postgraduate School, where he worked as an Adjunct Professor until 1997, when he became Professor Emeritus. He died a year later in 1998.
He was a founder and president of the Association for Computing Machinery. His philosophy on scientific computing appears as preface to his 1962 book on numerical methods: The purpose of computing is insight, not numbers.
Awards:
Turing Award, Association for Computing Machinery, 1968.
Fellow of the IEEE, 1968.
IEEE Emanuel R. Piore Award, 1979.
Member of the National Academy of Engineering, 1980.
Harold Pender Award, University of Pennsylvania, 1981.
IEEE Richard W. Hamming Medal, 1988.
Fellow of the Association for Computing Machinery, 1994.
Basic Research Award, Eduard Rhein Foundation, 1996.
Certificate of Merit, Franklin Institute, 1996
The IEEE Richard W. Hamming Medal, named after him, is an award given annually by Institute of Electrical and Electronics Engineers (IEEE), for "exceptional contributions to information sciences, systems and technology", and he was the first recipient of this medal.
Hamming discusses the use and potential of computers in the 1965 film Logic By Machine.
Ratings & Reviews
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Displaying 1 - 6 of 6 reviews
January 30, 2023
A short entertaining read that I would recommend specially to both my STEM and non-STEM friends. Trust me, it is not what you think it is. Hamming has a fairly conventionalist view of mathematics rather than a platonic view.
December 18, 2023
Prologue
Unreasonable Effectiveness
What is Mathematics?
- logic: long chains of close reasoning
- geometry: continuity, topology, ...
- number: arithmetic, algebra, ...
- artistic taste: aesthetic/elegance
- mark of great math: search for proper concepts & definitions
- research into "foundation of math" seems more like "top battlement" since we won't abandon much of math regardless of seeming illogicality made to appear by research
Some partial explanations
1. we see what we seek
- Pythagoras: discovered we live in L2; geometry postulates followed not preceded
- Galileo: "I try to put myself in his shoes so I might feel how he came to discover...learn to think like the masters did"; scholastic reasoning/argument by contradiction, not experimenting, shows falling bodies cannot possibly know boundary between
- Newton: Kepler's law -> inverse square law
- uncertainty principle
- leading digit in physical constants
- Einstein: theories of relativity unearthed via scholastic philosophy/mathematics, not experiments
- "Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea."
2. we pick/make the right kind of math to fit the situation
3. science answers few problems e.g. not Truth, Beauty, Justice
4. evolution of man provided the model
- evolution naturally select life forms with best reality model in mind
- evolution could well have imposed unthinkable thoughts
Unreasonable Effectiveness
What is Mathematics?
- logic: long chains of close reasoning
- geometry: continuity, topology, ...
- number: arithmetic, algebra, ...
- artistic taste: aesthetic/elegance
- mark of great math: search for proper concepts & definitions
- research into "foundation of math" seems more like "top battlement" since we won't abandon much of math regardless of seeming illogicality made to appear by research
Some partial explanations
1. we see what we seek
- Pythagoras: discovered we live in L2; geometry postulates followed not preceded
- Galileo: "I try to put myself in his shoes so I might feel how he came to discover...learn to think like the masters did"; scholastic reasoning/argument by contradiction, not experimenting, shows falling bodies cannot possibly know boundary between
- Newton: Kepler's law -> inverse square law
- uncertainty principle
- leading digit in physical constants
- Einstein: theories of relativity unearthed via scholastic philosophy/mathematics, not experiments
- "Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea."
2. we pick/make the right kind of math to fit the situation
3. science answers few problems e.g. not Truth, Beauty, Justice
4. evolution of man provided the model
- evolution naturally select life forms with best reality model in mind
- evolution could well have imposed unthinkable thoughts
July 12, 2022
This work is different from Wigner's.
The most annoying, but also the most important idea for me from this work is that we match the mathematics to the problem, rather than suddenly discovering that it works in many areas.
Hamming has shown this with many examples.
The most annoying, but also the most important idea for me from this work is that we match the mathematics to the problem, rather than suddenly discovering that it works in many areas.
Hamming has shown this with many examples.
May 10, 2020
One of the most inspiring papers about what mathematics is. Tons of profound insights with concise writing and examples.
January 3, 2025
Vague but reasonable
Displaying 1 - 6 of 6 reviews