Daniel Shanks
Daniel Shanks | |
|---|---|
Computing π | |
| Scientific career | |
| Fields | Mathematics |
Daniel Charles Shanks (January 17, 1917 – September 6, 1996) was an
to compute π
to 100,000 decimal places.
Life and education
Shanks was born on January 17, 1917, in
Ph.D. in Mathematics from the University of Maryland in 1954. Prior to obtaining his PhD, Shanks worked at the Aberdeen Proving Ground and the Naval Ordnance Laboratory, first as a physicist and then as a mathematician. During this period he wrote his PhD thesis, which completed in 1949, despite having never taken any graduate math courses.[1]
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After earning his PhD in mathematics, Shanks continued working at the
National Bureau of Standards before moving to the University of Maryland as an adjunct professor. He remained in Maryland for the rest of his life.[1]: 813 Shanks died on September 6, 1996.[1]
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Works
Shanks worked primarily in
Epstein zeta functions.[1]
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Numerical analysis
Shanks's most prominent work in numerical analysis was a collaboration with
compute the number π to 100,000 decimal digits on a computer.[2] This was done in 1961 on an IBM 7090, and it was a major advancement over previous work.[1]
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Shanks was an editor of the Mathematics of Computation from 1959 until his death. He was noted for his very thorough reviews of papers, and for doing whatever was necessary to get the journal out.[1]: 813
Number theory
Shanks wrote the book Solved and Unsolved Problems in Number Theory,perfect numbers, which had been checked to 1050, he famously remarked that "1050 is a long way from infinity."[3]: 217
Most of Shanks's number theory work was in
algorithms include: Baby-step giant-step algorithm for computing the discrete logarithm, which is useful in public-key cryptography; Shanks's square forms factorization, integer factorization method that generalizes Fermat's factorization method; and the Tonelli–Shanks algorithm that finds square roots modulo a prime, which is useful for the quadratic sieve method of integer factorization
.
In 1974, Shanks and
Brun's constant, the sum of the reciprocals of the twin primes, calculating it over the twin primes among the first two million primes.[4]
See also
- Infrastructure (number theory)
- Newman–Shanks–Williams prime
- Shanks transformation
- Shanks's square forms factorization
Notes
- ^ ISSN 0002-9920. Retrieved 2008-06-27.
- JSTOR 2003813.
- ^ ISBN 978-0-8218-2824-3.
- ^
Shanks, Daniel; JSTOR 2005836.
External links
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| National | |
| Academics | |
| People | |
| Other | |
