Daniel Shanks

Daniel Shanks (born January 17, 1917 in Chicago , † September 6, 1996 ) was an American mathematician who mainly dealt with number theory and numerical mathematics .

Life

Shanks first studied physics at the University of Chicago (Bachelor 1937). He then worked in 1940 on the Aberdeen Proving Ground of the US Army (the ballistics research center) and from 1941 in the Naval Ordnance Laboratory of the US Navy as a physicist and from 1950 as a mathematician. From 1951 to 1957 he headed the Numerical Analysis Section (later called Applied Mathematics Laboratory). He received his PhD in mathematics from the University of Maryland in 1954 . He had already completed his dissertation in 1949, and it was accepted because of its quality, but the university insisted on further formal qualifications from a university mathematics education, which he had previously lacked. From 1957 he worked at the Naval Ship Research and Development Center at the David Taylor Model Basin in Bethesda (Maryland) as a consultant and senior research scientist. In 1976, after his research funding was significantly reduced, he retired and became an adjunct professor at the University of Maryland after a year with the National Bureau of Standards .

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In his dissertation, he introduced the Shanks transformation to accelerate convergence . With John William Wrench, Jr. he calculated on 100,000 digits. He also studied prime numbers of form , for which he developed a forerunner of the algorithm later known as the square sieve (by Carl Pomerance ). He further developed methods for calculating the class number of quadratic number fields. He is best known as the author of a book on problems in elementary number theory (which also includes an essay on “correct” conjectures) and as the discoverer of a number of number theoretic algorithms such as the Baby Step-Giant Step method for computing the discrete logarithm or his factoring method with square forms (SQUFOF, square form factorization), which he never published. Some of his methods are widely used in cryptography, which gave the field of research an enormous boost during Shanks' lifetime. ${\displaystyle \pi }$ ${\displaystyle n^{2}+1}$

From 1959 until his death he was co-editor of the journal Mathematics of Computation (founded in 1943 under the name "Mathematical Tables and other Aids to Computation" (MTAC) by a committee of the National Research Council of the National Academy of Sciences of the USA and initially by Raymond Clare Archibald ).

In 1962 he gave a lecture at the International Congress of Mathematicians in Stockholm ( An inductive formulation of the Riemann Hypothesis ).

References

1. ↑ Nonlinear Transformation of divergent and slowly convergent sequences. Journal of Mathematics and Physics, Vol. 34, 1955, pp. 1-42.
2. ↑ Calculation of to 100,000 Decimals ${\displaystyle \pi }$ Mathematics of Computation, Vol. 16, 1962, pp. 76-99.
3. ↑ A sieve method for factoring numbers of the form . ${\displaystyle n^{2}+1}$MTAC, Vol. 13, 1959, p. 78
4. ^ Daniel Shanks: Analysis and Improvement of the Continued Fraction Method of Factorization , (unpublished, edited by S. McMath 2004)
   Daniel Shanks: SQUFOF Notes , (unpublished, edited by S. McMath 2004)
   Stephen S. McMath: Parallel integer factorization using quadratic forms , 2005
   S. McMath, F. Crabbe, D. Joyner: Continued fractions and parallel SQUFOF , Int. J. Pure Appl. Math. 34 (2007) No. 1, pp. 19-38
   Jason E. Gower, Samuel S. Wagstaff, Jr .: Square Form Factorization , Math. Comp. 77 (2008) No. 261, pp. 551-588. (PDF; 316 kB) Presentation, classification and analysis

Fonts

• Solved and Unsolved Problems in Number Theory. 5th edition, AMS Chelsea, 2002 (first 1962).

Web links

• Obituary by HCWilliams, Notices AMS 1997, PDF file (208 kB)
• M. Bullynck: Reading Gauss in the Computer Age: On the US Reception of Gauss's Number Theoretical Work (1938-1989). historical analysis