Daniel Shanks

Daniel Shanks ( born January 17, 1917 in Chicago; † 6 September 1996) was an American mathematician who worked primarily with number theory and numerical analysis.

Life

Shanks studied physics at the University of Chicago (Bachelor 1937). He then worked in 1940 on the Aberdeen Proving Ground U.S. Army ( the Ballistics Research ) and from 1941 at the Naval Ordnance Laboratory of the U.S. Navy as a physicist and from 1950 as a mathematician. 1951 to 1957 he headed the Numerical Analysis Section ( later Applied Mathematics Laboratory called ). It was created in 1954 received his doctorate at the University of Maryland in mathematics. He had completed in 1949, the thesis, and it was accepted because of their quality, the university was but on other formal qualifications from a university mathematics education that utterly lacked him until then. 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 a Senior Research Scientist. In 1976, he went after his research funds have been significantly reduced, to retire and was for a year at the National Bureau of Standards Adjunct Professor at the University of Maryland.

Work

In his thesis he introduced the Shanks transformation for convergence acceleration. With John William Wrench, Jr. (1911-2009) he averaged 100,000 points. He also studied primes of the form, for which he has developed a precursor of the later than quadratic sieve known ( by Carl Pomerance ) algorithm. Next he developed methods to calculate the class number of quadratic number field. He is best known as the author of a book on the problems in elementary number theory ( in which also an essay on "correct" assumptions is included) and as the discoverer of a number number-theoretic algorithms, such as the baby-step giant-step method for calculating the discrete logarithm or its factorization with quadratic forms ( SQUFOF, square form factorization ), which he, however, never published. Some of his methods are widely used in cryptography, through which the research area is still received an enormous boost to Shanks during his lifetime.

He was from 1959 until his death, co-editor of Mathematics of Computation (1943 under the name " Mathematical Tables and other Aids to Computation" ( MTAC ) founded by a committee of the National Research Council of the National Academy of Sciences of the United States and initially by RC Archibald out ).

In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm (An inductive formula tion of the Riemann Hypothesis ).

References

Writings

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