Daniel Shanks
Daniel Shanks (January 17, 1917 – September 6, 1996) was an American mathematician who worked primarily in numerical analysis and number theory. He was the first person to compute π to 100,000 decimal places. Life and education. Dan Shanks (he insisted that everyone call him Dan) was born on January 17, 1917, in Chicago, Illinois, and he is not related to the English mathematician William Shanks, who was also known for computation of π. He earned his Bachelor of Science degree in physics from the University of Chicago in 1937 and a Ph.D. in Mathematics from the University of  Maryland in 1954. In between these two, 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 also wrote his Ph.D. thesis (completed in 1949), despite having never taken any graduate math courses. After earning his Ph.D. in mathematics, Shanks continued working at the Naval Ordnance Laboratory and the Naval Ship Research and Development Center at the David Taylor Model Basin, where he stayed until 1976. He then spent a year at 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. Dan Shanks died on September 6, 1996. Works. Shanks worked primarily in numerical analysis and number theory, but he had many interests and also did some work in black body radiation, ballistics, mathematical identities, and Epstein zeta functions. Numerical analysis. Shanks's most prominent work in numerical analysis was a collaboration with John Wrench and others to compute the number π to 100,000 decimals on a computer. This was done in 1961 on an IBM 7090 and it was a major advance over previous work. 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 being a jack-of-all-trades who did whatever was necessary to get the journal out. Number theory. Shanks wrote the book "Solved and Unsolved Problems in Number Theory". Hugh Williams described it as "a charming, unconventional, provocative, and fascinating book on elementary number theory." It is a wide-ranging book, but most of the topics depend on quadratic residues and Pell's equation. The third edition contains a long essay on "judging conjectures". Shanks contended that  there should be a lot of evidence that something is true before we classify it as a conjecture (otherwise it should be an Open Question and we should not take sides on it), and his essay gives many examples of bad thinking deriving from premature conjecturing. Writing about the possible non-existence of odd perfect numbers, which had been checked to 10, he famously remarked that "10 is a long way from infinity." Most of Shanks's number theory work was in computational number theory. He developed a number of fast computer factorization methods based on quadratic forms and the  class number. His algorithms include: Baby-step giant-step algorithm for computing the discrete logarithm, which is useful in public-key cryptography; Shanks's square forms factorization, an 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 John Wrench did some of the first computer work on estimating the value of Brun's constant, the sum of the reciprocals of the twin primes, calculating it over the twin primes among the first two  million primes.