John Barkley Rosser

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John Barkley Rosser Sr. (born December 6, 1907 in Jacksonville , Florida , † September 5, 1989 in Madison , Wisconsin ) was an American logician and mathematician.

Life

Rosser received his Bachelor of Science in 1929 and his Master of Science in 1931 from the University of Florida . He received his PhD from Princeton University in 1934 . He then taught at Princeton, Harvard and Cornell and continued his career at the University of Wisconsin-Madison . He lectured there at the age of 70 and died at home in Madison, Wisconsin in 1989.

In addition to his teaching activities, Rosser participated in numerous committees and associations. He has chaired the Association for Symbolic Logic and the Society of Industrial and Applied Mathematics , served on the Spacecraft Advisory Board on the Apollo Project Advisory Board . He made early contributions to computer science and helped develop the Polaris missile . He was the director of the U.S. Army Mathematics Research Center at the University of Wisconsin-Madison . In addition, he wrote mathematical textbooks. In 1967 Rosser was elected to the American Academy of Arts and Sciences .

He is the father of economic mathematician John Barkley Rosser Jr .

Services

Rosser was a student of Alonzo Church . He has contributed to many fields including symbolic logic , ballistics , missile development, and analytical number theory .

Rosser contributed to Church-Rosser's theorem in the lambda calculus , developed the Rosser sieve , a sieving method in analytical number theory , found and proved Rosser's theorem from the theory of prime numbers, and in 1936 proved a stronger version of Gödel's first incompleteness , by showing that the condition of -Widerspruchsfreiheit to consistency can be mitigated. Instead of the sentence from the liar's paradox that says “I am not provable!”, He used the statement “For every proof for me there is a shorter proof for my logical negation !”.

Rosser's theorem

In 1939 he proved a theorem named after him about a lower bound for the nth prime number :

That was brought up in 1999 by Pierre Dusart

improved. M. Cipolla already knew in 1902 that this formula is asymptotic.

With Lowell Schoenfeld and JM Yohe, he calculated the first 3.5 million non-trivial zeros of the Riemann zeta function with the computer in 1968 and showed that they were on the critical straight line. They also formulated Rosser's rule.

Fonts

literature

Web links

Individual evidence

  1. ^ American Academy of Arts and Sciences. Book of Members ( PDF ). Retrieved April 10, 2016
  2. ^ Rosser, The n-th prime is greater than n log n, Proceedings of the London Mathematical Society, Volume 45, 1939, pp. 21-44
  3. Dusart, The kth prime is greater than k (log k + log log k − 1) for k ≥ 2, Mathematics of Computation, Volume 68, 1999, pp. 411-415
  4. Rosser had proven in 1939 . In 1941 he proved that applies to
  5. Rosser`s rule, Mathworld
  6. ^ Rosser, Yohe, Schoenfeld, Rigorous computation and the zeros of the Riemann zeta-function. (including discussion) , Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968), Vol. 1: Mathematics, Software, Amsterdam: North-Holland, 1969, pp. 70-76