John Barkley Rosser
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
- A Mathematical Logic Without Variables . Princeton Univ. Diss., Princeton, NJ 1934, pp. 127-150, 328-355
- Explicit bounds for some functions of prime numbers , Amer. J. Math. 63 (1941), pp. 211-232
- Burali-Forti paradox , Journal of Symbolic Logic, Volume 7, 1942, pp. 1-17
- with Lowell Schoenfeld : Approximate formulas for some functions of prime numbers , Illinois J. Math. 6 (1962), pp. 64-94
- with L. Schoenfeld: Sharper bounds for the Chebyshev functions θ (x) and ψ (x) (PDF; 1.8 MB), Math. Comp. 29 (1975), no. 129, pp. 243-269
- Logic for Mathematicians . 2nd edition. Chelsea Publ. Co., New York 1978, 578 pp., ISBN 0-8284-0294-9
literature
- Christopher von Bülow: Evidence Logic - Gödel, Rosser, Solovay , Logos-Verlag, 2006, ISBN 3-8325-1295-0
- For life and achievements, see biographical notes in “A Guide to the J. Barkley Rosser Papers,” 1931–1989 Archives of American Mathematics, Center for American History, The University of Texas at Austin .
Web links
- English overview of the writings of John Barkley Rosser (with further links).
- Interview with Rosser and Stephen Kleene about their life at Princeton: Stephen C. Kleene and J. Barkley Rosser, 1983 .
- A Guide to the J. Barkley Rosser Papers, 1931-1989 , Briscoe Center for American History, University of Texas at Austin
Individual evidence
- ^ American Academy of Arts and Sciences. Book of Members ( PDF ). Retrieved April 10, 2016
- ^ Rosser, The n-th prime is greater than n log n, Proceedings of the London Mathematical Society, Volume 45, 1939, pp. 21-44
- ↑ 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
- ↑ Rosser had proven in 1939 . In 1941 he proved that applies to
- ↑ Rosser`s rule, Mathworld
- ^ 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
personal data | |
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SURNAME | Rosser, John Barkley |
ALTERNATIVE NAMES | Rosser Sr., John Barkley |
BRIEF DESCRIPTION | American mathematician and logician |
DATE OF BIRTH | December 6, 1907 |
PLACE OF BIRTH | Jacksonville , Florida , USA |
DATE OF DEATH | 5th September 1989 |
Place of death | Madison , Wisconsin , USA |