# Paul Stein

**Paul R. Stein**,

an American physicist and mathematician, and staff member at Los Alamos National Laboratory since 1950, working on problems that range from mathematical biology to nonlinear transformations and experimental number theory ^{[2]}. In the late 1950s, along with Mary Menzel and Stanislaw Ulam, Paul Stein performed one of the earliest digital simulations of discrete dynamics in two-dimensions ^{[3]}. In their work they created a robot mathematician to scan the results of simulations for chaotic attractors ^{[4]}.

# MANIAC I

Paul Stein was member of a group of H-bomb researchers around Stanislaw Ulam, Mark Wells and John Pasta et al., who wrote the chess-playing program ^{[5]} ^{[6]} for the MANIAC I in 1956. It played Los Alamos Chess on a 6×6 board without bishops.

# Photos

Los Alamos scientists Paul Stein (left) and Nick Metropolis playing chess with the MANIAC computer ^{[7]} ^{[8]}

# Selected Publications

^{[9]}

- Paul Stein, Stanislaw Ulam (
**1957**).*Experiments in chess on electronic computing machines*. Chess Review, 13 January 1957. - James Kister, Paul Stein, Stanislaw Ulam, William Walden, Mark Wells (
**1957**).*Experiments in Chess*. Journal of the ACM, Vol. 4, No. 2 - Mary Tsingou-Menzel, Paul Stein, Stanislaw Ulam (
**1959**).*Quadratic Transformations: Part I*. Los Alamos Scientific Laboratory report LA-2305, republished in Stanislaw Ulam (**1990**).*Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and his Los Alamos Collaborators*. Berkeley: University of California Press - John Riordan, Paul Stein (
**1972**).*Arrangements on Chessboards*. Journal of Combinatorial Theory Series A, Vol. 12, No. 1 - Nicholas Metropolis, Myron L. Stein, Paul Stein (
**1973**).*On finite limit sets for transformations on the unit interval*. Journal of Combinatorial Theory Series A, Vol. 15, No. 1 - Paul Stein (
**1982**).*Bernd Matthias - A Personal Memoir*. Los Alamos Science, No. 4 » Bernd Matthias - William A. Beyer, Paul Stein (
**1983**).*Brief History of Functional Iteration at Los Alamos*. Los Alamos National Laboratory - Paul Stein (
**1986**).*Experiments in Chess on Electronic Computing Machines: Some Early Efforts*. in Stanislaw Ulam (**1986**).*Science, Computers, and People - From the Tree of Mathematics*. Birkhäuser - Paul Stein (
**1987**).*Iteration of Maps, Strange Attractors, and Number Theory - An Ulamian Potpourri*. in*Stanislaw Ulam 1909-1984*. Los Alamos Science, No. 15, pdf

# References

- ↑ Image from Paul Stein (
**1987**).*Iteration of Maps, Strange Attractors, and Number Theory - An Ulamian Potpourri*. in*Stanislaw Ulam 1909-1984*. Los Alamos Science, No. 15, pdf - ↑ Paul Stein (
**1987**).*Iteration of Maps, Strange Attractors, and Number Theory - An Ulamian Potpourri*. in*Stanislaw Ulam 1909-1984*. Los Alamos Science, No. 15, pdf - ↑ Mary Tsingou-Menzel, Paul Stein, Stanislaw Ulam (
**1959**).*Quadratic Transformations: Part I*. Los Alamos Scientific Laboratory report LA-2305 - ↑ Ralph Abraham (
**2011**).*Image Entropy for Discrete Dynamical Systems*. pdf - ↑ Paul Stein, Stanislaw Ulam (
**1957**).*Experiments in chess on electronic computing machines*. Chess Review, 13 January 1957. - ↑ James Kister, Paul Stein, Stanislaw Ulam, William Walden, Mark Wells (
**1957**).*Experiments in Chess*. Journal of the ACM, Vol. 4, No. 2 - ↑ Los Alamos scientisits Paul Stern (left) and Nick Metropolis playing chess with the MANIAC computer, 1956, Courtesy of Los Alamos National Laboratory, hosted by The Computer History Museum
- ↑ see also Herbert L. Anderson (
**1986**).*Metropolis, Monte Carlo, and the MANIAC*. Los Alamos Science, pdf - ↑ dblp: Paul R. Stein