University of Texas, Dolph Briscoe Center for American History

A Guide to the J. Barkley Rosser Papers, 1931-1989

Descriptive Summary

Creator Rosser, J. Barkley (John Barkley), 1907-
Title J. Barkley Rosser Papers
Dates: 1931-1989
Abstract The J. Barkley Rosser Papers (1931-1989) consist of correspondence, manuscripts of publications and lectures, notes, reprints, calculations, and books. Topics covered include logic, analytic number theory, and ballistics.
Accession No. 91-1
Extent 10 ft., 8 in.
Language Materials are written in English.
Repository: Dolph Briscoe Center for American History, The University of Texas at Austin

Biographical Note

J. Barkley Rosser was born in Jacksonville, Florida in 1907. He earned both his Bachelor of Science (1929) and his Master of Science (1931) from the University of Florida. He obtained his Ph.D. from Princeton University in 1934. After getting his Ph.D., Rosser taught at Princeton, Harvard, and Cornell and spent the latter part of his career at the University of Wisconsin-Madison. He continued to lecture well into his late 70s, and died at his home in Madison in 1989.

Rosser contributed to many committees and professional associations in addition to his teaching: he served as president of the Association for Symbolic Logic and the Society of Industrial and Applied Mathematics; was a member of the space vehicle panel for the advisory committee of the Apollo project; was an early contributor to computer science theory; and helped develop the Polaris missile. While at the University of Wisconsin-Madison, he served as the director of the U. S. Army Mathematics Research Center. Rosser is known for his part in the Church-Rosser theorem, in lambda calculus, and he developed the Rosser sieve.

His areas of expertise include symbolic logic, ballistics, rocket development, and numerical analysis.

Scope and Contents

The J. Barkley Rosser Papers (1931-1989) consist of correspondence, manuscripts of publications and lectures, notes, reprints, calculations, and books. Topics covered include logic, analytic number theory, and ballistics.

Forms part of the Archives of American Mathematics.


Access Restrictions

Unrestricted access.

Use Restrictions

These papers are stored remotely at CDL. Advance notice required for retrieval. Contact repository for retrieval.

Index Terms

Subjects (Persons)
Rosser, J. Barkley (John Barkley), 1907-
Schoenfeld, Lowell, 1920-
Subjects (Organizations)
The University of Wisconsin-Madison. Mathematics Dept.
Mathematics Research Center (United States. Army)
Mathematics--Study and teaching--United States
Logic, Symbolic and mathematical
Number theory.
Numerical analysis.
Rockets (Ordnance)
Magic squares.

Related Material

Materials relating to Dr. Rosser's work at the Army Math Research Center can be found at the Wisconsin Historical Society in Madison, Wisconsin.

Administrative Information

Preferred Citation

J. Barkley Rosser Papers, 1931-1989, Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas at Austin.

Detailed Description of the Collection



91-1/1 Candy, A. L., 1938-1941
Church, Alonzo [includes correspondence photocopied by Church], ca. 1983
Erdos, Paul, 1938-1939
Sacks, Gerald [includes mathematical work], 1961 and undated
Schoenfeld, Lowell, 1955-1976
91-1/2 Thays, Leslie, 1973 and undated
Van Waarden, John, 1975-1977
American Mathematical Monthly [problem and solution], 1974
Centre de Recherches Mathematiques, 1972-1973
Hawaii lectures, 1981
Journal of Symbolic Logic, 1965
Magic squares [Coxeter, Stern, Thomas], 1938-1941
New Orleans talks, 1980
Lawrence Rad. Lab., 1971-1974
Rational proofs, 1938-1939
Stewart Committee, 1983
Sieve method, 1955
Miscellaneous mathematics related correspondence [includes requests for reprints], 1963-1989
“Miscellaneous,” 1961-1963
Assorted, undated



91-1/2 Books:
Mathematical Theory of Rocket Light, New York and London: McGraw-Hill Book Company, Inc. [bound photocopy], 1947
Theory and Application of $intsb {0sp z}esp {-xsp {2}}dx$ and $intsb {0sp z}esp {-psp {2}ysp {2}}dyintsp ysb 0 esp {-xsp {2}}dx$, Brooklyn: Mapleton House Publishers [bound photocopy], 1948
Many-Valued Logics, Amsterdam: North-Holland Publishing Company [bound photocopy], 1952
91-1/3 Logic for Mathematicians:
Logic for Mathematicians, New York: McGraw-Hill Book Company, Inc. [includes correspondence], 1953
Logic for Mathematicians, New York: Chelsea Publishing Company [includes correspondence], 1978
Chapter 1, undated
Chapter 2, undated
Chapter Three and Four, undated
Chapter 3 and 4, undated
Chapter 5, undated
Chapter 6, undated
91-1/2 Simplified Independence Proofs: Boolean Valued Models of Set Theory, New York: Academic Press, 1969
Pocket Calculator Supplement for Calculus, Reading, Massachusetts: Addison-Wesley Publishing Company, 1979
91-1/4 Reprints:
“Explicit Bounds for Some Functions of Prime Numbers,” January 1941
“Axiom Schemes for M-Valued Propositional Calculi” [with A. R. Turquette], 1945
“Axiom Schemes for M-Valued Functional Calculi of First Order, Part I: Proof of Plausibility” [with A. R. Turquette], December 1948
“A Note on the Deductive Completeness of M-Valued Propositoinal Calculi” [with A. R. Turquette], January 1950
“Real Roots of Real Dirichlet L-series,” December 1950
“Real Roots of Real Dirichlet L-series, II,” undated
“Transformations to Speed the Convergence of Series," January 1951
“Axiom Schemes for M-Valued Functional Calculi of First Order, Part II: Deductive Completeness” [with A. R. Turquette], March 1951
“Explicit Remainder Terms for Some Asymptotic Series,” July 1955
“Deux Esquisses de Logique,” 1955
“Some Sufficient Conditions for the Existence of an Asymptotic Formula or an Asymptotic Expansion,” 1959
“Approximate Formulas for Some Functions of Prime Numbers” [with Lowell Schoenfeld], March 1962
“Rigorous Computation and the Zeros of the Riemann Zeta-Function” [with Lowell Schoenfeld and J. M. Yohe], 1969
“Mathematics Courses in 1984," June-July 1972
“Sharper Bounds for the Chebyshev Functions theta (x) and psi (x)” [with Lowell Schoenfeld]:
Draft, 1974
Published reprint, January 1975
“Nine-Point Difference Solutions for Poisson’s Equation,” April 1975
“Effect of Discontinuous Boundary Conditions on Finite-Difference Solutions,” 1976
“Finite-difference Solution of Poisson’s Equation in Rectangles of Arbitrary Proportions,” 1977
“Majorization Formulas for a Biharmonic Function of Two Variables,” April 1980
“Mathematics and Mathematicians in World War II” [includes galley proof], October 1982
“Mathematics and Mathematicians in World War II,” A Century of Mathematics in America, Part I [includes galley proof], 1982
"Highlights of the History of the Lambda-Calculus," October 1984
“Stuff on Asymptotic,” 1951-1955 and undated
“On the Extension of Certain Theorems of Mathematical Physics and Their Subsequent Application to Problems of Wave Mechanics” [Master’s thesis], 1931
“Factorial Expansions for Certain Bessel Functions,” undated
“The Goldback-Vinogradoff Theorem” [Xerox master copy], “ 1949 and undated
91-1/3 “Non-mathematical Theory of Rocket Flight,” undated
91-1/4 “Rational Proofs of the Existence of Primes in Arithmetic Sequences,” 1939
“Real Roots of Real Dirichlet L-Series III,” 1952 and undated
91-1/5 “Some New Extension of Brun’s Method,” 1955 and undated
“Unusual Properties of Laguerre Polynomials” [with Ragab and Schoenfeld], undated
Analytic Number Theory:
General correspondence, 1949-1951
Correspondence with Chelsea Publishing Company, 1948
Corrections, 1948 and undated
Bibliography, undated
“Primes in an Arithmetic Progression, Page’s Theorem,” undated
Correspondence with Schoenfeld, 1948
“Notes in Anal. # Th. Chap I,” undated
Chap II, 1950 and undated
Chap III, undated
Chap IV and V, undated
Supplement to diabolic squares [“Magic Squares, Supplement”], undated
Propositional Calculus, undated
Chapter IX, undated
Early drafts, undated
91-1/6 Original [includes reprints by Rieger and Kuhn], 1953-1954 and undated
Printed matter [chapters I-VIII], undated
Carbon, undated
Appendices, undated
Assorted typed manuscripts, undated
Untitled [handwritten], undated
Technical reports:
“Numerical Computation of Low Moments of Order Statistics from a Normal Population,” 1951 and undated
91-1/7 “Axiomatization of Infinite Valued Logics,” September 1960
“A Table of Ei(x) (x-1)e-x,” March 1961
“Table for Estimating Functions of Primes,” September 1961
91-1/8 “Estimation of Capacity with Bounds for the Error, I” [April 1966], [includes correspondence and research materials], 1950, 1962-1973
“Block Relaxation by Computer,” April 1964
“The Direct Solution of Difference Analogs of Poisson’s Equation,” October 1967
“The Riemann Zeta-Function Magnetic Tapes” [with D. R. Musser, Lowell Schoenfeld, and J. M. Yohe], March 1969
“An Iterative Algorithm for Calculating Potentials Near Small Groups of Finite Charged Plates” [with F. S. Acton], December 1970
91-1/7 “Approximation of the Riemann Zeta-Function” [with Lowell Schoenfeld]:
Early draft, 1970
Published report, June 1971
References, 1924, 1967-1975
91-1/8 “Bounds for Some Coefficients Related to the Zeta Function,” July 1972
“Potentials of Charged Plates, Part I,” April 1973
“Finite-Difference Solution of Poisson’s Equations in Rectangles of Arbitrary Shape,” September 1973
“Potentials of Charged Plates, Part III,” December 1973
“A Power Series Solution of a Harmonic Mixed Boundary Value Problem” [with N. Papamichael], December 1973
“Finite-Difference Solution of Poisson’s Equation in Rectangles of Arbitrary Shape,” February 1974
“Potentials of Charged Plates,” October 1974
“Fourier Series in the Computer Age,” February 1974
“A Power Series Solution of a Harmonic Mixed Boundary Value Problem” [with N. Papmichael], January 1975
“Nine-Point Difference Solutions for Poisson’s Equation,” March 1975
91-1/6 “Calculation of Potential in a Sector, Part I” [includes notes], May 1975
91-1/8 “High Precision Coefficients Related to the Zeta Function” [with Fred D. Crary], May 1975
“Fourier Transform Evaluation,” June 1976
“Cancellation and Rounding Errors” [with J. Michael Yohe], August 1976
“Solution of Partial Differential Equations by Means of Finite Elements: An Introductory Sketch,” December 1976
91-1/7 “Harmonic Functions on Regions with Reentrant Corners, Part I” [includes draft], 1977 and undated
“Majorization Formulas for a Biharmonic Function of Two Variables” [includes draft], August 1978
91-1/8 “Highlights of the History of the Lambda-Calculus,” October 1982
91-1/6 “A Numerical Bound in the Three Prime Theorem” [Obsolete], undated


Work by others:

91-1/8 Bateman, Paul, “Imaginary Quadratic Fields with Unique Factorization” [with Emil Grosswald], 1961
Brun, Viggo, 1916-1931
Church, Alonzo, “Russell’s theory of Identify of Propositions” [includes correspondence], ca. 1985
Erdös, Paul, 1935-1950
91-1/9 Feferman, Solomon, “Transfinite recursive progressions of axiomatic theories,” undated
Grimm, Gottfried, Zeroes of L-series, 1932
Grosswald, Emil, “”L-functions and quadratic fields with unique factorization,” 1963-1964
Harrington, Walter Joel, “A Study of Certain Functions Auxiliary to Brun’s Method in Number Theory,” 1941
Hiz, H. [includes notes by Rosser], 1957 and undated
Hlavka, James L., “Evaluation of a Lower Bound for Vinogradov’s Three Prime Theorem, with an Improved Error Term” [includes corrections], undated
Jones, J. P., “The Existential Gödel-Rosser Theorem,” 1979-1981
Klop, Jan William, “A Counterexample to the Church-Rosser Property for Lambda Calculus with Subjective Pairing,” January 1979
Kuhn, Pavel [reprints and correspondence], 1939, 1954 and undated
McCurley, Kevin, “Explicit Estimates for Functions of Primes in Arithmetic Progressions,” 1981
Mitchell, Emerson, mathematical calculations, 1974 and undated
Rademacher, Hans, undated
Ragab, F. M., “Four titles re: Laguerre Polynomials,” undated
Richert, H. E., “Die Brun-Selbergsche Siebmethode,” 1962-1963
Scarpellin, Bruno, “Non-Axiomatizability of the Infinitely-many-valued Predicate Calculus x” [includes correspondence and notes], 1950, 1960 and undated
91-1/10 Schoenfeld, Lowell, “Every Odd Integer Having at Least 350,000 Digits is the Sum of Three Odd Primes” [lecture], 1957-1959
Schoenfeld, Lowell, three manuscripts, undated
Schoenfeld-Selberg [“Chapter V: The Goldbach-Snirel’man Thorem”], December 22, 1954
Schroer, David Edward, “The Church-Rosser Theorem,” [Ph.D. thesis], June 1965
91-1/11 Teichroew, D., 1954-1955
Laguerre polynomials reprints, undated
Laplace Transforms, 1944
Linear equation reprints, 1946-1958
Partial difference equations reprints, 1951-1959
Brunel University, 1978-1982
Photocopied mathematical notes, 1949 and undated
91-1/12 Reprints [assorted], 1941-1954
Assorted reprints [Dutch], 1938-1940, 1950-1953


Mathematical work:

91-1/12 Block relaxation by computer [see filigree], 1962-1966 and undated
Computation of Ei(x), undated
Direct solution of the difference analog of Poisson’s Equation, undated
Elementary proof – prime number theorem, undated
Estimation of S (1, 2, r), undated
Expansion of x^n e^-x, undated
Exponential integer, undated
Filigree, 1967 and undated
91-1/13 Logic, ca. 1963 and undated
Jan Lulsasiewicz, 1958 and undated
Miscellaneous results about M(x) and g(x), undated
“Numerical Computation of Low Moments of Order Statistics from a Normal Population,” 1951-1952
Orbits [“stuff from Curtiss Schafer, etc.”], undated
Order statistics [includes correspondence], 1951-1955 and undated
Ramsey’s theorem and creative sets, undated
“Reconsideration of Certain Points,” undated
Rose, G. F., “Propositional Calculus and Realizability,” 1953 and undated
Three-prime theorem with Lowell Schoenfeld:
First part, sections I, II [includes correspondence], 1948
Second part, part of section III, 1948
Third part, last of section III, 1948
91-1/14 Fourth part, sections IV, V and Vinogradov results, 1948
Section I: Basic Inequalities and Lemmas, undated
Section III: Regions in which <(s, x)  0 and Estimates for Functions Involving < (s, x), undated
Section IV: The Number of Primes in a Progression and Section V: Vinogradov’s Estimate, undated
Section VI: The Three Prime Theorem, undated
Intro and Biblio, undated
Changes [8 sets of revisions], undated
Changes to Section IV, undated
Untitled pages, undated
From Lowell Schoenfeld, August 1965
Real roots of real Dirichlet L-series, 1950 and undated
“Reconsideration of Certain Points,” undated
91-1/15 Study of Fn (a,b), undated
Study of Gn (X), undated
Tables of Gn (X), undated
Table of Zeta Function [printout], undated
W. J. Dixon, 1951 and undated
Zeroes of L-series, undated
Miscellaneous notes on eigenvalues, undated
Miscellaneous notes, undated
Unlabeled [includes printouts], undated
4RM55b Unlabeled, undated
91-1/16 Unlabeled, undated
Untitled, undated
Unfoldered, undated
4RM55c Unfoldered, undated
4RM55b Tables and computer printouts:
Table I. values of 4^r[alpha]2t (r, r), undated
Table II. Values of 4^r[beta]A(r), undated
Table III. Table of accurate and approximate means undated
Table IV. Table of accurate and approximate extreme means, undated
Computer printouts [on the 1604], undated
Computer printouts, undated


Research notes:

91-1/16 Ed Cannon Comp. of Ei (X), undated
Eigenvalues, 1952, 1962 and undated
Euler-MacLaurin, undated
Laplace transform notes, undated
The method of Hestenes and Stiefel, undated
Order statistics, 1954 and undated
Problems on asymptotic series [includes correspondence], undated
91-1/17 Tables of [psi](x) and X(x), undated
“Stuff on forcing” [includes reprints and mathematics work], 1963-1967
Bibliographic citation cards, undated
Miscellaneous, undated



91-1/17 Attendance [Analytic number theory], undated
Mathematics 100 and 110, 1947-1949
Mathematics 381/382 assignments, 1956-1957
4RM194 Restricted: Mathematics 381/382 gradebooks and assignments, undated
Restricted: 381 and 382 homework [includes grade book], undated
91-1/17 Math. 381 final exam, 1957
Mathematics 381, 1953-1955
Math 381 prelim and final exam, January 1959
Math. 382 final exam student work, 1957 and undated
Math. 382 homework assignments, 1961 and undated
91-1/18 Mathematics 382 theorems, undated
382 prelim, undated
Prelim Math. 382, 1957 and undated
Final exam for Logic [Math382, David N. Freeman], 1957
Logic homework 1955, undated
Math 423/424, 1962-1963
615 homework assignments, Sept-Oct-Nov, 1955-1957
Notes used in Mathematics 615, 1955-1958
615 Homework Dec-Jan, 1955-1959
615 homework 1955, 1955-1956
91-1/19 615 homework 1956, 1957 and undated
615 Homework 1957-8, September 1957-January 1958
615 1957, January 1958 and undated
615 homework 1958, 1958-1959
615 homework 1958, 1959 and undated
615 notes, undated
Remarks about rigor in 615, undated
Homework 616 Feb-Mar, 1956 and undated
91-1/20 616 assignments, Feb-Mar, 1956-1959
Homework 616 Apr-May, 1956
616 homework April-May, 1956-1959
Homework 616 1957 Feb and March, 1957 and undated
Homework 616 1957 April and May, undated
Mathematics 616, 1959
91-1/21 616 problems, 1961
Thm. A, B, C, D. Asymptotic Exp. Laplace Trans. [Mathematics 621-622], undated
Math. 622, “The Horn-Jeffreys-Langer Method (Commonly known as the BWK or WKB method)” [includes Langer reprints], 1948-1949
4RM194 Restricted: Answers for 621 [includes gradebooks], November-December 1948
91-1/21 Answers in 621, September-October 1948
Mathematics 621, final exam and answers, 1949
Final exam 621, 1949
621 prelim and solutions, 1950
621 final, January 1951
621 course notes, undated
Answers in 621-622, January-February 1949
Problems and answers in 622, 1948
91-1/22 Final exam 622 [includes answers], 1948
Math 622, final exam and answers, June 1949
622 homework, 1949
622 course notes, 1950-1951
Homework 622, 1951
Final exam 622 [includes answers], 1951
Math 622 term examination, May 1952
Homework from 622, 1949
426 Assignments, 1963 and undated
91-1/23 Algebra [Cornell University], ca. 1938, 1964
Orientation lectures [“Numerical Solutions of Ordinary Differential Equations”], 1964-1966
Computer Science 412, 1975-1977
Theorems master set [logic], undated
Exercises master set [logic], undated
4RM194 Restricted: Arthur Shaw student work [includes grade book], undated
91-1/23 Davis 2323, undated
Unlabeled course assignments, undated
Unfoldered [includes correspondence], 1957 and undated



91-1/23 Taft lectures [University of Cincinnati], 1969-1970
“Mathematization of U. S. Society from World War II to Present and Beyond” [James Madison University], 1982
91-1/24 “Calculation of Potential in a Sector” [includes overhead transparencies], undated
The Euler-Mascheroni constant, undated
Thursday talks, undated


Conferences and Institutes:

91-1/24 “A Report of the Institute in the Theory of Numbers” [includes paper by Rosser and errata], 1959-1960
Joint Mathematics Meeting, 1960
1982 ACM Symposium on LISP and Functional Programming, 1982
NATO Advanced Study Institute, 1973


Professional organizations:

91-1/24 American Mathematical Society:
Committee on Information Exchange and Publication in the Mathematical Sciences, 1965-1966
“Uses of the computer in teaching mathematics courses” special section, 1975
1982 Toronto meeting, 1982


Swarthmore College Honors Examination:

91-1/24 1942-1943
91-1/25 1961-1962


Security clearance:

91-1/25 General, 1955-1970
National Academy clearance, 1968
NSA 1976, undated

91-1/25 Institute for Defense, 1976 and undated

91-1/25 Princeton Mathematics Community in the 1930s [interview with Kleene and Rosser], 1984-1985

91-1/25 Digital computer needs in universities and colleges, 1966-1967

91-1/25 Rosser’s retirement, 1978

91-1/25 Overhead projector transparencies, undated



91-1/25 Grand Guard 50th reunion, 1979
Insurance, 1967-1972
TIAA-CREF, 1964-1970



4RM203c Rosser as graduate student at Princeton, ca. 1931
Group photograph at Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland, undated
Visit of President’s Scientific Advisory Committee to the Kennedy Space Center, June 1, 1966
Portrait, 1965
Rosser at his desk in his office at UCLA as Director of the Institute for Numerical Analysis, ca. 1950
Group photograph, LISP Conference in Pittsburgh, August 1982