# Cornell Mathematics Doctorates, 1940-1959.

The first Cornell campus elm trees where a gift of the Class of 1872 (they offered 72 elm trees). The John Ostrander's elm trees (pictured here in 1953, between Stimson and Goldwin Smith Halls) where planted in 1877. Ostrander was a local farmer and he was not rich. He offered the best elm trees from his farm.

Before 1940, one hundred and one Ph.D.s were awarded in mathematics at Cornell including twenty two to women. The first, in 1872, went to Henry Turner Eddy who was Assistant Professor in Mathematics at the time.

The Cornell mathematics graduate program owes its early success to the leadership of James Oliver, Chair from 1874 to his death in 1895. The most prolific graduate advisor before 1940 was the algebraic geometer Virgil Snyder who supervised 43 Cornell Ph.D.s.

This page gives the complete chronological list of the people who earned a doctorate in mathematics at Cornell between 1940 and 1959 included. The list is organized by periods of 5 years. Sixty Ph.D.s were awarded during this period at a very steady average of about 3 per year (only 5 went to women).

This is a very successful time for the Cornell Mathematics Graduate Program which corresponds to the renaissance of the department during and after WWII. Mary Dolciani, Irving Reiner, Murray Rosenblatt, Joanne Elliott, Steven Orey, Daniel Ray, Jean-Pierre Meyer, Louis De Branges and Harry Kesten graduated during this period and the most active advisors were Mark Kac (16), John Barkley Rosser (8), Ralph Agnew, Burton W. Jones and Harry Pollard (6) and William Feller (5).

### 1940-1944 (12 doctorates)

### Seymour Sherman, 1940

Title: A Comparison of Linear Measures in the Plane. Advisor: John Adam Fitz Randolph. Career: University of Chicago; staff engineer, military operations research division of the Lockheed Aircraft Corporation; Indiana University where he Seymour Sherman Memorial Lecture Series are held.

### George Brinton Thomas, 1940

Title: Regular Ternary Quadratic Forms. Advisor: Burton W. Jones. Career: Massachusetts Institute of Technology. Author of "Thomas Caculus" first published by Addison-Wesley in 1951 as "Calculus and Analytic Geometry". The book is still in use at many Institutions and High Schools, including at Cornell.

### Walter Joel Harrington, 1941

Title: A Study of Certain Functions Auxiliary to Brun's Method in Number Theory. Advisor: John Barkley Rosser. Career: Allegheny Ballistics Lab in Cumberland, Md.; Cornell, Pennsylvania State University and at North Carolina State University.

### Donald Smith Miller, 1941

Title: Some Properties of Caratheodory and Gillespie Linear Measure. Advisor: John A. F. Randolph. Career: Co-authored papers with Dunford and Besicovitch and taught at Cornell until 1946.

### William Dean Wray, 1941

Title: Some Applications of Uniformity Trials. Advisor: John H. Curtiss. Career: Williams College; On June 8, 1942, Wray was sworn in as a civilian junior cryptanalyst with the Navy. He became a cryptologist. After the war, he worked for the newly created Armed Forces Security Agency which later became the National Security Agency. His services were recognized posthumously by The Exceptional Civilian Service Award. A road at Fort Meade is named after him.

### Robert Ruel Raphael Luckey, 1942

Title: Certain Applications of Fourier Integrals. Advisor: Mark Kac. Career: Houghton College.

### Gordon Loftis Walker, 1942

Title: Direct Product and Lorentz Matrices. Advisor: James Wallace Givens. Career: Temple University; Purdue University; The American Optical Company; Executive Director of the American Mathematical Society.

### Bernard Hinkle Bissinger, 1943

Title: Generalizations of Continued Fractions. Advisor: Ralph Agnew. Career: Lebanon Valley College.

### William Hetherington Durfee, 1943

Title: Congruence of Quadratic Forms over Valuation Rings Advisor: Burton W. Jones. Career: at Mount Holyoke College. Son of Walter H. Durfee (Ph.D. 1930) and father of A. H. Durfee (Ph.D. 1971). Grandson of William Pitt Durfee, Johns Hopkins Mathematics Ph.D. 1883.

### Theodore Hailperin, 1943

Title: A Set of Axioms for Logic. Advisor: John Barkley Rosser. Career: Lehigh University.

### Charles Jr. Hatfield, 1944

Title: On the Average Number of Roots of Certain Random Functions. Advisor: Mark Kac. Career: University of Missouri at Rolla.

### Alfred Milton Peiser, 1944

Title: Some Applications of Fourier Analysis and Calculus of Probability to the Study of Real Roots of Algebraic Equations. Advisor: Mark Kac. Career: Hydrocarbon Research, Inc.

### 1945-1949 (18 doctorates)

### Jerome Colbert Smith, 1945

Title: Asymptotic Distributions of Sums of Rademacher Functions and of Cosines with Big Gaps. Advisor: Mark Kac. Career: Lafayette College.

### Edward Joseph Scott, 1946

Title: Summability of the Geometric Series. Advisor: Ralph Agnew. Career: The University of Illinois, Urbana–Champaign.

### Mary Patricia Dolciani, 1947

Title: On the Representation of Integers by Quadratic Form. Advisor: Burton W. Jones. Career: Vassar College; Hunter College, City University of New York, Dean for Academic Development at The City University of New York. he Mathematical Association of America building in Washington D.C. is named The Dolciani Mathematical Center in her honor.

### Clifford Dixon Firestone, 1947

Title: Sufficient Conditions for the Modelling of Axiomatic Set Theory. Advisor: John Barkley Rosser. Career: Rutgers University; Applied Physics Laboratory, MD.

### William Judson LeVeque, 1947

Title: On the Distribution of Values of Number-Theoretic Functions. Advisor: Burton W. Jones and Mark Kac. Career: University of Michigan; Executive director of the American Mathematical Society.

### Abraham Morton Mark, 1947

Title: Limit Theorems in the Theory of Probability. Advisor: Mark Kac. Career: Southern Illinois University.

### Irving Reiner, 1947

Title: A Generalization of Meyer’s Theorem. Advisor: Burton W. Jones Career: University of Illinois at Urbana Champaign (married Irma Moses).

### Norman Gustav Gunderson, 1948

Title: Derivation of Criteria for the First Case of Fermat's Last Theorem and the Combination of These Criteria to Produce a New Lower Bound for the Exponent. Advisor: John Barkley Rosser. Career: Rochester University.

### Mario Leon Juncosa, 1948

Title: On the Asymptotic Behavior of the Minimum in a Sequence of Random Variables. Advisor: William Feller. Career: National Defense Research Institute.

### Mary Ann Lee, 1948

Title: Summability of Diagonal Series Formed from the Terms of Double Series. Advisor: Ralph Agnew. Career: Sweet Briar College.

### Irma Ruth Moses, 1948

Title: On the Representation, in the Ring of P-Adic Integers, of a Quadratic Form in N Variables By One in M Variables. Advisor: Burton W. Jones. Career: Temple University; University of Illinois, Urbana-Champaign (married Irving Reiner).

### Wallace Edward Barnes, 1949

Title: Abel Transforms and Partial Sums of Tauberian Series. Advisor: Ralph Agnew. Career: Director, Westinghouse Learning Corporation.

### Tseng Tung Cheng, 1949

Title: On the Sum of Independent Random Variables. Advisor: William Feller. Career: Xiamen University (previously, National Amoy University).

### George Laush, 1949

Title: Relations Among the Weierstrass Methods of Summability. Advisor: Ralph Agnew. Career: University of Pittsburgh.

### Murray Rosenblatt, 1949

Title: On Distributions of Certain Weiner Functionals. Advisor: Mark Kac. Career: Brown University, Indiana University and the Univesrity of California San Diego; Fellow of the Institute of Mathematical Statistics, American Association for the Advancement of Science and the American Mathematical Society. Member of the National Academy of Science.

### Murray Rose Spiegel, 1949

Title: On the Random Vibrations of Harmonically Bound Particles in a Viscous Medium. Advisor: Mark Kac. Career: Rensselaer Polytechnic Institute.

### Maria Alice Weber, 1949

Title: The Solution of a Linear Differential Equation of Parabolic Type. Advisor: William Feller. Career: Goucher College, California State University Northridge. Married Robert Steinberg.

### George Milton Wing, 1949

Title: The Mean Convergence of Orthogonal Series. Advisor: Harry Pollard. Career: Los Alamos National Laboratory; University of California Los Angeles, University of California Berkeley, the University of New Mexico, and Southern Methodist University. His Alma Mater, University of Rochester, organizes the G. Milton Wing Lecture Series.

### 1950-1954 (15 doctorates)

### Joanne Elliott, 1950

Title: On Some Singular Integral Equations of the Cauchy Type. Advisor: Harry Pollard. Career: Rutgers University.

### Ernest Elyash, 1950

Title: Several Limiting Laws of the Komogorov-Smirnov Type. Advisor: Mark Kac. Career: University of Massachusetts, Amherst.

### Samuel Goldberg, 1950

Title: On a Singular Diffusion Equation. Advisor: William Feller. Career: Oberlin College; Program Officer for the Sloan Foundation.

### Walter Lynn Murdock, 1950

Title: On the Distribution of Eigenvalues of Kernels and Matrices. Advisor: Mark Kac. Career: unknown.

### George Siefert, 1950

Title: Some Third Order Boundary Value Problems. Advisor: William Feller. Career: Iowa State University.

### Jerome Blackman, 1951

Title: Studies in the Heat Equation. Advisor: Harry Pollard. Career: University of Syracuse.

### Gerson Bernhard Robison, 1951

Title: Invariant Integrals over a Banach Space. Advisor: Bertram Yood. Career: SUNY New Paltz.

### Robert Lewis Beinert, 1951

Title: Abstract Parametrization of an Elliptic Curve. Advisor: Robert Walker. Career: Hobart and William Smith Colleges.

### Jack Cree Rogers, 1952

Title: Cross Sections in Fibre Bundles. Advisor: Paul Olum. Career: unknown.

### John Wells Brace, 1953

Title: Transformations on Banach Spaces. Advisor: Bertram Yood. Career: University of Maryland.

### Tseng-Yeh Chow, 1953

Title: A Study of Extremal Value Problems of Functions Regular in Annulus. Advisor: Wolfgang Fuchs. Career: Rensselaer Polytechnic Institute.

### Steven Orey, 1953

Title: Formal Development of Ordinal Number Theory and Applications to Consistency Proofs. Advisor: John Barkley Rosser. Career: University of Minnesota.

### Daniel Burrill Ray, 1953

Title: On Spectra of Second Order Differential Operators. Advisor: Mark Kac. Career: Massachusetts Institute of Technology.

### Jean-Pierre Meyer, 1954

Title: Classification of Mappings of a Three-Dimensional Complex into a Two-Dimensional Projective Space. Advisor: Paul Olum. Career: Johns Hopkins University.

### Charles Standish, 1954

Title: A Class of Measure Preserving Transformations. Advisor: Mark Kac. Career: Union College; Senior Scientist at IBM.

### 1955-1959 (15 doctorates)

### George Edwin Collins, 1955

Title: The Modeling of Zermelo Set Theories in New Foundations. Advisor: John Barkley Rosser. Career: The University of Wisconsin.

### Lonnie Cross, 1955

Title: On the Distribution of Eigenvalues of the Equation: Integral of A(S-T) PHI (T) with Respect to T Between Lower Limit -A and Upper Limit A=Rho (Integral of B(S-T)). Advisor: Mark Kac. Career: Cross is known as Abdulalim A. Shabazz. Clark Atlanta University; Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring.

### Elliott Mendelson, 1955

Title: The Independence of the Axiom of Choice. Advisor: John Barkley Rosser. Career: Queens College of the City University of New York.

### Morris Tenenbaum, 1955

Title: Transforms of Tauberian Series by Riesz Methods of Different Orders. Advisor: Ralph Agnew. Career: Co-author with Harry Pollard of "Ordinary Differential Equations", now a Dover Books on Mathematics.

### Robert McCallum Blumenthal, 1956

Title: An Extended Markov Property. Advisor: Gilbert Hunt. Career: University of Washington.

### Angelo Margaris, 1956

Title: A Problem of Rosser and Trucquette in Many Valued Logic. Advisor: Lisl Gaal. Career: The Ohio State University and Rhodes College in Memphis.

### Jerome Sacks, 1956

Title: Asymptotic Distributions of Stochastic Approximation Procedures. Advisor: Jack Kiefer. Career: Northwestern University; Rutgers University; University of Illinois at Urbana Champaign; Director of the National Institute of Statistical Sciences.

### Louis de Branges, 1957

Title: Local Operators on Fourier Transforms. Advisor: Harry Pollard. Career: Purdue University. Famous for his 1984 proof of the long-standing Bieberbach conjecture, now called de Branges' theorem; Plenary speakers at the 1986 International Congress of Mathematicians in Berkeley;1989 Ostrowski Prize; 1994 Leroy P. Steele Prize for seminal contribution to research.

### Norman Bernard Stein, 1957

Title: The Third Obstruction in Complex Projective Spaces. Advisor: Paul Olum. Career: University of Rochester.

### Harry Kesten, 1958

Title: Symmetric Random Walks on Groups. Advisor: Mark Kac. Career: Cornell University. Speaker at the International Congress of Mathematicians in Nice (1970) and Warsaw (1983) and a plenary speaker in Beijing in 2002; Brouwer Medal; the Leroy Steele Prize for Lifetime Achievement; George Pólya Prize. Fellow of the American Academy of Arts and Sciences; member of the National Academy of Sciences; correspondent member of the Royal Dutch Academy of Sciences.

### Stanislaw Leja, 1958

Title: Inversion of a Function with the Kernel [[(1+|x-y|)^2][c^2+|x-y|^2 ]]^( -1). Advisor: Harry Pollard. Career: Western Michigan University.

### Edward Norman, 1958

Title: Topics in Discrete Convolution Transforms. Advisor: Harry Pollard. Career: Drexel Institute of Technology.

### Anatole Joffe, 1959

Title: Sojourn Time for Stable Processes. Advisor: Mark Kac. Career: University de Montréal.

### David Brophel Lissner, 1959

Title: Matrices over Polynomial Rings. Advisor: Israel N. Herstein. Career: Syracuse University.

### Joseph Dela Rutledge, 1959

Title: A Preliminary Investigation of the Infinitely-Many-Valued Predicate Calculus. Advisor: John Barkley Rosser. Career: Research scientist at IBM; Involved in the development of the “pointing stick”, a distinctive feature of the ThinkPad.