# 130th Anniversary History of the NC State Mathematics Department

# 130 Years of Mathematics at NC State: 1889-2019

OVERVIEW:

Mathematics has been taught at NC State University since the first academic session of the North Carolina College of Agriculture and Mechanics Arts in the fall of 1889. Four years of mathematics were offered: for freshmen, arithmetic and algebra; for sophomores, algebra and plane geometry; for juniors, solid geometry, analytic geometry and for seniors, calculus. The first Professor of Mathematics was J. H. Kinealy.

The 1890 catalog – Mathematics program.

NC State’s freshman class, 1889.

NC State’s first class graduated in 1893.

The Department of Civil Engineering and Mathematics established in 1895. By 1905, the enrollment of the College reached almost 500, and it was decided to make mathematics into a separate department. The Department of Mathematics at North Carolina College of Agriculture and Mechanic Arts was founded in 1906, with Robert E. L. Yates (1866-1937) as the first head. Yates had been elected adjunct professor of mathematics at N. C. State College in 1891 and was promoted to the chair of pure mathematics in 1906. He was made Professor Emeritus of mathematics at N. C. State College in 1932.

In 1928, the Mathematics Department moved to the Engineering School. The department remained in the School of Engineering until 1960 when it joined with the Chemistry, Physics, and Experimental Statistics departments to form the School of Physical Sciences and Applied Mathematics. The school became the College of Physical and Mathematical Sciences in 1987. In 2013 the Department of Mathematics became part of NC State’s College of Sciences.

DEPARTMENT HEADS:

- 1906-1932: Robert E. L. Yates
- 1932-1957: Hilbert Fisher
- 1957-1967: John Cell
- 1967-1968: Hubert Park
- 1968-1977: Nicholas Rose
- 1977-1980: James M. Ortega
- 1980-1989: Ernest Burniston
- 1989-1999: Robert H. Martin, Jr.
- 1999-2002: Ernest Burniston
- 2002-2003: Bernard Mair
- 2003-2004: Jean-Pierre Fouque
- 2005-2015: Loek Helminck
- 2015-present: Alina Chertock

From left to right:

Yates, Fisher, Cell, Park, Rose, Ortega.

BUILDINGS:

The Department of Mathematics has been located in several places on the north campus, including Tompkins Hall until 1962.

Tompkins Hall in the 1950s.

The mathematics faculty in 1958.

The department moved to Harrelson Hall in 1962 and stayed there until 2010.

Harrelson Hall (clockwise from top left):

Construction in 1960, completion in 1961,

classroom in the 1970s, destruction in 2016.

The mathematics faculty in 1977.

In 2009 SAS Hall was completed and dedicated as the new home of the Departments of Mathematics and Statistics. The 10,700 square-meter building houses state-of-the-art classrooms, computer labs, tutorial centers, as well as meeting and study space for students and faculty.

SAS Hall in 2019.

RESEARCH IN MATHEMATICS:

The first Ph.D.’s were hired by Fisher in 1934 (J. G. Estes and J. M. Clarkson) and in 1935 (J. W. Cell, J. Levine, and R. C. Bullock).

Estes, who was a doctoral student of N. Wiener at MIT, authored the very first publication affiliated with the department (see below). He died prematurily on June 1, 1935.

Left: *The Technician,* October 5, 1934;

Center: Estes’ orbituary; Right:*The Technician,* September 27, 1935.

In the early days, research was not regarded as an important component of the work of faculty members. For instance, when Jack Levine, one the most productive early researcher at NC State, was recruited in 1935 as an instructor, his teaching load was 16 credits per quarter while it was 18 credits per quarter for non-researchers. Nonetheless, as early as the mid-1930s, some faculty were actively engaged in high level research. Listed below are some of the earliest papers published by the department.

- J. G. Estes,

The lift and the moment of an arbitrary aerofoil-Joukovsky potential,

J. Math. Phys.,

vol. 14, pp. 100-124, 1935. - J. Levine,

Groups of motions in conformally flat spaces,

Bull. Amer. Math. Soc.,

vol. 45, pp. 766-773, 1936. - J. M. Clarkson,

An involutorial line transformation determined by a congruence of

twisted cubic curves,

Bull. Amer. Math. Soc.,

vol. 43, pp. 142-144, 1937. - J. Levine,

Metric spaces with geodesic Ricci curves. I,

Bull. Amer. Math. Soc.,

vol. 44, pp. 145-152, 1938. - J. W. Cell, An accurate method for obtaining the derivative

function from observational data,

Amer. Math. Monthly,

vol. 46, pp. 87-92, 1939. - L. S. Winton,

A compatible integro-differential system,

Duke Math. J.,

vol. 6, pp. 562-578, 1940. - J. Levine,

Invariants of systems of second order linear

differential equations,

Duke Math. J.,

vol. 7, pp. 298-311, 1940.

The April 1939 meeting of the American Mathematical Society was attended by Cell, Clarkson, Levine, Mumford, Nahikian, and Park.

Jack Levine (1907-2005) received his Ph.D. from Princeton in 1934, joined NC State in 1935, became full professor in 1946 and emeritus in 1976. He continued to teach until the mid 1990s. He published continuously from 1933 to 1993 in the areas of tensor analysis, differential geometry, and cryptography. From left to right: June 1935 offer letter; undated picture; excerpt from the March 14, 1951 issue of *The Technician*; at an event honoring his career.

The research activity of the Department of Mathematics increased significantly in the 1960s, with an steadily growing number of faculty publishing regularly and also advising Ph.D. students (the Ph.D. program in mathematics at NC State was approved in 1962).

Here is a selection of publications from the 1960s.

- L. Carlitz and J. Levine,

Some problems concerning Kummer’s congruences for the Euler

numbers and polynomials,

Trans. Amer. Math. Soc.,

vol. 96, pp. 23-37, 1960. - J. W. Cell and W. J. Harrington,

Repeated integrals of the square-wave functions and related sets

of orthogonal functions,

Duke Math. J.,

vol. 28, pp. 409-419, 1961. - R. A. Struble,

An application of the method of averaging in the theory of

satellite motion,

J. Math. Mech.,

vol. 10, pp. 691-704, 1961. - J. Levine and H. M. Nahikian,

On the construction of involutory matrices,

Amer. Math. Monthly,

vol. 69, pp. 267-272, 1962. - J. Bishir,

Maximum population size in a branching process,

Biometrics,

vol. 18, pp. 394-403, 1962. - R. A. Struble and S. M. Yionoulis,

General perturbational solution of the harmonically forced duffing

equation,

Arch. Ration. Mech. Anal.,

vol. 9, pp. 422-438, 1962. - J. Levine,

Analysis of the case n=3 in algebraic cryptography with involutory

key-matrix and known alphabet,

J. Reine Angew. Math.,

vol. 213, pp. 1-30, 1963. - W. J. Harrington and R. C. Bullock,

The motion of a spinner rocket inside a smoothbore launcher,

J. Franklin Inst.,

vol. 277, pp. 552-565, 1964. - J. H. Heinbockel,

Factorization of linear second order differential operators,

Math. Mag.,

vol. 37, pp. 302-304, 1964. - T. G. Proctor and R. A. Struble,

Motion of two weakly coupled nonlinear oscillators,

Arch. Rational Mech. Anal.,

vol. 18, pp. 293-303, 1965. - K. Koh and A. Mewborn,

A class of prime rings,

Canad. Math. Bull.,

vol. 9, pp. 63-72, 1966. - D. J. Hansen,

A functional characterization of a Boolean determinant,

J. London Math. Soc.,

vol. 41, pp. 723-727, 1966. - J. Brawley, Jr.,

Similar involutory matrices (mod p^m),

Amer. Math. Monthly,

vol. 73, pp. 499-501, 1966. - P. A. Nickel,

A note on principal functions and multiply-valent canonical

mappings,

Pacific J. Math.,

vol. 20, pp. 283-288, 1967. - R. E. Chandler and K. Koh,

Applications of a function topology on rings with unit,

Illinois J. Math.,

vol. 11, pp. 580-585, 1967. - W. J. Harrington,

A property of Mellin transforms,

SIAM Rev.,

vol. 9, pp. pp. 542-547, 1967. - H. J. Charlton,

A note on arc-preserving functions for manifolds,

Canad. Math. Bull.,

vol. 10, pp. 597-598, 1967. - J. A. Marlin,

Solutions of perturbed Hamiltonian systems,

Arch. Ration. Mech. Anal.,

vol. 24, pp. 274-301, 1967. - D. E. Garoutte and P. A. Nickel,

A note on extremal properties characterizing weakly λ-valent

principal functions,

Pacific J. Math.,

vol. 25, pp. 109-115, 1968. - E. E. Burniston,

On the flexure of an infinite elastic plate containing a large

unstressed circular hole,

SIAM J. Appl. Math.,

vol. 16, pp. 109-125, 1968. - H. R. van der Vaart,

Determining the absolutely continuous component of a probability

distribution from its Fourier-Stieltjes transform,

Ark. Mat.,

vol. 7, pp. 331-342, 1968. - W. G. Dotson, Jr. and W. R. Mann,

A generalized corollary of the Browder-Kirk fixed point theorem,

Pac. J. Math.,

vol. 26, pp. 455-459, 1968. - J. M. A. Danby,

Motion of a satellite of a very oblate planet,

Astron. J.,

vol. 73, pp. 1031-1038, 1968. - N. J. Rose and R. D. Bronson,

On optimal terminal control,

IEEE Trans. Automatic Control,

vol. 14, pp. 443-448, 1969. - C. D. Meyer, Jr.,

On ranks of pseudoinverses,

SIAM Rev.,

vol. 11, pp. 382-385, 1969. - J. Luh,

On the theory of simple Γ-rings,

Michigan Math. J.,

vol. 16, pp. 65-75, 1969. - D. F. Ullrich,

Boundary value problems for a class of nonlinear second-order

differential equations,

J. Math. Anal. Appl.,

vol. 28, pp. 188-210, 1969. - R. T. Ramsay,

On compactification and structure of topological groups,

Proc. Amer. Math. Soc.,

vol. 20, pp. 585-589, 1969.

SNAPSHOTS – THE DEPARTMENT IN 1962:

In 1962, the Ph.D. program was approved, and the department moved

from Tompkins Hall to Harrelson Hall.

The Department of Mathematics in 1962:

Struble’s book announcement in *The Technician* (February 12 issue); the Applied Math Club;

Petrea named freshman instructor of the year

(*The Technician,* March 8 issue);

analog computing (*The Technician,* December 5 issue).

FURTHER READINGS:

- J. W. Brawley, Jr.,

In memory of Jack Levine (1907-2005),

Cryptologia,

vol. 30, pp. 83-97, 2006. - D. A. Lockmiller,

History of the North Carolina State College of Agriculture and

Engineering of The University of North Carolina, 1889-1939,

North Carolina Office of Archives and History, 1939. - N. J. Rose,

History of the Mathematics Department at North Carolina State

University — 1889-2009,

2nd ed., 2009.

P. L. Combettes, 2019.