# Lois Wilfred Griffiths

### Quick Info

Born
27 June 1899
Chagrin Falls, Ohio, USA
Died
9 November 1981
Skokie, Illinois, USA

Summary
Lois Wilfred Griffiths was an American mathematician best known for her work in polygonal numbers.

### Biography

Lois Griffiths' parents were Frederick William Griffiths and Lena Jones. Lena had studied at Kansas State Normal School and had been a school teacher. Frederick Griffiths was born in Wales and had emigrated to the United States in 1880. He was awarded a B.A. by Oberlin College in 1893 and a B.D. by Oberlin Theological Seminary in 1896. He was ordained and married Lena Jones in 1896. He was a minister in Michigan before moving to Ohio in 1898 where Lois and her brother Harold (born 1898) were born. Soon after the birth of Lois, the family moved to Jennings, Oklahoma Territory, where they lived during 1899-1900. After working for the Minneapolis Journal, Frederick Griffiths and his family moved to Seattle in 1904.

Lois was educated at elementary and secondary schools in Washington State before entering the University of Washington. Her brother, Harold F Griffiths, also studied at the University of Washington where he was in the Naval Unit and was a member of the University of Washington "Food Production Squad". During her undergraduate years Lois was assistant to Comptroller Condon of the University of Washington. She graduated with bachelor's degree in 1921 and remained at the University to study for her Master's degree. She received her Master's degree in 1923 after writing Contact Curves of the Rational Cubic which was published in type-written form by the University of Washington. She published a paper based on this work entitled Contact curves of the rational plane cubic in the Bulletin of the American Mathematical Society in 1925. She had been elected to membership of the American Mathematical Society at the thirtieth summer meeting of the Society held in Vassar College, New York, in September 1923. Entering the University of Chicago in October 1925, Griffiths undertook research for a doctorate in mathematics working with her thesis supervisor Leonard Dickson. She received the degree in 1927 after submitting her dissertation Certain quaternary quadratic forms and diophantine equations by generalized quaternion algebras.

Immediately following the award of her doctorate, Griffiths was appointed as an Instructor in Mathematics at Northwestern University in Evanston, Illinois, where she spent the whole of her teaching career. She was promoted to an assistant professorship of mathematics in 1930 then, after spending research leave in Cambridge, England, in 1936-37, she was promoted to associate professor at Northwestern University in 1938. She published papers such as Generalized Quaternion Algebras and the Theory of Numbers (1928) and Representation of Integers in the Form $x^{2} + 2y^{2} + 3z^{2} + 6w^{2}$ (1929), both in the American Journal of Mathematics, and A generalization of the Fermat theorem on polygonal numbers (1930) in the Annals of Mathematics. She continued to publish papers on representing numbers in certain forms with work such as Representation by Extended Polygonal Numbers and by Generalized Polygonal Numbers (1933) and Representation as Sums of Multiples of Generalized Polygonal Numbers (1936).

In 1945 Griffiths produced a typewritten set of notes Determinants and systems of linear equations. She expanded the notes into a book which was published by John Wiley and Sons as Introduction to the theory of equations in 1945. In the Preface she states clearly that her aim is to guide students:-
... slowly through the proofs of the important general theorems in the elementary theory of algebraic equations.
Thomas Arnold Brown in a review indicates the style of the book [2]:-
A very slight background of mathematical knowledge is demanded from the reader. Nevertheless the volume deliberately represents an innovation in literary mathematical presentation. Even moderately elaborate theorems are resolved into simple elements; illustrative examples and particular cases are introduced to pave the way for the formal proofs which follow; and there is much restatement. While such methods are admirable for the classroom and will no doubt prove helpful to the lone worker of mediocre mathematical attainments, there remains a danger that the gifted student may find the going tedious and feel the waft of any stimulus to inspire him to further study.
Two later typewritten sets of notes by Griffiths Outline of the theory of groups (1948) and Matrices and linear dependence (1949) were never published. Before writing her textbook, Griffiths had published a number of excellent reviews of important algebra texts. She reviewed Introduction to the Theory of Groups of Finite Order by Robert D Carmichael in 1939 [5], An Introduction to Abstract Algebra by Cyrus Colton MacDuffee in 1941 [4], and A Survey of Modern Algebra by Garrett Birkhoff and Saunders Mac Lane in 1942 [3]. In addition she continued her work on polygonal numbers, publishing papers such as: Universal functions of extended polygonal numbers (1941); Universal functions of polygonal numbers (1942); A note on representation by polygonal numbers (1942); Universal functions of polygonal numbers. II (1944); Universal functions of polygonal numbers. III (1945); and A note on linear homogeneous Diophantine equations (1946).

Griffiths attended meetings of both the American Mathematical Society and the Mathematical Association of America. For example, she attended the Fifteenth Summer Meeting of the Mathematical Association in 1931 and she delivered the lecture Universal functions of polygonal numbers at the meeting of the Mathematical Association of America held in Chicago on 1 September 1941. She attended the American Mathematical Society meeting in Chicago in April 1947 and delivered the lecture Linear homogeneous diophantine equations on the afternoon of Friday 26 April. She also attended the November meeting of the American Mathematical Society in Evanston in 1954.

As to her hobbies, Griffiths loved walking, gardening and cooking. She [1]:-
... liked classical music and kept notes on what she listened to on the radio.
She was honoured with life membership of the Northwestern University Alumni Association in 1954.

Lena Griffiths, Lois Griffiths' mother, came to live with her in Evanston in around 1945 and she continued to live with her daughter until her death in 1956. Lois Griffiths retired from her position at Northwestern University in 1964 and at that time she was made professor emeritus.

### References (show)

1. J Green and J LaDuke, Pioneering Women in American Mathematics : The Pre-1940 PhD's (American Mathematical Society, Providence, RI, 2009).
2. T A Brown, Review: Introduction to the Theory of Equations by Lois Wilfred Griffiths, The Mathematical Gazette 33 (303) (1949), 57-58.
3. L W Griffiths, Book Review: A Survey of Modern Algebra by Garrett Birkhoff; Saunders MacLane. Natl. Math. Mag. 16 (5) (1942), 268-269.
4. L W Griffiths, Book Review: An Introduction to Abstract Algebra by Cyrus Colton MacDuffee, Natl. Math. Mag. 15 (4) (1941), 211-212.
5. L W Griffiths, Book Review: Introduction to the Theory of Groups of Finite Order by Robert D Carmichael, Natl. Math. Mag. 13 (7) (1939), 353-354.
6. L W Griffiths, On Hypergroups, Multigroups, and Product Systems. Amer. J. Math. 60 (2) (1938), 345-354.
7. The Eatonville Dispatch, A Weekly Paper For Tacoma Eastern People (6 September 1918).
8. The Eatonville Dispatch, A Weekly Paper For Tacoma Eastern People (6 December 1918).