James McMahon (mathematician) facts for kids
James McMahon (born April 22, 1856 – died June 1, 1922) was an Irish mathematician. He spent most of his career teaching at Cornell University in Ithaca, New York. McMahon was a dedicated teacher. He was also an early supporter of making the teaching of advanced math a professional field in America.
He was a professor and the head of the Mathematics Department at Cornell. McMahon was one of the first members of the American Mathematical Society in 1891. For seven years, he helped edit the Annals of Mathematics journal. He also held important roles in the American Association for the Advancement of Science. He was Secretary (1897), General Secretary (1898), and Vice-President (1901). McMahon was even featured in the book American Men (and Women) of Science.
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Early Life and Cornell
James McMahon was born in County Armagh, Ireland, on April 22, 1856. His parents were Robert McMahon and Mary Hewitt. He began his studies at Trinity College, Dublin in 1879. He did very well, graduating in 1881 with top honors in Metaphysics and Classical Studies.
McMahon won the Wray Prize in 1880 for his work in Metaphysics. He also received Trinity's Brooke Prize for Classical Studies. He earned his first degree in 1881 and later received more advanced degrees.
In January 1883, McMahon came to Ithaca, New York. He started at Cornell University as a math examiner. He also taught for Andrew Dickson White's "Correspondence University," which was an early form of distance learning.
In 1884, James McMahon became an instructor at Cornell. He became an assistant professor in 1890 and a full professor of mathematics in 1904. He was one of the most important mathematicians at Cornell during this time.
In 1893, McMahon helped start the Sigma Xi Society. This group was created to be an honor society for science students. It was like Phi Beta Kappa, which focused more on arts and literature. The first meeting of Sigma Xi was held at Cornell University. McMahon helped decide how the society would grow. He also served as Vice President and President of the Theta Chapter of Phi Beta Kappa.
On June 26, 1890, James McMahon married Katharine Crane. She was the sister of another Cornell professor. In 1895, McMahon and his wife moved into a house near Professor Crane. James McMahon lived there until he passed away in 1922.
His Work in Mathematics
McMahon's most important work in applied mathematics was published after he died. In 1902, he gave a speech about how math functions could be used to solve problems in physics. His work in geometry focused on finding ways to use abstract math theories in real-world science and engineering.
As the study of statistics grew, people started using geometry to show their data. This mix of statistics and geometry led to more interest in geometric theories. A mathematician named Karl Pearson asked for someone to write a book about "Spherical Polyhedrometry." This was about using geometry to understand relationships in statistics.
McMahon took on this challenge as he was nearing retirement. The Carnegie Institute gave him a retirement fund. This allowed him to step down as head of Cornell's Math Department. He could then spend his last years working on this new math field.
McMahon and his wife rented a cottage in Key West, Florida. They spent the winters there while he worked on "Spherical Polyhedrometry." The results of his work were published in 1923, after his death. The paper was called Hyperspherical Geometry; and its Application to Correlation Theory for N Variables.
Public Views
In 1916, McMahon publicly supported President Woodrow Wilson for re-election. As the head of the Math Department at Cornell, Professor McMahon gave three reasons why he favored Wilson.
One main reason was Wilson's support for international law, even when many people in the country disagreed. McMahon also liked Wilson's efforts to create a proper government in Mexico. Finally, McMahon praised Wilson's many "positive and forward-looking achievements." He also admired Wilson's "enlightened Americanism."
McMahon took a break from teaching in 1920–1921. When he returned in 1921, he had a Carnegie pension. This allowed him to focus on his "Spherical Polyhedrometry" work until he died later that year.
Memberships
Professor McMahon was a member of several important groups. These included the Phi Beta Kappa Society and the Sigma Xi Society. He was also part of the London Mathematical Society and the American Mathematical Society. He was a member of the Circolo Matematico di Palermo and the Brotherhood of Saint Andrew. He served as treasurer for the Brotherhood of Saint Andrew.
McMahon was also a member of Phi Kappa Psi and, through that, the Irving Literary Society. He was a fellow of the American Association for the Advancement of Science. From 1916 to 1922, he served as a Vestryman for St. John's Episcopal Church in Ithaca.
Selected Works
- 1889 On the Expression for the Hessian of a Binary Quantic in Terms of the Roots, 5 Annals of Mathematics 17.
- 1893 On the descending series for Bessel's functions of both kinds, 8 Annals of Mathematics 57.
- 1894 On the Roots of the Bessel and Certain Related Functions, 9 Annals of Mathematics 23–30.
- 1898 Elements of Differential Calculus, (with Virgil Snyder, Lucien A. Wait, ed.), Cornell Mathematical Series.
- 1902 Some recent applications of function-theory to physical problems, address before the Section of Mathematics and Astronomy, American Association for the Advancement of Science.
- 1906 The Cornell Chapter of Phi Beta Kappa, (with C.S. Northrup), Theta of New York.
- 1909 Address to the Phi Beta Kappa Initiates, (Apr. 21, 1909).
- 1923 Hyperspherical Goniometry; and its Application to Correlation Theory for N Variables, 15 Biometrika 173–208. (See goniometry.)
Books
- Elements of the Differential Calculus (with Virgil Snyder) American Book Company, 1898
- Elementary Geometry–Plane American Book Company, 1903
- Hyperbolic Functions Tract No 4 in the Mathematical Monograph series edited by Mansfield Merriman & Robert S. Woodward, Wiley & Son, 1906
