Cassius Jackson Keyser

Cassius Jackson Keyser (May 15, 1862 – May 8, 1947) was an American mathematician of pronounced philosophical inclinations.

Cassius Jackson Keyser
PSM V74 D209 Cassius Jackson Keyser
Born15 May 1862
Rawson, Ohio, United States
Died8 May 1947 (aged 84)
New York City, New York, United States
Alma materColumbia University
Known forFoundation of mathematics
Spouse(s)Ella Maud Crow
Scientific career
InstitutionsUniversity of Missouri, New York State Normal School (now SUNY New Paltz), Washington University, Columbia University
Doctoral studentsEric Temple Bell, Emil Post, Edward Kasner


Keyser's initial higher education was at North West Ohio Normal School (now Ohio Northern University), then became a school teacher and principal. In 1885, he married a fellow student at the Normal School, Ella Maud Crow of Ridgeway, Ohio. He completed a second undergraduate degree, a BSc, at the University of Missouri in 1892. After teaching there, at the New York State Normal School (now SUNY New Paltz), and at Washington University, he enrolled as a graduate student at Columbia University, earning the MA in 1896 and the Ph.D. in 1901. He spent the rest of his career at Columbia, becoming the Adrain Professor of Mathematics (1904–27) and Head of the department (1910–16). He retired in 1927.

Keyser was one of the first Americans to appreciate the new directions in the foundation of mathematics, heralded by the work of Europeans such as Richard Dedekind, Georg Cantor, Giuseppe Peano, Henri Poincaré, David Hilbert, Ernst Zermelo, Bertrand Russell, and A. N. Whitehead. He was also one of the first to appreciate the mathematical and philosophical importance of his fellow American Charles Sanders Peirce. Alfred Korzybski, founder of general semantics, named Keyser as a major influence. While at Columbia, Keyser supervised only two PhDs, but they both proved quite consequential: Eric Temple Bell and the logician Emil Post.

He became a member of the American board of the Hibbert Journal, and made contributions to that and other philosophical journals. Together with the New International Encyclopedia and his Columbia colleague John Dewey, Keyser helped found the American Association of University Professors (AAUP). He was a fellow of the American Academy for the Advancement of Science, and a member of the American Mathematical Society.


  • Mathematics and the Question of the Cosmic Mind, with Other Essays.
  • 1914. Science and Religion: The Rational and the Super-Rational
  • 1916. The Human Worth of Rigorous Thinking. Columbia Univ. Press.
  • 1922. Mathematical Philosophy, a Study of Fate and Freedom.[1]
  • 1927. Mole Philosophy & Other Essays.
  • 1932. The meaning of mathematics.
  • 1935. A glance at some of the ideas of Charles Sanders Peirce.
  • 1935. Three great synonyms: Relation, transformation, function.
  • 1936. Panthetics.
  • 1938. A mathematical prodigy: history and legend.
  • 1938. Roger Bacon.
  • 1938. Benedict Spinoza.
  • 1939. The Role of Mathematics in the tragedy of our modern culture.
  • 1941. Charles Sanders Peirce as a pioneer. Internet Archive Eprint. A lecture given on May 18, 1935 at the Galois Institute of Mathematics at Long Island University.
  • 1942. Thinking about thinking.
  • 1947. Mathematics as a culture clue.
  • 1952. The rational and the superrational: studies in thinking.
  • 2005. Mathematics. Michigan Historical Reprint Series.
  • 2005. Mathematical Philosophy: A Study of Fate and Freedom (Lectures for the Educated Laymen). Michigan Historical Reprint Series.

See also


  1. ^ Young, J. W. (1923). "Mathematics for the Layman". Bull. Amer. Math. Soc. 29 (6): 271–274. doi:10.1090/S0002-9904-1923-03723-3.

Further reading

  • Grattan-Guinness, I. (2000). The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel. Princeton, N.J.: Princeton University Press. ISBN 0-691-05857-1.

External links

1947 in philosophy

1947 in philosophy

Archives of American Mathematics

The Archives of American Mathematics, located at the University of Texas at Austin, aims to collect, preserve, and provide access to the papers principally of American mathematicians and the records of American mathematical organizations.

Charles Sanders Peirce

Charles Sanders Peirce (, PURSS; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism". He was educated as a chemist and employed as a scientist for 30 years. Today he is appreciated largely for his contributions to logic, mathematics, philosophy, scientific methodology, and semiotics, and for his founding of pragmatism.

An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself, first and foremost, a logician. He made major contributions to logic, but logic for him encompassed much of that which is now called epistemology and philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder, which foreshadowed the debate among logical positivists and proponents of philosophy of language that dominated 20th-century Western philosophy; additionally, he defined the concept of abductive reasoning, as well as rigorously formulated mathematical induction and deductive reasoning. As early as 1886 he saw that logical operations could be carried out by electrical switching circuits; the same idea was used decades later to produce digital computers.In 1934, the philosopher Paul Weiss called Peirce "the most original and versatile of American philosophers and America's greatest logician." Webster's Biographical Dictionary said in 1943 that Peirce was "now regarded as the most original thinker and greatest logician of his time." Keith Devlin similarly referred to Peirce as one of the greatest philosophers ever.

Elizabeth Buchanan Cowley

Elizabeth Buchanan Cowley (1874–1945) was an American mathematician.

Emil Leon Post

Emil Leon Post (; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory.

Eric Temple Bell

Eric Temple Bell (February 7, 1883 – December 21, 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as John Taine.

List of American philosophers

This is a list of American philosophers; of philosophers who are either from, or spent many productive years of their lives in the United States.

List of International Congresses of Mathematicians Plenary and Invited Speakers

This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an ICM has been called "the equivalent, in this community, of an induction to a hall of fame." (The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers".

List of names in A Biographical Dictionary of Modern Rationalists

Joseph McCabe published A Biographical Dictionary of Modern Rationalists in 1920 (London: Watts & Co.). Most (though not all) of those listed were also included in A Biographical Dictionary of Ancient, Medieval and Modern Freethinkers (1945)

Ohio Northern University

Ohio Northern University is a private, United Methodist Church–affiliated university in Ada, Ohio. Founded by Henry Solomon Lehr in 1871, ONU is accredited by The Higher Learning Commission.

Rawson, Ohio

Rawson is a village in Hancock County, Ohio, United States. The population was 570 at the 2010 census.

Rawson was the birthplace of Cassius Jackson Keyser, an American mathematician.

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