Morris Kline: Mathematician, Historian, and Critic of Mathematics Education
Morris Kline was a multifaceted mathematician whose career spanned academic instruction, wartime engineering, and a passionate crusade to reform how mathematics is taught and researched. While originally trained in topology—the study of the properties of geometric shapes that remain unchanged under continuous deformation—Kline shifted his focus toward applied mathematics. This transition was sparked by Richard Courant, who convinced him that the most significant contribution a mathematician could make to society was to foster a deeper understanding of the physical world.
Influenced by the works of Leonhard Euler and the writings of Hermann Weyl, Kline dedicated his life to bridging the gap between abstract mathematical theory and its practical utility.
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Professional Career and Military Service
Kline's early professional years included a tenure as an instructor at New York University (NYU) until 1942. However, the onset of World War II redirected his expertise toward national defense. He was posted to the Signal Corps of the United States Army in Belmar, New Jersey, where he served as a physicist in an engineering lab focused on the development of radar.
Following the war, Kline's interest in electromagnetism persisted. From 1946 to 1966, he served as the director of the Division of Electromagnetic Research at the Courant Institute of Mathematical Sciences. He eventually returned to full-time teaching at NYU, achieving the rank of full professor in 1952 and remaining there until 1975. Throughout his academic career, he authored more than a dozen books and numerous papers, including a calculus textbook published in 1967.
Key Facts
- Academic Shift: Moved from topology to differential equations and applied mathematics.
- Wartime Contribution: Worked on radar development for the U.S. Army Signal Corps.
- Leadership: Directed the Division of Electromagnetic Research at the Courant Institute (1946–1966).
- Educational Philosophy: Advocated for intuition and concrete application over premature rigor and abstraction.
- Major Works: Authored Why Johnny Can't Add and Mathematical Thought from Ancient to Modern Times.
Critique of Mathematics Education
Kline was a vocal critic of the New Math movement, a mid-century effort to reform mathematics education. He argued that the movement failed because it prioritized abstract jargon and rigor over student intuition. In his 1973 book, Why Johnny Can't Add: the Failure of the New Math, Kline asserted that abstraction should be the final stage of mathematical development, not the first.
He believed that students should first understand the concrete applications and usefulness of mathematics before being introduced to formal rigor. He criticized textbook authors for their lack of understanding regarding pedagogy—the method and practice of teaching—and educational psychology.
The Dilemma of University Education
In 1977, Kline expanded his critique to higher education in Why the Professor Can't Teach: The Dilemma of University Education. He argued that the intense pressure on U.S. professors to conduct original research detracted from the quality of teaching. He championed expository writing—the act of explaining complex ideas clearly—as a vital form of scholarship. While some critics dismissed his views, many instructors praised him for highlighting the conflict between research demands and educational excellence.
Contributions to the History of Mathematics
In 1972, Kline published Mathematical Thought from Ancient to Modern Times, a comprehensive survey covering mathematics from ancient Babylon, Egypt, and Greece through the early twentieth century. The work was noted for its extensive use of primary sources.
| Reviewer | Praised Aspects | Criticisms/Observations |
|---|---|---|
| Gian-Carlo Rota | Balance of depth and accessibility; Euclidean geometry. | Dated handling of functional analysis. |
| Ivor Grattan-Guinness | Post-1800 developments; sociology of mathematics. | Errors in complex variables and linear algebra; omitted statistics. |
| Carl Benjamin Boyer | Non-Euclidean geometry; Navier–Stokes equations. | N/A |
| Lester Paldy | Application of math to physical phenomena. | N/A |
Views on Mathematical Research
Kline believed that mathematical research should be driven by the needs of other fields, such as computer science and physics. In his work Mathematics: The Loss of Certainty, he lamented the "isolation of mathematics," arguing that many researchers preferred to create pure mathematics with no practical consequence rather than engaging with the deep contexts of applied problems.
He attributed this trend to the "publish or perish" culture of academia, which he felt encouraged the production of abstract work over useful discovery. His perspective was described by William Barrett of The New York Times as a readable account of the decline of the field due to conflicting schools of thought.
Frequently Asked Questions
What was Morris Kline's primary objection to the New Math movement?
Kline argued that New Math focused too heavily on abstraction and jargon at the introductory level, ignoring the necessity of building intuition and understanding concrete applications before introducing formal rigor.
How did World War II influence Kline's career?
During the war, Kline served as a physicist for the U.S. Army Signal Corps, where he worked on radar development. This experience reinforced his commitment to applied mathematics and electromagnetism.
What did Kline believe was the main problem with university professors?
He argued that the institutional pressure to conduct original research misdirected professors, leading them to neglect the art of teaching and the value of expository scholarship.
Which mathematical topics did Kline excel in according to historians?
Reviewers generally agreed that Kline was at his strongest when discussing Euclidean geometry, calculus, and the historical application of mathematics to physical phenomena.
What was Kline's view on the purpose of mathematical research?
Kline believed the greatest contribution mathematicians could make was to help humanity understand the world, urging research to focus on solving problems posed by other scientific fields.