Mathematics: The Loss of Certainty
|Publisher||Oxford University Press|
|Followed by||Mathematics and the Search for Knowledge|
This book traces the history of how new results in mathematics have provided surprises to mathematicians through the ages. Examples include how 19th century mathematicians were surprised by the discovery of non-Euclidean geometry and how Godel's incompleteness theorem disappointed many logicians.
Kline furthermore discusses the close relation of some of the most prominent mathematicians such as Newton and Leibniz to God. He believes that Newton's religious interests were the true motivation of his mathematical and scientific work. He quotes Newton from a letter to Reverend Richard Bentley of December 10, 1692:
When I wrote my treatise about our system The Mathematical Principles of Natural Philosophy, I had an eye on such principles as might work with considering men for the belief in a Deity; and nothing can rejoice me more than to find it useful for that purpose.
He also believes Leibniz regarded science as a religious mission which scientists were duty bound to undertake. Kline quotes Leibniz from an undated letter of 1699 or 1700:
It seems to me that the principal goal of the whole of mankind must be the knowledge and development of the wonders of God, and that this is the reason that God gave him the empire of the globe.
Kline also argues that the attempt to establish a universally acceptable, logically sound body of mathematics has failed. He believes that most mathematicians today do not work on applications. Instead they continue to produce new results in pure mathematics at an ever-increasing pace.
- "Review of Mathematics: The Loss of Certainty". The Wilson Quarterly (1976-). 5 (2): 160–161. 1981-01-01. JSTOR 40256113.
- Weinstein, Scott (1981-01-01). Kline, Morris; Kleine, eds. "THE LOSS OF CERTAINTY". ETC: A Review of General Semantics. 38 (4): 425–430. JSTOR 42575575.
- Long, Calvin T. (1981-01-01). "Review of MATHEMATICS: The Loss of Certainty (L)". The Mathematics Teacher. 74 (3): 234–235. JSTOR 27962408.
- Boas, R. P. (1981-01-01). Kline, Morris, ed. "Nevertheless, Let's Get on with the Job". The Two-Year College Mathematics Journal. 12 (2): 141–142. JSTOR 3027376. doi:10.2307/3027376.
- Guberman, J. (1983-01-01). "Review of Mathematics: The Loss of Certainty". Leonardo. 16 (4): 328–328. JSTOR 1574971. doi:10.2307/1574971.
- Stewart, Ian (1982-01-01). "Review of Mathematics, The Loss of Certainty". Educational Studies in Mathematics. 13 (4): 446–447. JSTOR 3482328.
- Dahan-Dalmédico, Amy (1983-01-01). "Review of Mathematics, The Loss of Certainty". Revue d'histoire des sciences. 36 (3/4): 356–358. JSTOR 23632221.
- Quadling, Douglas (1981-01-01). "Review of Mathematics: The Loss of Certainty". The Mathematical Gazette. 65 (434): 300–301. JSTOR 3616614. doi:10.2307/3616614.
- Robles, J. A. (1981-01-01). "Review of Mathematics, the Loss of Certainty". Crítica: Revista Hispanoamericana de Filosofía. 13 (39): 87–91. JSTOR 40104258.
- Ayoub, Raymond G. (1982-01-01). "Review of Mathematics: The Loss of Certainty". The American Mathematical Monthly. 89 (9): 715–717. JSTOR 2975679. doi:10.2307/2975679.
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