Zitate von Morris Kline

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Morris Kline

Geburtstag: 1. Mai 1908
Todesdatum: 10. Juni 1992

Morris Kline war ein US-amerikanischer Mathematiker, der sich mit Geschichte, Philosophie und Didaktik der Mathematik beschäftigte.

Kline war Sohn eines Buchhalters, wuchs in Brooklyn und Queens in New York City auf und studierte an der New York University , wo er 1936 promoviert wurde. Danach war er von 1938 bis 1975 Assistent und später Professor an der New York University, von einer Zeit im Zweiten Weltkrieg als Zivilangestellter der US-Armee abgesehen.

Kline ist durch eine Vielzahl von Büchern bekannt, in denen er die Mathematik popularisierte. In didaktischen Fragen unterstrich er, stets die Verbindungen zu Anwendungen herzustellen, in der Grundschule mit mathematischen Rätseln und Anwendungen im Sport, in der High School mit Wahrscheinlichkeit und Statistik und auf dem College mit Physik und Computern. In seinem Buch Why Johnny can't Add von 1973 kritisierte er die in den 1960er Jahren aufgekommene „Neue Mathematik“, deren Denken von Bourbaki beeinflusst war. In Why the Professor can't teach beklagt er das didaktische Defizit vieler Professoren, die vor allem unter dem Druck stehen, Forschungsarbeiten zu veröffentlichen. Sein Hauptwerk ist seine umfangreiche und detaillierte Mathematikgeschichte Mathematical Thought from Ancient to Modern Times von 1972. Kulturellen Strömungen in der Mathematik ging er in Mathematics – the loss of certainty von 1980 nach.

Er war seit 1939 verheiratet und hatte zwei Töchter. Wikipedia

Zitate Morris Kline

„The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. …Simplicius“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Kontext: The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine.... Simplicius cites others who worked on the problem and says further that people "in ancient times" objected to the use of the parallel postulate.

„To avoid any assertion about the infinitude of the straight line, Euclid says a line segment“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 175
Kontext: To avoid any assertion about the infinitude of the straight line, Euclid says a line segment (he uses the word "line" in this sense) can be extended as far as necessary. Unwillingness to involve the infinitely large is seen also in Euclid's statement of the parallel axiom. Instead of considering two lines that extend to infinity and giving a direct condition or assumption under which parallel lines might exist, his parallel axiom gives a condition under which two lines will meet at some finite point.

„For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Kontext: Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length—for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.

„He had doubted the correctness of the law of refraction of light but when he found in 1661 that he could deduce it from his Principle, he not only resolved his doubts about the law but felt all the more certain that his Principle was correct.“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 580
Kontext: Fermat knew that under reflection light takes the path requiring least time and, convinced that nature does indeed act simply and economically, affirmed in letters of 1657 and 1662 his Principle of Least Time, which states that light always takes the path requiring least time. He had doubted the correctness of the law of refraction of light but when he found in 1661 that he could deduce it from his Principle, he not only resolved his doubts about the law but felt all the more certain that his Principle was correct.... Huygens, who had at first objected to Fermat's Principle, showed that it does hold for the propagation of light in media with variable indices of refraction. Even Newton's first law of motion, which states that the straight line or shortest distance is the natural motion of a body, showed nature's desire to economize. These examples suggested that there might be a more general principle. The search for such a principle was undertaken by Maupertuis.

„The relationship of point to line“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 176
Kontext: The relationship of point to line bothered the Greeks and led Aristotle to separate the two. Though he admits points are on lines, he says that a line is not made up of points and that the continuous cannot be made up of the discrete. This distinction contributed also to the presumed need for separating number from geometry, since to the Greeks numbers were discrete and geometry dealt with continuous magnitudes.

„The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes.“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 57
Kontext: The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces."

„The method has the form of the now-standard method of differential calculus, though it begs entirely the difficult theory of limits.“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 346
Kontext: Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard method of differential calculus, though it begs entirely the difficult theory of limits.

„Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes“

—  Morris Kline

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Kontext: Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length—for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.

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