Carl B. Boyer
Carl B. Boyer: A Pioneer in the History of Science
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Full Name and Common Aliases
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Carl Benjamin Boyer was a renowned American historian of science, born on November 3, 1906.
Birth and Death Dates
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Born: November 3, 1906
Died: February 26, 1973
Nationality and Profession(s)
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American, Historian, Mathematician, and Science Writer
Carl Boyer was a leading authority on the history of mathematics and science. He is widely recognized for his contributions to the field of science historiography.
Early Life and Background
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Boyer's passion for mathematics and science began at an early age. He studied mathematics at Columbia University, where he earned his undergraduate degree in 1928. Later, he went on to earn his Ph.D. in mathematics from Columbia University in 1932. His interest in the history of science developed during his graduate studies.
Major Accomplishments
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Boyer's most significant contributions include:
Writing The History of the Calculus (1949), a comprehensive and influential book on the development of calculus.
Publishing A History of Mathematics (1968), an authoritative and accessible account of the history of mathematics.
Serving as the president of the American Association for the Advancement of Science in 1955.
Contributing to various scientific journals, including Scientific American, where he wrote numerous articles on science and its history.
Notable Works or Actions
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Some of Boyer's notable works include:
The History of the Calculus, which won the National Book Award in 1949.
A History of Mathematics, which has been widely praised for its clear and engaging writing style.
His numerous articles and reviews published in scientific journals, demonstrating his expertise in science historiography.Impact and Legacy
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Boyer's work had a profound impact on the field of science historiography. He:
Laid the foundation for modern science history by highlighting the importance of understanding the historical context of scientific developments.
Demonstrated the relevance and interest of mathematical and scientific ideas to a broad audience through his accessible writing style.
Inspired future generations of historians, mathematicians, and scientists with his innovative approach to storytelling.
Why They Are Widely Quoted or Remembered
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Carl Boyer's influence can be seen in various areas:
His emphasis on the importance of historical context has influenced the way historians approach scientific developments.
His writing style has inspired many science writers and communicators to make complex ideas accessible to a broad audience.
* His contributions to science historiography continue to shape our understanding of mathematical and scientific discoveries.
Throughout his career, Carl Boyer demonstrated a unique ability to bridge the gap between academia and the general public. His commitment to sharing the history of mathematics and science with a wider audience has left an enduring legacy in the world of science communication.
Quotes by Carl B. Boyer
Carl B. Boyer's insights on:
Definitions of number, as given by several later mathematicians, make the limit of an infinite sequence identical with the sequence itself. Under this view, the question as to whether the variable reaches its limit is without logical meaning. Thus the infinite sequence .9, .99, .999,... is the number one, and the question, “Does it ever reach one?” is an attempt to give a metaphysical argument which shall satisfy intuition.
Berkeley was unable to appreciate that mathematics was not concerned with a world of “real” sense impressions. In much the same manner today some philosophers criticize the mathematical conceptions of infinity and continuum, failing to realize that since mathematics deals with relations rather than with physical existence, its criterion of truth is inner consistency rather than plausibility in the light of sense perception of intuition.
Now we can see what makes mathematics unique. Only in mathematics is there no significant correction – only extension. Once the Greeks had developed the deductive method, they were correct in what they did, correct for all time. Euclid was incomplete and his work has been extended enormously, but it has not had to be corrected. His theorems are, every one of them, valid to this day.
A quantity is something or nothing: if it is something, it has not yet vanished; if it is nothing, it has literally vanished. The supposition that there is an intermediate state between these two is a chimera.D'Alembert
The Greek thinkers was no way of bridging the gap between the rectilinear and the curvilinear which would at the same time satisfy their strict demands of mathematical rigor and appeal to the clear evidence of sensory experience.
Carnot, one of a school of mathematicians who emphasized the relationship of mathematics to scientific practice, appears, in spite of the title of his work, to have been more concerned about the facility of application of the rules of procedure than about the logical reasoning involved.
Most of his predecessors had considered the differential calculus as bound up with geometry, but Euler made the subject a formal theory of functions which had no need to revert to diagrams or geometrical conceptions.
These results were obtained by making up tables in which were listed the volumes for given sets of values of the dimensions, and from these selecting the best proportions.
Recognizing that geometry is entirely intellectual and independent of the actual description and existence of figures, Fontenelle did not discuss the subject fro the point of view of science or metaphysics as had Aristotle and Leibnez.
Leibniz in this respect had perhaps even less caution than many of his contemporaries, for he seriously considered whether the infinite series 1 -1+1-1+... was equal to 1/2.