Transcendental Curves in the Leibnizian Calculus
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Book Overview Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern ma...
Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass.
As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis.
Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it.
Book Details Format: Paperback | Pages: 282 | Language: English | Publisher: ACADEMIC PR INC | ISBN: 012813237X
FormatPaperback
Pages282
LanguageEnglish
ISBN012813237X
EAN9780128132371
PublisherACADEMIC PR INC
Publication Date1970-01-01
Edition1
AccessoriesNo Accessory
ConditionNew
Product TypeQUALITY PAPERBACK BOOKS
Weight1.08 Pounds
Length9.25 Inches
Width7.5 Inches
Height0.6 Inches
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