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Transcendental Curves in the Leibnizian Calculus (Paperback)
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Transcendental Curves in the Leibnizian Calculus (Paperback)
Series: Studies in the History of Mathematical Inquiry
Expected to ship within 12 - 19 working days
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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.
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