Nov 26, 2012

THE SECOND CRISIS IN THE FOUNDATION OF MATHEMATICS_Documented by Marsigit



THE CRISIS IN THE FOUNDATION OF MATHEMATICS
[Crisis #2]
After the Invention of
 Calculus by Newton and Leibniz

Newton dealt with the analysis of motion; he viewed curves as the locus of motion of a point and believed that notions of motion and flow must be used when analyzing continua. He called his discovery the method of fluxions. Curve was a mapping between abscissa and ordinates. Variables were called "fluents"; rates of change were called "fluxions." The moment of a fluent was the delta of a variable.

Leibniz's notation:. dy and dx are both very small that they are insignificant, however, their ratio is a number; thus ratios were stressed, not the individual components.

Impact of Newton and Leibniz was due to systematicity and applicability-- not at all a conceptual improvement. There was no longer confusion, math had a new science: infinitesimal analysis; it was so powerful that the face of mathematics was changed forever. It was called the Second Great Crisis because: math is proceeding on the basis of conceptually unclear notions; Physics was being based on these questionable ideas. These problems brought serious attacks against mathematics.

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