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discovery of number systems
Leibniz together with other researchers discover the complex numbers. -
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vector systems
At the time some early period vector systems were discussed, tested, and in some cases extended. Scientists recognized the need for a vector method and specifying its characteristics within a vector system. -
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application of vector systems
Scientists realized that many problems could be handled by considering the vector part separately, and so Vector Analysis began. This work is mainly due to the American physicist Josiah Willar Gibbs -
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vector analysis
Tait developed quaternion analysis as a tool for research in the physical sciences, and created many new theorems in quaternion analysis that could be translated into modern vector analysis. -
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century xix
geometry is criticized as a rigorous model; its place is taken by arithmetic. In this way, an "arithmetization" of mathematics is produced. -
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need to invigorate
it makes mathematics stop being, in part, an idealization of nature; and come to be considered as a creation of the human being -
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calculus demonstrations
The proofs were a mixture of formal proofs with geometric and physical considerations about the problems. Thus, the demonstrations of many results were not found anywhere and the statements were mere generalizations of concrete experiences. The rigor was based on the experimental verification a posteriori of the results obtained.