Titlebook: Handbook of the History and Philosophy of Mathematical Practice; Bharath Sriraman Living reference work 20200th edition Origins.Natural H

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The Notion of Space in Grothendieck,in algebraic geometry, where he introduces schemes and toposes as generalizations of classical notions of spaces, passing through tame topology and ending with the formulation of a geometry of forms, we show how the ideas of Grothendieck evolved from pure mathematical considerations to physical and

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The Ghost and the Spirit of Pythagoras,time. Arguably, the greatest discovery of Pythagorean mathematics of (sixth-fifth century BC) was that of the incommensurability of the side and the diagonal of the square. This discovery established the complex relationships between geometry and arithmetic and, correlatively, the possibility of a t

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The Ethics of Mathematical Practice,rceived as irrelevant. Many mathematicians and others resist the idea that we need to consider the ethics of both pure and applied mathematics. The foundations of this resistance are analyzed and located in background philosophies and ideologies of purism and neutrality. The range of social practice

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Argumentation in Mathematical Practice,derstanding of mathematical practice, it is not sufficient. Important aspects of mathematical reasoning closely resemble patterns of reasoning in nonmathematical domains. Hence the tools developed to understand informal reasoning, collectively known as argumentation theory, are also applicable to mu

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,Proofs, Arbitrary Exemplifications, and Inductive Generalizations in Euler’s Mathematical Practice, findings, procedures, and theorems; instead, in Euler’s writings, they could also have two other different functions. Firstly, he used examples as a proof for a general statement, namely, he considered a proposition as proved if verified for some examples. Euler felt the need of general and rigorou

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Algebraic Versus Geometric Thought and Expression in the Early Calculus,ay. For instance, functions such as sin(.) and log(.) were largely absent from the early calculus, with geometric paraphrases used in their place. From a modern standpoint, one may be inclined to assume that the eventual triumph of the more analytic perspective was a straightforward case of progress

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,Descartes’ Transformation of Greek Notion of Proportionality,ir ratios, and proportions. Viewed from the modern perspective, the theory of proportions is a technique of processing ratios. In early modern mathematics, it was replaced by implicit rules of an ordered field, then, in the nineteenth century, by the arithmetic of real numbers. We formalize Euclid’s

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