Genius and Biographers: The Fictionalization of Evariste Galois
About: This article is published in American Mathematical Monthly.The article was published on 1982-02-01. It has received 38 citations till now. The article focuses on the topics: Genius.
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TL;DR: In the area of convergent thinking, knowledge is of particular importance: it is a source of ideas, suggests pathways to solutions, and provides criteria of effectiveness and novelty as discussed by the authors.
Abstract: Free production of variability through unfettered divergent thinking holds out the seductive promise of effortless creativity but runs the risk of generating only quasicreativity or pseudocreativity if it is not adapted to reality. Therefore, creative thinking seems to involve 2 components: generation of novelty (via divergent thinking) and evaluation of the novelty (via convergent thinking). In the area of convergent thinking, knowledge is of particular importance: It is a source of ideas, suggests pathways to solutions, and provides criteria of effectiveness and novelty. The way in which the 2 kinds of thinking work together can be understood in terms of thinking styles or of phases in the generation of creative products. In practical situations, divergent thinking without convergent thinking can cause a variety of problems including reckless change. Nonetheless, care must be exercised by those who sing the praises of convergent thinking: Both too little and too much is bad for creativity.
735 citations
Cites background from "Genius and Biographers: The Fiction..."
...In 1832, the French mathematician, Evariste Galois, now regarded as one of history’s most original mathematicians, was killed at the age of 20 in a duel so hopelessly uneven that he knew that he was doomed (see Rothman, 1982)....
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TL;DR: In this article, a social approach is proposed to distinguish between large and small amounts of novelty, as well as between “orthodox” and “radical” novelty.
Abstract: Early thinking in the modern era often regarded creativity as a somewhat asocial means of individual expression, self‐realization, and self‐fulfillment. However, it also is a socially influenced phenomenon that serves society. A social approach offers the opportunity of distinguishing between large and small amounts of novelty, as well as between “orthodox” and “radical” novelty. Disciplines, teachers, and students differ from one another on these dimensions. This explains some differences among teachers in the way they see creativity and creative students. The social approach also emphasizes the importance of groups, role models and mentors, and classroom climate, all of which teachers can influence. A social analysis suggests guidelines for instruction and assessment that differ from those derived from cognitive or personal approaches.
95 citations
TL;DR: In this article, the authors divide the process of creativity into seven phases that depend upon different cognitive processes (e.g. divergent versus convergent thinking) and personal properties, and map the four Ps of creativity (person, process, product and press) onto the phases.
Abstract: Many teachers are interested in fostering creativity, and there are good reasons for doing so. However, the question of how to do it is made difficult by the paradoxes of creativity: mutually contradictory findings that are, nonetheless, simultaneously true (e.g. convergent thinking hampers creativity but is also necessary for it). These paradoxes can be resolved by dividing the process of creativity into seven phases that depend upon different cognitive processes (e.g. divergent versus convergent thinking) and personal properties (e.g. openness versus compulsiveness), are facilitated by different environmental conditions (e.g. tolerance of errors versus demands for accuracy) and lead to different kinds of product (e.g. something radically new versus novelty that nonetheless fits into the conventional framework). Mapping the four Ps of creativity (person, process, product and press) onto the phases provides a system for analysing both teaching methods and learning activities of individual students.
76 citations
Cites background from "Genius and Biographers: The Fiction..."
...In 1832 the Frenchman was killed at the age of 20 in a duel so uneven that he knew that he was doomed (see Rothman, 1982, for a description of Galois’ life and death)....
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TL;DR: In this article, the authors argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz.
Abstract: Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.
74 citations
Book•
01 Jan 2009
TL;DR: In this paper, the authors draw on complementary views of creativity and innovation - as a business process and as a social-psychological model - to create a more detailed and more highly differentiated model which is capable of serving as a practical foundation for diagnosing, analyzing, optimizing and fostering creativity in a variety of organizational settings.
Abstract: Innovation is universally recognized as key components of first world economies that is vital for continued prosperity. Innovation is driven by the generation of effective novelty - in other words, creativity. However, both in higher education and also in business and industry, insufficient effort is being made to encourage and develop creativity, with negative consequences for innovation. This is partly due to inadequate understanding of what creativity is and how it can be fostered. This book draws on complementary views of creativity and innovation - as a business process and as a social-psychological model - to create a more detailed and more highly differentiated model which is capable of serving as a practical foundation for diagnosing, analyzing, optimizing and fostering creativity and innovation in a variety of organizational settings. It is built around a large number of case studies and down-to-earth examples, and offers many concrete suggestions for fostering what the authors call 'functional' creativity.
72 citations
Cites background from "Genius and Biographers: The Fiction..."
...It is tempting to think of exploration as essentially a process of evaluation, and Runco (2003) supported this view....
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