Journal ArticleDOI
Mathematical Intuition Vs. Mathematical Monsters
TLDR
This work examines several famous geometrical, topological and set-theoretical examples of "monsters" to see to what extent intuition is undermined in its everyday roles.Abstract:
Geometrical and physical intuition, both untutored andcultivated, is ubiquitous in the research, teaching,and development of mathematics. A number ofmathematical ``monsters'', or pathological objects, havebeen produced which – according to somemathematicians – seriously challenge the reliability ofintuition. We examine several famous geometrical,topological and set-theoretical examples of suchmonsters in order to see to what extent, if at all,intuition is undermined in its everyday roles.read more
Citations
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Journal ArticleDOI
Modelling mathematical argumentation: the importance of qualification
TL;DR: The authors report data from task-based interviews conducted with highly talented postgraduate mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use of Toulmin's full argumentation scheme.
Journal ArticleDOI
What Is a Random Sequence
TL;DR: The author examines the role of randomness in the construction of sequences in theorems, and concludes that sequences can be constructed in a number of ways that are random in nature.
Journal ArticleDOI
Mathematics in Philosophy, Selected Essays.
Stewart Shapiro,Charles Parsons +1 more
Book ChapterDOI
On Formal and Informal Provability
TL;DR: In this paper, a philosophical study of mathematical proof and provability is presented, both conceptually and extensionally, with the main focus on informal provability, and the main method of doing so being to demarcate informal provablity from formal provability by formal means.
Book ChapterDOI
Why Does Theoretical Physics Fail to Explain and Predict Earthquake Occurrence
TL;DR: The intrinsic randomness of earthquake occurrence, necessitating the use of stochastic point processes and appropriate complex statistical techniques, has been studied in this article, and the quality of current earthquake data statistical analysis is low, since little or no study of random and systematic errors is performed.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Book
Proofs and Refutations
Margarita R. Levin,Imre Lakatos +1 more
TL;DR: In this article, the authors present a problem and a conjecture, and a proof of the problem and the conjecture, as well as a proof against the conjecture by lemma-incorp oration.
Journal ArticleDOI
The Mathematical Experience.
TL;DR: This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about and will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.