Journal ArticleDOI
A one-sentence proof that every prime p Ξ1(mod 4) is a sum of two squares
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A one-sentence proof that every prime p ≡ 1 (mod 4) is a Sum of Two Squares is given in this paper, where every prime is a sum of two squares.Abstract:
(1990). A One-Sentence Proof That Every Prime p ≡ 1 (mod 4) Is a Sum of Two Squares. The American Mathematical Monthly: Vol. 97, No. 2, pp. 144-144.read more
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Partition bijections, a survey
TL;DR: In this article, an extensive survey of bijective proofs of classical partitions identities is presented, and various extensions and generalizations are added in the form of exercises; see Section 2.
Book
Numbers and Functions: From a Classical-Experimental Mathematician's Point of View
TL;DR: This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics, on exploring the connections between these functions and topics in number theory and combinatorics.
Journal ArticleDOI
Mathematical Method and Proof
TL;DR: It is argued that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations.
Posted Content
Some Fundamental Theorems in Mathematics
Abstract: An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 135 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [5] without leading to panic. The order is not a ranking but more like a time-line when things were written down. Since [280] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context” we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The number of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable” theorems with proofs included. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [110, 106, 20, 137, 312, 215, 78], for history [124, 316, 193, 40, 30, 116, 195, 188, 347, 63, 311, 43, 140, 174], for popular, beautiful or elegant things [8, 267, 113, 101, 13, 338, 339, 28, 107, 133, 229, 309, 113, 1, 70, 85, 71, 255]. For comprehensive overviews in large parts of mathematics, [41, 93, 94, 32, 297] or predictions on developments [31]. For reflections about mathematics in general [84, 233, 29, 163, 227, 56, 284]. Encyclopedic source examples are [105, 352, 336, 57, 109, 88, 126, 108, 61, 319].
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