By Nathalie Sinclair, William Higginson

The essays during this ebook discover the traditional affinity among the mathematical and the cultured, targeting the elemental connections among those modes of reasoning and speaking. From ancient, philosophical and mental views, with specific awareness to yes mathematical components corresponding to geometry and research, the authors research the ways that the cultured is ever found in mathematical pondering and contributes to the expansion and cost of mathematical knowledge.

This ebook contains the next essays:

• A old stare upon the Mathematical Aesthetic, by means of Nathalie Sinclair and David Pimm

• Aesthetics for the operating Mathematician, by means of Jonathan M. Borwein

• good looks and fact in arithmetic, by means of Doris Schattschneider

• Experiencing Meanings in Geometry, by means of David W. Henderson and Daina Taimina

• the cultured Sensibilities of Mathematicians, through Nathalie Sinclair

• The that means of development, through Martin Schiralli

• arithmetic, Aesthetics and Being Human, through William Higginson

• Mechanism and Magic within the Psychology of Dynamic Geometry, by means of R. Nicholas Jackiw

• Drawing at the picture in arithmetic and paintings, by means of David Pimm

• good gadgets, by means of Dick Tahta

• Aesthetics and the ‘Mathematical Mind’, through David Pimm and Nathalie Sinclair

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**Example text**

What was done to the public Library I shall elsewhere shew: as for those belonging to Colleges, they suffered the same fate almost as the public, though not in so gross a manner. From Merton Coll. Library a cart load of MSS and above were taken away, such that contained the Lucubrations (chiefly of controversial Divinity, Astronomy and Mathematicks) of divers of the learned Fellows thereof, in which Studies they in the two last centuries obtained great renown. (in Gutch, 1796, pp. 106-107) [2] This twentieth-century return to the question of the psychology of the mathematician connects for us with thirteenth-century Henry of Ghent’s potent phrase ‘the melancholy disposition of the mathematical mind’.

What is ‘easy’ is changing and I see an exciting merging of disciplines, levels and collaborators. Mathematicians are more and more able to: • marry theory and practice, history and philosophy, proofs and experiments; • match elegance and balance with utility and economy; • inform all mathematical modalities computationally – analytic, algebraic, geometric and topological. This is leading us towards what I term an experimental mathodology as a philosophy and a practice (Borwein and Corless, 1999).

Fear of mathematics certainly does not hasten an aesthetic response. Gauss, Hadamard and Hardy Three of my personal mathematical heroes, very different individuals from different times, all testify interestingly on the aesthetic and the nature of mathematics. Gauss Carl Friedrich Gauss is claimed to have once confessed, “I have had my results for a long time, but I do not yet know how I am to arrive at them” (in Arber, 1954, p. 47). [1] One of Gauss’s greatest discoveries, in 1799, was the relationship between the lemniscate sine function and the arithmetic–geometric mean iteration.