By Nathalie Sinclair, William Higginson

This choice of essays explores the traditional affinity among the mathematical and the classy, concentrating on basic connections among those modes of reasoning and speaking. From old, philosophical and mental views, with specific realization to sure mathematical components akin to geometry and research, the authors study ways that the cultured is ever-present in mathematical pondering and contributes to the expansion and price of mathematical wisdom.

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Elegance’, in particular, seems to have been coopted by mathematicians in their rather restricted aesthetic language, as conveying a sense of both succinctness and sophistication. In ordinary parlance, ‘elegance’ might be seen as a classical, class-ridden term – not so much socio-economic ‘class’ perhaps as intellectual ‘class’ (though Bertrand Russell, for example, certainly partook of both). Of course, there must be a sociological proviso here – it was only very few (privileged) Greeks, and then for a long time a very few (privileged) other individuals, who could sit and think as opposed to practice or teach.

The cognitive unconscious. Most thought is unconscious – not repressed in the Freudian sense, but simply inaccessible to direct conscious introspection. We cannot look directly at our conceptual systems and at our low-level thought processes. This includes most mathematical thought. 3. Metaphorical thought. For the most part, human beings conceptualise abstract concepts in concrete terms, using ideas and modes of reasoning grounded in sensori-motor systems. The mechanism by which the abstract is comprehended in terms of the concept is called conceptual metaphor.

Dase used his calculating ability to calculate π to 200 places in 1844. This was published in Crelle’s Journal for 1844. Dase also constructed 7 figure log tables and produced a table of factors of all numbers between 7 000 000 and 10 000 000. 34 Mathematics and the Aesthetic Gauss requested that the Hamburg Academy of Sciences allow Dase to devote himself full-time to his mathematical work but, although they agreed to this, Dase died before he was able to do much more work. Pentium farming I finish this sub-section with another result obtained through integer relations methods or, as I like to call it, ‘Pentium farming’.