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Friday, March 17, 2006

Selling mathematicial concepts

On page 1 of Introduction to Coalgebra: Towards Mathematics of States and Observations, Bart Jacobs writes: This chapter is devoted to “selling” and “promoting” coalgebras. Do the scare quotes suggest a certain unease that commercial terms are needed to talk about this kind of activity? Employing humour, Miles Reid has a section entitled 'Commercial break' in his textbook Undergraduate Algebraic Geometry (CUP) where he tells us:
Complex curves (= compact Riemann surfaces) appear across a whole spectrum of math problems, from Diophantine arithmetic through complex functions theory and low dimensional topology to differential equations of math physics. So go out and buy a complex curve today. (p. 45)

As readers will have gathered, I'm all for mathematicians promoting their ideas, concepts, and theories. In chapter 9 of my book I discuss the range of ways in which mathematical concepts are viewed, from useless, through mildly and very useful, right up to essential. Promoting a concept is about trying to shift its rank upwards so that it receives its due.


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