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The Mathematical Mind

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Ahmes’ Legacy

Part of the book series: Mathematics in Mind ((MATHMIN))

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Abstract

As argued throughout this book, puzzles have played as much a role as any other human artifact, mental tool, or device in human history as sparks for discovery. The Ahmes Papyrus is more than a source of ancient mathematics. It is the first text to show, rather conspicuously, that puzzles and mathematics have a common origin. As mentioned, each puzzle in the work is both a creative (dialectic) conundrum and a mini-treatise in mathematical thinking. This has been called “Ahmes’ legacy” in this book, which claims above all else that puzzles are mirrors of the inner workings of the mathematical mind. The classic puzzles of Ahmes, Alcuin, Fibonacci, Euler, Cardano, Lucas, Carroll, and many others are miniature models of that mind, showing how the flow of thought goes from experience, to imaginative hunches, and then on to a solution. Once the mathematical archetype is extracted from the solution via generalization, the puzzle becomes a kind of intellectual meme that makes its way into other mathematical minds to suggest new ways of doing mathematics. Mathematical cognition can thus be characterized as a blended form of imaginative-reflective thinking (Poe’s bi-part soul) that is sparked by the imagination’s interpretation of experiences via their serendipitous connectivity. This view is consistent with the neuroscientific work being conducted in so-called blending theory today (Fauconnier and Turner 2002, Danesi 2016), whereby the brain is seen as an organ that connects imaginative thoughts with each other in order to produce a new unit of thought. In effect, the meaning of something is not in its individual parts, but in the way they are connected or combined.

I know that two and two make four and should be glad to prove it too if I could—though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure.

—Lord Byron (1788–1824)

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  1. Department of Anthropology, University of Toronto, Toronto, ON, Canada

    Marcel Danesi

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Danesi, M. (2018). The Mathematical Mind. In: Ahmes’ Legacy. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-319-93254-5_5

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