Awakening the Mathematical Brain

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The dorsolareral prefrontal cortex is activated in expert mathematician's brains when intepreting mathematical statments.

 

This brain region is associated with, but not exclusively responsible for, executive functions, including working memory, cognitive flexibility planning, inhibition, and abstract reasoning.

Cover walks on a grid

James Tanton discusses with Sunil Singh, in the video interview below, the problem he thought about as a young child, that led – years later – to an epiphany and to a deeper understanding of mathematical thinking:

The thought that led James to a solution – a reason why some squares in a 5\times 5 grid cannot be the origin of a walk through adjacent squares that reaches each square exactly once – came from coloring squares alternately one of two colors:

In the grid colored as shown, there are 13 blue squares and 12 yellow squares. Now a moment’s thought will reveal that starting from a yellow square there is no walk through adjacent squares – which, as you can see, flips alternately between the two colors –  that reaches each square exactly once.

BY BY BY BY BY BY BY BY BY BY BY BY B  (doesn’t rule out such a walk)

YB YB YB YB YB YB YB YB YB YB YB YB Y (proves there’s no such walk)

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