Undergrad Here There be Dragons in Sympletic Geometry

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The discussion highlights an article addressing foundational issues in symplectic geometry, emphasizing its unstable basis and ongoing efforts for improvement. It draws parallels between these mathematical challenges and foundational problems in other scientific fields such as physics, psychology, and economics. The conversation underscores the notion that mathematics, often perceived as objective, is influenced by human factors and subjective interpretations. This reflects a broader theme of how foundational issues can affect various disciplines. The insights shared illustrate the complexity and interconnectedness of mathematical foundations with human endeavors.
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Fascinating piece on the foundations of symplectic geometry. It reminds me a lot of foundational issues in other areas of science - physics, psychology and economics to name a few.

Despite all the purported intrinsic objectivity of what is deemed to be part of the subject matter of mathematics (whatever that may be), this just goes to show how much mathematics actually is like any other human endeavour.
 
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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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