Conjecture Connecting All Branches of Math

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The discussion centers on an optimistic conjecture that proposes a connection between all branches of mathematics, initially inspired by the Taniyama-Shimura conjecture, which links topology and number theory. The conversation references Singh's book on Fermat's Last Theorem as a source of this conjecture. Participants explore other instances of interconnected mathematical fields, specifically mentioning Perelman's proof of the Poincaré conjecture and its relationship to differential equations and algebraic topology. The Langlands program is also highlighted as a significant example of such connections. Overall, the thread emphasizes the idea of unity across diverse mathematical disciplines.
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I'm looking for the name of the optimistic conjecture that, if I remember correctly, conjectures the existence of a certain kind of connection between every branch of mathematics.

I read about it in Singh's book on Fermat's last theorem. Fueled by the enthusiasm following the discovery of a proof of the Taniyama-Shimura conjecture connecting topology and number theory, this conjecture was made.
 
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What are other instance where two seemingly disconnected branches of mathematics intertwine as in the Taniyama-Shimura conjecture?

Can Perelman's proof of the Poincaré conjecture be said to connect differential equations to algebraic topology in this way?
 
probably, thx
 
yes langlands.
 

Thread 'Area of Overlapping Squares'

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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