The most difficult equation in mathematics

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The discussion centers around identifying one of the most difficult equations in mathematics, with a focus on the equation 2^{\aleph_0}=\aleph_k and its implications in set theory. Participants debate the difficulty of finding k for a given m in the context of the continuum hypothesis, which is undecidable within standard axioms of set theory. The conversation also touches on the generalization of equations and the challenges posed by various mathematical problems, including those listed in Hilbert's problems and the Clay Millennium Prize Problems. There is a consensus that measuring difficulty in mathematics is subjective and varies based on context and the mathematician's perspective. Ultimately, the complexity of these equations and problems highlights the intricate nature of mathematical inquiry.
  • #61
Here's one that I think is hard:

math = ?
 
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  • #62
math = math
 
  • #63
Not necessarily equation, but counting problems are always terribly hard. Here's one that's really difficult: How many DISTINCT valid (within the rules of the game) endings of a standard 9x9 Sudoku game are there?
 

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