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I am interested in the Hierarchy and Connections between various different open problems in Mathematics, and the most general conjectures in various fields of Mathematics.

Examples of Hierachy

Solved

Unsolved

Examples of Big-Daddy-Conjectures

Questions

  1. Are there complete lists of the dependencies between different conjectures in mathematics available?
  2. What are the most general Conjectures in various fields of Mathematics?
  3. (How can one ask this questions in a better way?)
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    $\begingroup$ Schanuel's Conjecture implies a great many known theorems and open conjectures in transcendence theory. Schinzel's Hypothesis H implies a great many conjectures in prime number theory. $\endgroup$ – Gerry Myerson Jun 17 '14 at 9:48
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    $\begingroup$ I think that ABC conjecture implies FLT only for big enough exponents, so it is not clear if it is a strictly stronger statement. $\endgroup$ – Ferra Jun 17 '14 at 11:20
  • $\begingroup$ Thanks Ferra, I didn't think about this. I added this in the post. Are relations between ABC and FLT known that show that either the one is stronger than the other? For example, is it known that FLT could not imply ABC for big exponents? $\endgroup$ – NicoDean Jun 18 '14 at 13:19
  • $\begingroup$ I believe Schinzel's Hypothesis H doesn't necessarily imply the Hardy-Littlewood conjecture, but Bateman-Horn still implies both of them $\endgroup$ – JasonM May 31 '16 at 6:25
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The Riemann Hypothesis is a special case of the Generalized Riemann Hypothesis, which is a special case of the Grand Riemann Hypothesis.

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  • $\begingroup$ Very interesting, thanks. Didnt know about the Grand RH. If you have another two hierarchies, the bounty is yours ;) $\endgroup$ – NicoDean Jul 19 '14 at 21:57

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