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
Fermat's Last Theorem $\subset$ Tanijama-Shimura Conjecture $\subset$ Serre's modularity conjecture
Fermat's Last Theorem $\subset$ Euler's conjecture (counterexamples known, therefore too strong)
Poincarè conjecture $\subset$ Geometrization conjecture
Unsolved
Fermat's Last Theorem with big exponents $\subseteq$ ABC-conjecture
Twin Prime Conjecture $\subset$ Hardy–Littlewood conjecture $\subset$ Schinzel's hypothesis H $\subset$ Bateman–Horn conjecture
Riemann hypothesis $\subset$ Generalized Riemann hypothesis $\subset$ Grand Riemann hypothesis
Cramér's conjecture $\subset$ Firoozbakht's conjecture
P vs. PSPACE $\subset$ P vs. NP-Problem $\subseteq$ Existance of One-Way-Functions
Examples of Overarching Conjectures
Schanuel's Conjecture in transcendence theory
Bateman–Horn conjecture in prime number theory
Existance of One-Way-Functions in complexity theory
Questions
- Are there complete lists of the dependencies between different conjectures in mathematics available?
- What are the most general Conjectures in various fields of Mathematics?
- (How can one ask this questions in a better way?)
The Riemann Hypothesis is a special case of the Generalized Riemann Hypothesis, which is a special case of the Grand Riemann Hypothesis.