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https://en.wikipedia.org/wiki/Superpermutation#Lower_bounds,_or_the_Haruhi_problemWe should solve an unsolved math problem and name it something like "Cobson problem"
If 4cuck did it, why can't we do the same?
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what is there to solve?
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Thrembo+Thrembo^3=?
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Up
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>>15383168If I solve one of these and get the prize money I'll buy the Sharty and fix it up I promise
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Because 4chad is white while soycuck.shitty is full of brown zoom-zooms
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>>15383211Bait nophony fell for
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soy babies will never
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bvmp
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Q: Are hyperbolic volumes of 3-manifold rationally independent?
A: Yes, hyperbolic volumes of 3-manifolds are indeed rationally independent in a certain sense.
The "volume of a hyperbolic 3-manifold" refers to the volume of the manifold when equipped with a hyperbolic structure, i.e., a geometry modeled on hyperbolic space. These volumes are known to be irrational for most hyperbolic 3-manifolds. In fact, for many manifolds, the volume is transcendental over the rationals, meaning that it is not just irrational, but not the root of any non-zero polynomial with rational coefficients.
Regarding rational independence itself, the volumes of distinct hyperbolic 3-manifolds are believed to be rationally independent. This means that there are no nontrivial linear relations with rational coefficients between the volumes of hyperbolic 3-manifolds. In other words, if you take a set of hyperbolic 3-manifolds and their volumes, no nontrivial rational combination of these volumes can sum to zero.
This conjecture is part of broader conjectures in the study of volumes of hyperbolic 3-manifolds and the structure of the moduli space of hyperbolic 3-manifolds. There is no general proof for all 3-manifolds, but it is supported by significant computational evidence, particularly for small and well-understood manifolds, and by results in number theory, especially around transcendence and algebraic independence.
In summary, while there's no complete proof for all hyperbolic 3-manifolds, the volumes are *generally* believed to be rationally independent based on known results and conjectures.