Long-Standing Problem of 'Golden Ratio' and Other Irrational Numbers Solved with 'Magical Simplicity' | Space

[Samiya Illias]

https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/

[Bruno Marchal]

> On 21 Sep 2019, at 11:15, Samiya Illias <samiya...@gmail.com> wrote:
>
>
> https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/


That is actually very interesting, but not directly related to our discussion, except such conjecture illustrates the non fiction and non conventional aspect of the number relations.

But the simple diagonal argument proving that there is no total universal computable function proves this better, by showing that no matter how much axioms we add to our theories, some similar conjectures can remain unsolved for long, if not forever, despite being intuitively clearly either true or false. Note that such a “certainty” does not exist outside the arithmetical (computer science theoretical) realm. I mean the certainty that the proposition are either true or false.

Bruno



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[Lawrence Crowell]

On Saturday, September 21, 2019 at 4:15:17 AM UTC-5, Samiya wrote:

https://www.scientificamerican.com/article/new-proof-solves-80-year-old-irrational-number-problem/

This is curious. The golden mean or φ = ½(1 + √5) is connected to a range of mathematics with exceptional and sporadic groups and algebras. The roots and weights of E8, the Leech group and its lattice Λ_{24} have magnitudes given by φ.

LC