Is there a proof for the (non)existence of a formula for prime numbers?

[question]

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We discuss about whether it is possible or not to prove or disprove the existence of a formula for the prime numbers.

https://doi.org/10.31219/osf.io/sb7td

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 167, 2020 [GO]

Transdenumerability of the reals

[white paper]

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We show that the real numbers are transdenumerable by setting a one to one map with the set of the transfinite ordinals introduced by Cantor.

https://doi.org/10.31219/osf.io/fu7bx

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 156, 2020 [GD]

On the arithmetic of automated theorem proving

[white paper]

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We propose a model to assign prime numbers to axioms and theorems, then by comparing equivalent numbers, it results in new equivalent theorems.

https://doi.org/10.31219/osf.io/wbf85

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 132, 2020 [FC]

Using prime numbers for automatic theorem proving

[original idea]

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We apply an analogous setting from Gödel’s numbering system to automatic theorem proving.

https://doi.org/10.31219/osf.io/g7usc

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 119, 2020 [EP]

Complex complex numbers

[original idea]

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We apply in the complex numbers the same line of thought that led to the very creation of the complex themselves. In addition, we consider multiple imaginary numbers and generalize both ideas altogether.

https://doi.org/10.31219/osf.io/485kj

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 105, 2020 [EB]

Cycle decomposition for the permutations of an infinite set

[original insight]

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We present two cycle decompositions for the permutations of an infinite set.

https://doi.org/10.31219/osf.io/u6zwt

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 92, 2020 [DO]