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# Trending Papers in mathematics

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Massively collaborative mathematics
Published: Oct 2009
• We can use the internet to build tools that expand our ability to solve the most challenging intellectual problems. Tools which actively amplify our collective intelligence in much the same way as for millennia we've used physical tools to amplify our strength.
• Formally recognizing contributions to a Polymath project is difficult; research papers from such a project are usually written under a pseudonym. This is a particular issue for early career mathematicians considering devoting substantial research time to a Polymath project.
Submitted by Thomas Vu
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Generating finitely many circles from one circle using Banach-Tarski decomposition paradox
From Paper: Replicating circles from Banach-Tarski decomposition
Published: Aug 2020
We prove the Banach-Tarski decomposition paradox applied to a circle.
Submitted by Matheus Lobo
4
On the arithmetic of automated theorem proving
Published: Aug 2020
We propose a model to assign prime numbers to axioms and theorems, then by comparing equivalent numbers it results in new equivalent theorems.
Submitted by Matheus Lobo
6
A theorem in group theory about left and right cosets of a subgroup
From Paper: A subgroup has equally many left and right cosets
Published: Aug 2020
• This paper is a mathematical proof that aims to establish the theorem that a subgroup has the same number of left and right cosets
Submitted by Matheus Lobo
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A semigroup is a rectangular band if and only if it is nowhere commutative
Published: Jul 2020
We prove the proposition addressed in the title of this paper.
Submitted by Matheus Lobo
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An element of a finite monoid is right invertible if and only if it is left invertible
We prove the proposition addressed in the title of this paper.
Submitted by Matheus Lobo
3
A right zero semigroup is left-cancellative
We prove the proposition addressed in the title of this paper.
Submitted by Matheus Lobo
2
A semigroup with a right zero equal to a right identity is trivial
We prove the proposition addressed in the title of this paper.
Submitted by Matheus Lobo
2
A simple group of order 60 is isomorphic to a subgroup of S6
We show that the permutation of six Sylow 5-subgroups by conjugation is a faithful action, so that G is isomorphic to a subgroup of S6.
Submitted by Matheus Lobo
2
3-cycle commutator
We show within the maximum number of steps that if only one point is moved by two permutations, the commutator is a 3-cycle.
Submitted by Matheus Lobo