Join today and earn 25 RSC

What is ResearchCoin?

Trending

Today

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

Slide 1 of 1

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

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

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

Slide 1 of 1

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

Slide 1 of 1

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

A right zero semigroup is left-cancellative

We prove the proposition addressed in the title of this paper.

Submitted by Matheus Lobo

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

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

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

Load More Papers