Related papers: Chang's Conjectures and Easton collapses

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

In 1982-83, E. Nochka proved a conjecture of Cartan on defects of holomorphic curves in $\Bbb P^n$ relative to a possibly degenerate set of hyperplanes. This was further explained by W. Chen in his 1987 thesis, and subseqently simplified by…

We prove Dejean's conjecture. Specifically, we show that Dejean's conjecture holds for the last remaining open values of n, namely 15 <= n <= 26.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.

This note points out that the assertions of [1] are groundless and incorrect.

The Manin conjecture is established for Ch\^atelet surfaces over Q arising as minimal proper smooth models of the surface Y^2+Z^2=f(X) where f is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not…

We adopt a physically motivated empirical approach to the characterisation of the distributions of twin and triplet primes within the set of primes, rather than in the set of all natural numbers. Remarkably, the occurrences of twins or…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…

The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which are Nielsen transformations augmented by arbitrary…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

We generalize the theory of ordering character triples, developed by Navarro and Sp\"ath, by taking into account the action of Galois automorphisms on characters. This new technique, together with previous results of Ladisch and Turull,…

Simple demonstrations based on the equivalence principle are given of how a folded chain and a horizontal flat chain fall down when one chain end is fixed to a rigid support.

The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph and a matching. We show that this conjecture holds for the class of connected plane cubic graphs.

We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.

The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…

In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…