Related papers: Wetzel's Problem, Paul Erdos, and the Continuum Hy…
Remarks on the life and work of Paul Erdos.
The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…
In 1964, Paul Erd\H{o}s published a paper settling a question about function spaces that he had seen in a problem book. Erd\H{o}s proved that the answer was yes if and only if the continuum hypothesis was false: an innocent-looking question…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
We give an historical account, including recent progress, on some problems of Erd\H os in number theory.
We prove several extensions of the Erdos-Fuchs theorem.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
The Halting Problem is a version of the Liar's Paradox.
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…
The mechanism of continuous set of different universes formation is elaborated. It provides tool to solve the problem of observed smallness of physical parameters. Solution of two puzzles - the hierarchy and the cosmological constant…
The purpose of this text is twofold. First we discuss some divisor problems involving Paul Erd\H os (1913-1996), whose centenary of birth is this year. In the second part some recent results on divisor problems are discussed, and their…
Je retracerai l'histoire des conjectures de Weil sur le nombre de solutions d'\'equations polynomiales dans un corps fini et quelques unes des approches qui ont \'et\'e propos\'ees pour les r\'esoudre. The Weil conjectures: origins,…
The Collatz conjecture is a famous math problem that was introduced by Lothar Collatz in 1937, and nobody has yet succeeded in proving or disproving it. In this article, I will analyze this problem with a new approach and I will discuss my…
The paradoxes of thermodynamics and statistical physics are unavoidable in the study of physical paradoxes because of their importance at the time they came to be as well as the frequency of their appearance in historical studies of…
Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see \cite{rg}). In this paper we prove an extension of Mordell's theorem and formulate a conjecture…
The document tries to put focus on sequences with certain properties and periods leading to the first value smaller than the starting value in the Collatz problem. With the idea that, if all starting numbers lead ultimately to a smaller…