Related papers: The Erdos Paradox
We find identities for two series proposed by Bart Goddard in terms of elementary functions.
This is the fourth of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It contains almost no new results. This time we…
A conjecture regarding the structure of expander graphs is discussed.
Intellectual space is defined as the set of all proofs of mathematical logic, contained in The Book conceived by Erdos. Physical and intellectual spaces are visualized, making use of concepts from intuitive set theory.
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
In the paper, using the language of spin-half particles, Hardy's paradox is examined within different semantics: a partial one, a many-valued one, and one defined as a set of weak values of projection operators. As it is shown in this…
This is a literal word-for-word translation from the French of Phragmen's proof (the first such published) of Weierstrass' famous theorem characterizing all analytic functions which possess an algebraic addition theorem.
This article discusses the logical errors in the liar paradox, G\"odel's incompleteness theorems, Russell's paradox, and the halting problem. In order to avoid these errors, a redefinition of logic has been presented, which is concluded as…
The logic of abduction involves a collision between deduction and induction, where empirical surprises violate expectations and scientists innovate to resolve them. Here we reformulate abduction as a social process, occurring not only…
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
A new solution of Fermi's paradox sketched by SF writer Karl Schroeder in his 2002. novel "Permanence" is critically investigated. It is argued that this solution is tightly connected with adaptationism - a widely discussed working…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We investigate a restriction of Paul Erdos' well-known problem from 1936 on the discrepancy of homogeneous arithmetic progressions. We restrict our attention to a finite set S of homogeneous arithmetic progressions, and ask when the…
In this note our aim is to show a paradox in the spectral representation of stationary random processes.
Brief recollections by the author about how his work with Kip Thorne influenced his career in physics.
Nadel's Paradox states that it is not possible to take into account simultaneously cultural and relational dimensions of social structure. By means of a simple computational model, the authors explore a dynamic perspective of the concept of…
In this paper I shall try to sketch some typical aspects of Erich Lehmann's contributions to statistics through his research, his teaching, his service to the profession and his personality.
Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct. In this short note, we give the negative answer on this question in an elementary way.
We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic)…
In our effort to find an arithmetically pure proof of the Bertrand postulate, we investigate and solve (using only elementary arithmetical methods) another less usual inequality in positive integers inspired by the classical proof of the…