相关论文: Wetzel's Problem, Paul Erdos, and the Continuum Hy…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
The extended Riemann hypothesis (ERH) for Dedekind zeta functions remains one of the most elusive open problems in number theory. Over the last century, many equivalent statements to the classical Riemann hypothesis alone have been…
We provide algorithms for the absolute and alternating Ostrowski Expansions of the continuum and provide proofs for their uniqueness.
An technically interesting proof of a known theorem.
Two sides of cosmological constant problem are discussed: a mysterious compensation of all contributions to vacuum energy with the accuracy of 100-50 orders of magnitude and a surprising equality of a constant vacuum energy density to the…
This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…
The paper deals with continuous solutions of a Schilling's problem.
This is a brief overview of some turning points in the history of infinitesimals.
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
The perfect cuboid problem is an old famous unsolved problem in mathematics concerning the existence or non-existence of a rectangular parallelepiped whose edges, face diagonals, and space diagonal are of integer lengths. Recently Walter…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
The conditions under which, the continuity equation can be substituted by an ordinary non differential equation, will be discussed. Since continuity equation is a fundamental equation, this result will be applicable in a vast area of…
Remarks on mathematical proof and the practice of mathematics.
There are important problems in physics related to the concept of probability. One of these problems is related to negative probabilities used in physics from 1930s. In spite of many demonstrations of usefulness of negative probabilities,…
In 1930s Paul Erdos conjectured that for any positive integer $C$ in any infinite $\pm 1$ sequence $(x_n)$ there exists a subsequence $x_d, x_{2d}, x_{3d},\dots, x_{kd}$, for some positive integers $k$ and $d$, such that $\mid \sum_{i=1}^k…
We trace the evolution of the theory of stochastic partial differential equations from the foundation to its development, until the recent solution of long-standing problems on well-posedness of the KPZ equation and the stochastic…
This paper is a short survey of the recent results on examples of periodic two-dimensional continued fractions (in Klein's model). In the last part of this paper we formulate some questions, problems and conjectures on geometrical…
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.