相关论文: Wetzel's Problem, Paul Erdos, and the Continuum Hy…
We discuss the significance of some interesting results by Barbara Rokowska about combinatorial constructions. Her interest in finite mathematics and number theory began with an embellishment and detailing of some work by Erdos. Rokowska…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
This is a survey about the Skorokhod embedding problem. It presents all known solutions together with their properties and some applications. Some of the solutions are just described, while others are studied in detail and their proofs are…
This paper gives a counterexample to the impossibility, by G\"odel's second incompleteness theorem, of proving a formula expressing the consistency of arithmetic in a fragment of arithmetic on the assumption that the latter is consistent.…
These informal notes, initially prepared a few years ago, look at various questions related to infinite processes in several parts of mathematics, with emphasis on examples.
In this article, we establish an additive decomposition of the discrete zeta function (for $s \in \mathbb{N}^*$, $s > 1$), more precisely of the function $4(\zeta(s)-1)$, as a series whose general term is of the form $1/x_n(s) + 1/y_n(s) +…
The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…
Ap\'ery's remarkable discovery of rapidly converging continued fractions with small coefficients for $\zeta(2)$ and $\zeta(3)$ has led to a flurry of important activity in an incredible variety of different directions. Our purpose is to…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
We discuss the classical, and forgotten, notion of perpetuants. We give a proof of the Theorem of Stroh computing their dimensions, and exhibit a basis of perpetuants, thus closing an old line of investigation.
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…
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…
We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.
A counterpoint theory for the whole continuum of the octave is obtained from Mazzola's model via extended counterpoint symmetries, and some of its properties are discussed.
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…
A satisfactory resolution of the persistent quantum measurement problem remains stubbornly unresolved in spite of an overabundance of efforts of many prominent scientists over the decades. Among others, one key element is considered yet to…