Related papers: Much ado about Zero
Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we…
Zeno's paradoxes are explained as being the result of inappropriate combination of discrete and continuous mathematical systems. It is proposed that the source of this confusion lies in the course of development of the number system, which…
Some basic sociophysical notions are described by a physicist, tentatively for a sociologically-oriented reader.
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally,…
This paper discusses the distributions of missing sums and differences.
The term big data has become ubiquitous. Owing to a shared origin between academia, industry and the media there is no single unified definition, and various stakeholders provide diverse and often contradictory definitions. The lack of a…
We discuss a non-intuitive situation concerning percentages.
A brief review of the problem of neutrino masses and oscillations is given. In the beginning we present an early history of neutrino masses, mixing and oscillations. Then we discuss all possibilities of neutrino masses and mixing (neutrino…
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…
In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…
Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.
These informal notes are concerned with sums and averages in various situations in analysis.
The use of historical estimates in current studies is common in a wide variety of application areas. Nevertheless, despite their routine use the uncertainty associated with historical estimates is rarely properly accounted for in the…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
First a formula for the number of zeros of the orthogonal polynomial in the intervals is presented. Then a criteria about the appearance of a zero in a gap is given. Finally a necessary and sufficient condition is derived such that the…
This paper is a short historical note about the origin of the Pole-Barn and the Fat Man Paradoxes
The article attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers - finding the probability of co-primality of two randomly selected natural numbers.…
In this Letter we comment on one particular aspect of Hypatia's enigmatic biography by translating into English a short poem that appeared in a recent review of the third revised Polish edition of Maria Dzielska's book about Hypatia. It…
Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal…