Related papers: Did Hypatia Know about Negative Numbers?
In this short paper we reply to the Comment [arXiv:1108.4543] by M. J. T. F. Cabbolet on Villata's theory of antigravity [arXiv:1103.4937]. The criticisms of methodological and ontological kind presented by that author come from a…
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
In the first part of this short work (in the form of a comment) we add the plots of two more values of the Li-Keiper coefficients lambda5 and lambda6, computed as in our recent work where the first four values were in particular given. This…
This article (written in Polish) is aimed for a wide mathematical audience. It is intended as an introductory text concerning problems of the asymptotic theory of symmetric groups.
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
In this review article, we discussed the Mathematics and mechanics behind the Enigma machine with an analysis of security strength. The German army used the Enigma machine during the second world war to encrypt communications. Due to its…
The possible discovery of astronomical effects due to precession - such as the shift in the declination of heliacal raising of bright stars or the precession of the equinoxes - is reviewed for various ancient cultures in the world. Although…
We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also,…
Underlying the Riemann Hypothesis there is a question whose full answer still eludes us: what do the zeros of the Riemann zeta function really mean? As a step toward answering this, Andr\'e Weil proposed a series of conjectures that include…
To the astrophysicist faced with the puzzle of dark matter, this one appears under two different aspects: on the one hand in cosmology, i.e. at very large scales, where it seems to be made of a bath of particles; on the other hand at the…
At a social gathering of mathematicians, Herb Wilf noted that the numbers $\zeta(k) - 1$ sum to 1, and challenged the assembly to interpret the sequence as probabilities in some interesting number theoretic context. This short note provides…
One source of beauty in mathematics is totally unexpected connections between two fundamentally different objects. For instance, is it not surprising that the time period of a real simple pendulum is linked with a function arising out of…
The Cosmological Constant $\Lambda$, in different incarnations, has been with us for 100 years. Many surveys of dark energy are underway, indicating so far that the data are consistent with a dark energy equation of state of $w=-1$, i.e. a…
In this article I discuss the fragments of Hipparchus' star catalogue and compare them to Hipparchus' Exegesis to trace the early history of stellar catalogues in Greek astronomy.
The theory of numbers was supposed to be the less useful branch of mathematics. At the same time, cryptography was thought to be a military or a diplomatic issue. In this note we show how the two concepts are today strictly related and how…
Comment on "Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies" [arXiv:1102.2774]
These notes are very informal notes on the Langlands program. I had some pleasure in daring to ask colleagues to explain to me the importance of some of the recent results on Langlands program, so I thought I will record (to the best of my…
Many widely different problems have a common mathematical structure wherein limited knowledge lead to ambiguity that can be captured conveniently using a concept of invisibility that requires the introduction of negative values for…
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…
The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing…