Related papers: Did Hypatia Know about Negative Numbers?
More than a paper, this is just a little divertissement about coauthoring, the Hirsch h-index, and bibliometric evaluation in general. Without pretending to yield any general conclusions, what I found rummaging through the physics…
In his famous presentation at the International Congress of Mathematicians held in Paris in 1900, David Hilbert included the Riemann Hypothesis on zeros of $\zeta -$function as number 8 in his list of 23 challenging problems published…
We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.
There have been many theories about the paradoxes of numbers, but this is far and away more paradoxical than most. In this paper we will present the Zoli Numbers which have some innovative characteristics. The basic concept of these numbers…
The discovery of black-hole evaporation represented in many respects a revolutionary event in scientific world; as such, in giving answers to open questions, it gave rise to new problems part of which are still not resolved. Here we want to…
In different passages of his dialogues, Plato showed deep mathematically-based physical insights. Regrettably most readers overlooked the respective statements, or they utterly did not understand those hints since they were full of…
If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) have some surprising properties. We give formulae for the n-th…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian…
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle
We give an informal survey of the historical development of computations related to prime number distribution and zeros of the Riemann zeta function.
Evolutionary role of the separation into two sexes from a cyberneticist's point of view. [I translated this 1965 article from Russian "Nauka i Zhizn" (Science and Life) in 1988. In a popular form, the article puts forward several useful…
In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of…
The aim of this short note is to provide a proof to a statement of Sierpi\'nski concerning the number of possible sums of a series (of type $\lambda<\aleph_1$) of arbitrary ordinal numbers.
A signed probability distribution may extend a given traditional probability from observable events to all events. We formalize and illustrate this approach. We also illustrate its limitation. We argue that the right question is not what…
The aim of this paper is threefold: a) Finding new direct and inverse results in the additive number theory concerning Minkowski sums of dilates. b) Finding a connection between the above results and some direct and inverse problems in the…
Proverbs are among the most fascinating language phenomena that transcend cultural and linguistic boundaries. Yet, much of the global landscape of proverbs remains underexplored, as many cultures preserve their traditional wisdom within…
In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
What would you do if you were asked to "add" knowledge? Would you say that "one plus one knowledge" is two "knowledges"? Less than that? More? Or something in between? Adding knowledge sounds strange, but it brings to the forefront…