Related papers: Did Hypatia Know about Negative Numbers?
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
Our number system is a magnificent tool. But it is far from perfect. Can it be improved? In this paper some possibilities are discussed, including the use of a different base or directed (negative as well as positive) numerals. We also put…
We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to areas related to partial sums of powers. We apply these…
Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of…
About Conway's surreal numbers: A letter to a friend (written in French). In memoriam John Horton Conway.
In this article we find some properties of certain types of entropies of a natural number. Also, regarding the entropy H of a natural number, introduced by Minculete and Pozna, we generalize this notion for ideals and we find some of its…
In this short note,we correct a well-known counter example of the famous book of Dacorogna[2].
In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present…
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 note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
In this article, I explain why I abandoned my original plan to write a novel about a mathematician proving Fermat's Last Theorem, letting my protagonist solve the entirely fictional Wild Number Problem instead. I enumerate the steps that…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
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…
Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…
This work summarises some of the attempts to explain the phenomenon of dark energy as an effective description of complex gravitational physics and the proper interpretation of observations. Cosmological backreaction has been shown to be…
This letter is a comment on an article by T.C. Halsey and M.H. Jensen in Nature about using recurrence times as a reliable tool to estimate multifractal dimensions of strange attractors. Our aim is to emphasize that in the recent…
The history of the development of the concept of complex numbers from the 16th to 19th centuries. The origin and refinement of the geometric and physical meaning of complex numbers, the emergence of vectoral analysis.
A contribution to Frank Wilczek's 70th birthday's festschrift, this brief note considers how much power can be extracted from dark matter.
This is a short metaphysical fable accentuating the conceptual difficulties involved, and succinctly criticizing the approaches pursued since the inception of quantum theory, in dealing with what is known collectively as `the measurement…