Related papers: Origin of the numerals, Al biruni testimony

The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we…

It may seem a funny notion to write about theorems as old and rehashed as Descartes's rule of signs, De Gua's rule or Budan's. Admittedly, these theorems were proved numerous times over the centuries. However, despite the popularity of…

In this article, we introduce and study a new integer sequence referred to as the higher order Mersenne sequence. The proposed sequence is analogous to the higher order Fibonacci numbers and closely associated with the Mersenne numbers.…

We examine an identity originally stated in Ramanujan's ``lost notebook'' and first proven algebraically by Andrews and combinatorially by Kim. We give two independent combinatorial proofs and interpretations of this identity, which also…

The parity conjecture has a long and distinguished history. It gives a way of predicting the existence of points of infinite order on elliptic curves without having to construct them, and is responsible for a wide range of unexplained…

An interesting episode in the history of the prime number theorem concerns a formula proposed by Legendre for counting the primes below a given bound. We point out that arithmetic bias likely played an important role in arriving at that…

The traditional cultures of Aboriginal Australians include a significant astronomical component, which is usually reported in terms of songs or stories associated with stars and constellations. Here we argue that the astronomical components…

Each number field has an associated finite abelian group, the class group, that records certain properties of arithmetic within the ring of integers of the field. The class group is well-studied, yet also still mysterious. A central…

We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…

``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts of an international community in many variants and with the…

The understanding of probability can be difficult for a few young scientists. Consequently, this new mathematical symbol, related to binomial coefficients and simplicial polytopic numbers, could be helpful to science education. Moreover,…

In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…

The author proposes, a priori, a simple set of principles that can be developed into a range of algorithms by which means the Torah might be decoded. It is assumed that the Torah is some form of transposition cipher with the unusual…

This paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. The paper reviews the distinctions. The von Neumann construction of the ordinal numbers includes a…

Provenance is an increasing concern due to the ongoing revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to…

In this paper we present a new mathematical conception based on a new method for ordering the integers. The method relies on the assumption that negative numbers are beyond infinity, which goes back to Wallis and Euler. We also present a…

We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary…

The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…

We present a modern reconstruction of the classical formula, first derived by medieval Arab astronomers, that describes the trajectory of the tip of a gnomon's shadow during the day as a function of latitude, solar declination, and gnomon…

Despite recent successes in language models, their ability to represent numbers is insufficient. Humans conceptualize numbers based on their magnitudes, effectively projecting them on a number line; whereas subword tokenization fails to…