Related papers: Origin of the numerals, Al biruni testimony
This study reconstructs the origin of a constant, here called $\Xi$ (Xi), as a primary scaling factor in Old Babylonian mathematics and astronomy. $\Xi$ arises from the practical necessity of precise measurements on the sky or a circle,…
This is a collection of definitions, notations and proofs for the Bernoulli numbers $B_n$ appearing in formulas for the sum of integer powers, some of which can be found scattered in the large related historical literature in French,…
We make a summary of the different types of proofs adding some new ideas. In addition we conjecture some relations which could be necessary in "modular type proofs" (not still found) of the Ramanujan-like series for 1/\pi^2.
We investigate the properties of arithmetic differentiation, an attempt to adapt the notion of differentiation to the integers by preserving the Leibniz rule, (ab)' = a'b + ab'. This has proved to be a very rich topic with many different…
Tafazzul Husain Khan (1727?--1800?), who began his career in the court of Awadh, spent the last two decades of his life as a trusted ally of the East India Company. What set him apart from other court officials was not so much his…
Al-Biruni (973-1048) was one of the greatest scientists of all times. He was an astronomer, mathematician and philosopher, and studied physics and natural sciences. In this paper, we will discuss some of his experimental methods and some…
Researchers have demonstrated that humans are unable to generate a sequence of random numbers that corresponds in a statistical sense to a simple distribution such as the uniform distribution. The purpose of this article is to present the…
This paper examines the theory of a Babylonian origin of Aryabhata's planetary constants. It shows that Aryabhata's basic constant is closer to the Indian counterpart than to the Babylonian one. Sketching connections between Aryabhata's…
Late-Babylonian mathematics (450-100 BC), represented by some 60 cuneiform tablets from Babylon and Uruk, is incompletely known compared to its abundantly preserved, well-studied Old-Babylonian predecessor (1800-1600 BC). With the present…
It is well known that the set of algebraic numbers (let us call it $A$) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using \G1-based…
We revisit several entries from Ramanujan's notebooks which follow from more elementary arguments than a first glance may suggest. Our goal is to demystify these results through more accessible proofs, while also shining some light on the…
The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…
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,…
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…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
From al-Sufi's tenth-century observation of the Andromeda Galaxy as a "little cloud" to contemporary space missions, Islamic astronomy represents a millennium-spanning tradition of innovation and knowledge. This study traces its trajectory…
I shall discuss the history of Indian astronomy, Aurveda (life science), chemistry and metallurgy to illustrate how downgrading experiments from scientific learning lead to the decline of ancient Indian science and civilization. We shall…
In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
Associate a unique numerical sequence called the modular signature with each positive integer, using modular residues of each integer under the prime numbers, and distinguishing between the core seed primes and non-core seed primes used to…