From Plato to Weil and beyond: Genericity through the history of mathematics

At the end of the 19th century, genericity took an important step toward mathematical analysis, due to the developments promoted by the Italian school of algebraic geometry. However, its origins can be traced back to ancient mathematics in the work of prominent philosophers and mathematicians, such as Plato and Euclid. In this article, we will try to show how a key notion in the structuralist turn of algebraic geometry evolved from a vague linguistic phenomenon and became a precise and fruitful mathematical concept.

Ancient Egyptian architecture

Architectural remains represent one of our main sources of information on ancient Egypt, and one of the first aspects of the ancient Egyptian civilization to have captured the attention of the earliest explorers. Since Egyptology was born, and while it developed as a discipline, the study of ancient Egyptian architecture evolved from initial cursory studies on portions of monuments emerging from the sand, to a wide spectrum of investigations, ranging from analyses of the chemical composition of building materials to the ancient mathematics lying at the basis of the ancient projects, and from the detailed study of specific buildings to the large-scale analysis of the relationship between architecture and landscape.

Radix-10 Fixed Point Division Hardware

Standardization of decimal floating-point formats by IEEE in IEEE 754-2008 Standards fuelled the interest on decimal floating-point architectures among the global research community. Although decimal arithmetic architecture research attracted computer scientists for the last two decades, the major thrust was observed past the year 2008. Multiple proposals have been witnessed for decimal arithmetic units, mostly adders/subtractors, and multipliers. Very few designs have been proposed in the division domain. This article proposes decimal division hardware based on sutras from Vedic Mathematics, the ancient mathematics system. We present a Reduced Magnitude Divisor Generator which converts each digit of the actual divisor into a reduced digit set [-5, 5] using a unique combination/modification of the Vedic Sutras. The divisor digit magnitude reduction also minimizes the product set of multiplication as the single-digit multiplier belongs to the reduced digit set [0, 5] barring the sign. The sign of the dividend or the divisor is not attended during division as a simple XOR operation on the two signs provides the sign of the quotient. Peer comparison has exhibited better results for our design in terms of space and time.