The mathematical sign for multiplication, denoted by the symbol “×” (based on cross of San Andreas) or simply an asterisk “*”, is used to represent the operation of multiplying two or more numbers. The development of the multiplication sign has a rich history that spans across different civilizations and mathematical traditions.
The concept of multiplication has been understood and practiced since ancient times. However, the need for a specific symbol or notation to represent multiplication arose gradually as mathematics advanced. In ancient civilizations, such as Babylonia and Egypt, multiplication was often represented through repeated addition or geometric methods.
The earliest recorded use of a specific symbol for multiplication can be traced back to the 15th century, in the work of German mathematician Johannes Widmann. In his influential book “Behende und hüpsche Rechenung auf allen Kauffmanschafften” (Quick and Neat Calculation in All Business Transactions), published in 1489, Widmann used a dot (·) to represent multiplication. This dot notation gained popularity in Germany and other European countries during the Renaissance period.
Around the same time, Italian mathematician Luca Pacioli, known for his collaboration with Leonardo da Vinci, introduced a more compact and visually distinct symbol for multiplication in his book “Summa de arithmetica, geometria, proportioni et proportionalità.” Pacioli used the letter “M” with a vertical line to signify multiplication. This notation, also known as “times,” gained traction and was widely adopted in Europe during the 16th and 17th centuries.
In the 17th century, the French mathematician René Descartes introduced another variant of the multiplication sign. Descartes used two perpendicular lines to denote multiplication in his influential work “La Géométrie.” This notation gained popularity in France and eventually spread to other parts of the world, becoming the widely accepted standard for multiplication.
In the late 19th century, the German mathematician Hermann Hankel further popularized the use of the “×” symbol in his influential textbook “Die Elemente der Zahlentheorie.” Hankel’s textbook had a significant impact on mathematics education, leading to the widespread adoption of the “×” symbol for multiplication.
It is worth noting that different notations for multiplication continue to exist across various mathematical traditions and textbooks. In addition to the “×” symbol and the dot notation (·), other symbols, such as the asterisk “*”, are commonly used in different contexts, including computer programming and calculators.
The development of the multiplication sign reflects the ongoing evolution of mathematical notation and the collective efforts of mathematicians over centuries. The need for a concise and unambiguous representation of multiplication led to the adoption of various symbols, with the “×” symbol emerging as the most widely recognized and used notation in mathematics today.