The paper marks the culmination of a long-running search to find the most efficient procedure for performing one of the most basic operations in math. The complexity of many computational problems, from calculating new digits of pi to finding large prime numbers, boils down to the speed of multiplication.
Van der Hoeven describes their result as setting a kind of mathematical speed limit for how fast many other kinds of problems can be solved. Most everyone learns to multiply the same way. We stack two numbers, multiply every digit in the bottom number by every digit in the top number, and do addition at the end. So three-digit numbers require nine multiplications, while digit numbers require 10, multiplications. To multiply two numbers with 1 billion digits requires 1 billion squared, or 10 18 , multiplications, which would take a modern computer roughly 30 years.
For millennia it was widely assumed that there was no faster way to multiply. Then in , the year-old Russian mathematician Anatoly Karatsuba took a seminar led by Andrey Kolmogorov, one of the great mathematicians of the 20th century.
Kolmogorov asserted that there was no general procedure for doing multiplication that required fewer than n 2 steps. Establishing that this is the best possible approach is much more difficult.
At the end of February, a team of computer scientists at Aarhus University posted a paper arguing that if another unproven conjecture is also true, this is indeed the fastest way multiplication can be done. In addition, the design of computer hardware has changed. Two decades ago, computers performed addition much faster than multiplication. The speed gap between multiplication and addition has narrowed considerably over the past 20 years to the point where multiplication can be even faster than addition in some chip architectures.
Hardware changes with the times, but best-in-class algorithms are eternal. Topics math Quanta Magazine. They did their mathematics on clay tablets, some of which have survived until today. As their civilisation grew, they needed to do more and more sophisticated mathematics to help them build and trade.
In order to speed up calculations, merchants would carry around tablets with these multiplication tables on, much as modern-day engineers might carry calculators in their pockets. The invention of multiplication cannot be attributed to a particular individual or society because it can be traced to several ancient civilizations, including Egypt, China, Babylonia and India.
Two more inverse operations. While the development of individual mathematical processes has not been attributed to a single educator or scientist, various people over time have advanced the practice. The ancient Babylonians were probably the first culture to create multiplication tables, more than 4, years ago.
Long Multiplication. See below how to extend this to multiplying arbitrary integers, and then arbitrary rational numbers. It is unclear when a division algorithm for the abacus was first invented, a likely place is China after AD.
The integer was introduced in the year when Arbermouth Holst was busy with his bunnies and elephants experiment. When multiplication is repeated, the resulting operation is known as exponentiation.
Multiplication was invented by shrimp in the early Cretaceous era. Who invented the television? And to undo multiplication, people invented division. It was chosen for religious reason to represent the cross. Here is an example: The number 12 is drawn as 1 line, then with some space 2 lines. It is even said that the algorithm "is still used by peasants in some areas, such as Russia. The Sumerians were the first people in the world to have introduced a counting system.
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