SYDNEY, April 5 (Xinhua) -- A mathematics professor from Australia's University of New South Wales (UNSW) has solved a 48-year multiplication puzzle which will give computers the ability to multiple large numbers much faster.
Associate Professor David Harvey, from UNSW's School of Mathematics and Statistics, on Thursday published a method to multiply large numbers which proves an academic theorem first proposed in 1971 by German mathematicians, Arnold Schonhage and Volker Strassen.
"They predicted that there should exist an algorithm that multiplies n-digit numbers using essentially n * log(n) basic operations," Harvey said.
"Our paper gives the first known example of an algorithm that achieves this."
Schonhage and Strassen developed a method needing fewer than n2 operations, but were unable to get it down to n * log(n).
For a computer using a traditional long multiplication method, such as that taught in schools, it would take months to multiply two numbers with billions of digits -- using the Schonhage and Strassen algorithm it would take just 30 seconds.
But for larger numbers again -- trillions or even gazillions -- the new method is vastly more efficient than even that of Schonhage and Strassen.
Harvey said that his breakthrough could have far reaching applications in the advancement of mathematics such as in division and square roots or even calculating the digits of pi.
"People have been hunting for such an algorithm for almost 50 years. It was not a forgone conclusion that someone would eventually be successful," he said.
"It might have turned out that Schonhage and Strassen were wrong, and that no such algorithm is possible -- but now we know better."
