Back in 1971 , two German mathematician mull it would be possible to multiply large numbers ( as in , veeery large numbers ) using an incredible fast method , lie with as theSchönhage - Strassen algorithm . However , this bright idea remained supposititious for several 10 – until now .
Associate Professor David Harvey , a mathematician from the University of New South Wales ( UNSW ) in Australia , has work the 48 - year multiplication puzzle first propose by Arnold Schönhage and Volker Strassen , a breakthrough which will tolerate computers to manifold heavy number with great efficiency and speed .
To understand how this method acting works , take your thinker back to the way you determine to reproduce number in elementary school . If you wanted to reproduce something like 159 x 314 , for example , you would publish the two numbers racket on top of each other , manifold every single digit of the number with each figure of the other issue , then add up the Modern numbers . This method acting requires you to calculate 9 separate multiplication operations .
Since both the numbers in this generation have 3 digit ( n = 3 ) , each n finger of the first number has to be multiply by each n finger of the 2d issue , which is the equivalent to n2 . In 1971 , Schönhage and Strassen proposed it is theoretically potential to do this times with far few operations , using justn * log(n ) operations , but were unable to prove it at the time . The raw work shows there is , indeed , an algorithm that does just this .
you could read the enquiry composition written by Harvey and his collaborator Joris van der Hoeven from the École Polytechnique in France on the clear admission archiveHAL . It ’s also explain rather nicely by Harvey himself in the telecasting below .
“ They predicted that there should exist an algorithm that multiplies n - digit numbers using fundamentally n * log(n ) basic operations,“Harvey said in astatement . “Our paper pay the first roll in the hay example of an algorithm that attain this . ”
If a computer were to utilize the one-time “ elementary school method ” to manifold two numbers with one million million of finger each , it would take months . However , it would take under 30 second gear using the Schönhage - Strassen algorithm .
Schönhage and Strassen also suggested that n * log(n ) is the “ good potential ” result . In effect , this would be the fastest generation algorithm possible . While it would take a huge amount of work to ever prove this , it ’s sure a tantalizing estimation .
So , this all sounds middling impressive , but what ’s the tangible enjoyment of all this ? By allowing faster multiplication , investigator could use it to account digits of sherlock more efficiently than before and work out problems involving huge prime Book of Numbers .
" People have been hunting for such an algorithm for almost 50 years . It was not a foregone conclusion that someone would eventually be successful , " Harvey summed up . " It might have sprain out that Schönhage and Strassen were wrong , and that no such algorithmic program is possible . But now we fuck better . "
