History
The standard procedure for multiplication of two n-digit numbers requires a number of elementary operations proportional to, or in the big-O notation. In 1952, Andrey Kolmogorov conjectured that the classical algorithm was asymptotically optimal, meaning that any algorithm for that task would require elementary operations.
In 1960, Kolmogorov organized a seminar on mathematical problems in cybernetics at the Moscow State University, where he stated the conjecture and other problems in the complexity of computation. Within a week, Karatsuba, then a 23-year-old student, found an algorithm (later it was called "divide and conquer") that multiplies two n-digit numbers in elementary steps, thus disproving the conjecture. Kolmogorov was very agitated about the discovery; he communicated it at the next meeting of the seminar, which was then terminated. Kolmogorov published the method in 1962, in the Proceedings of the USSR Academy of Sciences. The article had been written by Kolmogorov, possibly in collaboration with Yuri Ofman, but listed "A. Karatsuba and Yu. Ofman" as the authors. Karatsuba only became aware of the paper when he received the reprints from the publisher.
Read more about this topic: Karatsuba Algorithm
Famous quotes containing the word history:
“Revolutions are the periods of history when individuals count most.”
—Norman Mailer (b. 1923)
“Systematic philosophical and practical anti-intellectualism such as we are witnessing appears to be something truly novel in the history of human culture.”
—Johan Huizinga (1872–1945)
“Considered in its entirety, psychoanalysis won’t do. It’s an end product, moreover, like a dinosaur or a zeppelin; no better theory can ever be erected on its ruins, which will remain for ever one of the saddest and strangest of all landmarks in the history of twentieth-century thought.”
—Peter B. Medawar (1915–1987)