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:
“The history of progress is written in the blood of men and women who have dared to espouse an unpopular cause, as, for instance, the black man’s right to his body, or woman’s right to her soul.”
—Emma Goldman (1869–1940)
“Perhaps universal history is the history of the diverse intonation of some metaphors.”
—Jorge Luis Borges (1899–1986)
“In history the great moment is, when the savage is just ceasing to be a savage, with all his hairy Pelasgic strength directed on his opening sense of beauty;—and you have Pericles and Phidias,—and not yet passed over into the Corinthian civility. Everything good in nature and in the world is in that moment of transition, when the swarthy juices still flow plentifully from nature, but their astrigency or acridity is got out by ethics and humanity.”
—Ralph Waldo Emerson (1803–1882)