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:
“A country grows in history not only because of the heroism of its troops on the field of battle, it grows also when it turns to justice and to right for the conservation of its interests.”
—Aristide Briand (1862–1932)
“A poet’s object is not to tell what actually happened but what could or would happen either probably or inevitably.... For this reason poetry is something more scientific and serious than history, because poetry tends to give general truths while history gives particular facts.”
—Aristotle (384–323 B.C.)
“History, as an entirety, could only exist in the eyes of an observer outside it and outside the world. History only exists, in the final analysis, for God.”
—Albert Camus (1913–1960)