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:
“We may pretend that we’re basically moral people who make mistakes, but the whole of history proves otherwise.”
—Terry Hands (b. 1941)
“I saw the Arab map.
It resembled a mare shuffling on,
dragging its history like saddlebags,
nearing its tomb and the pitch of hell.”
—Adonis [Ali Ahmed Said] (b. 1930)
“This above all makes history useful and desirable: it unfolds before our eyes a glorious record of exemplary actions.”
—Titus Livius (Livy)