It was the first multiplication algorithm faster than long multiplication known to humans. Before 1960, few people thought it was possible to do it faster than O(n^2). Even one of the best mathematician in the 20th century, Kolmogorov, believed the long multiplication is probably asymptotically optimal in 1955, and asked people to try proving this conjecture in a 1960 conference. And within a week, his student Karatsuba found this algorithm. It's also one of the earliest divide-and-conquer algorithms discovered in computer science. Since then, faster and faster algorithms have been discovered.
Although in practice, the ALU itself is almost never the bottleneck of computation on a modern computer. The setup cost of these algorithms is often greater, making them only useful for bignum (Karatsuba is only faster for number longer than a few hundreds of decimal digits?) It also explains why faster algorithms haven't been discovered in the last 2000 years.
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The historical review paper by Karatsuba
* The Complexity of Computations