To multiply two numbers by hand takes a few steps but it's something we're taught in school. When dealing with big numbers, really big numbers, we need to a quicker way to do things.
At primary school we learn how to do long multiplication like this:Methods similar to this go back thousands of years, at least to the ancient Sumerians and Egyptians.In long multiplication, we have to multiply every digit of the first number by every digit of the second number. If the two numbers each have N digits, that’s N2 multiplications altogether. In the example above, N is 3, and we had to do 32=9 multiplications.
In 1960, Anatoly Karatsuba, a 23-year-old mathematics student in Russia, discovered a sneaky algebraic trick that reduces the number of multiplications needed. Very likely your device uses Karatsuba’s trick for this arithmetic. This is all part of the amazing software ecosystem that keeps our web pages loading as snappily as possible.
The first half of their conjecture is that it should be possible to multiply N-digit numbers using a number of basic operations that is proportional to at most N log . The paper has not yet been peer-reviewed, so some caution is warranted. It is standard practice in mathematics to disseminate research results before they have undergone peer review.
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