Breakthrough in quasi-linear multiplication | Tangente
Multiplying in quasi-linear time
Multiplying two integers dates back several thousand years. In 2019, at last, the algorithm was improved!

Multiplying two integers dates back several thousand years. In 2019, at last, the algorithm was improved!

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The news broke in late March: mathematicians David Harvey and Joris van der Hoeven showed that large integers can be multiplied in "quasi-linear" time, confirming a conjecture that dates back to 1971, when Volker Strassen first suggested it. Let's revisit one of arithmetic's basic operations!

The introduction of logarithms can be traced back to the Renaissance, when they were used to solve computational problems. They have since found more theoretical applications and today even lie at the heart of some cryptographic systems—and hence of our computers.

Complex numbers seem very far removed from the modern world’s concerns about profitability. Yet they underpin methods used to speed up the multiplication of large integers. They save time—a great deal of time—and therefore money!

“The” mean of two numbers is defined “naturally” according to the context. It is not always the familiar arithmetic mean! Several different notions coexist and are closely interconnected, as Liouville, Cauchy and Jensen clearly understood.
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