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Mathematicians Discover the Perfect Way to Multiply [Quanata] - mklabgr - 06-18-2026
Mathematicians Discover the Perfect Way to Multiply
[Quanta Magazine]
Summary
The article explains how mathematicians discovered a near-optimal way to multiply extremely large numbers, solving a problem that has challenged researchers for decades. Traditional school multiplication requires about (n^2) operations for numbers with (n) digits, but algorithms such as Karatsuba’s method and the Schönhage–Strassen algorithm gradually improved this by breaking numbers into smaller parts and replacing many multiplications with faster additions and transformations.
In 2019, David Harvey and Joris van der Hoeven introduced an algorithm that achieves multiplication in roughly (n \log n) steps, matching a long-sought theoretical limit suggested by earlier researchers. The breakthrough is important for computational mathematics, including tasks involving huge numbers such as calculating digits of π or searching for large primes, although it will not dramatically speed up everyday computing because existing methods are already very efficient.
ARTICLE