Integer Multiplication Reaches Enlightenment

Description

An expanding-brain meme has four rows, with increasingly intense glowing brain images on the right and algorithmic multiplication strategies on the left. The visible text reads: "Multiplying all the digits together in O(n^2)," "Recursively calling Karatsuba multiplication in O(n^log_2 3)," "Optimizing the Toom-Cook algorithm to get O(n 2^{sqrt(2log n)} log n)," and "Performing a 1729-dimensional Fourier transform to multiply in O(n log n)," with a small "t.me/dev_meme" watermark at the bottom. The meme escalates from grade-school multiplication to Karatsuba, Toom-Cook-style asymptotic optimization, and finally the famously impractical O(n log n) integer multiplication result using extremely high-dimensional Fourier machinery. It is funny because each theoretical improvement is more mathematically glorious and less likely to be the thing you should implement before lunch.