“Euraka!” moment in the north Georgia mtns
Smithsonian.com (“A Walk Through the Woods Leads to Insight on Numbers, Jan. 24, 2011) shares the story of an important recent discovery involving partition numbers by Ken Ono (Asa Griggs Candler Professor of Mathematics). He and post-doc Zach Kent were walking through the north Georgia woods when…
“We were standing on some huge rocks, where we could see out over this valley and hear the falls, when we realized partition numbers are fractal,” Ono says. “We both just started laughing.”
Fractals are a kind of geometric shape that looks incredibly complex but is actually composed of repeating patterns. Fractals are common in nature—snowflakes, broccoli, blood vessels—and as a mathematical concept they’ve been hauled into use for everything from seismology to music.
Ono and his team realized that these repeating patterns can also be found in partition numbers. “The sequences are all eventually periodic, and they repeat themselves over and over at precise intervals,” Ono says. That realization led them to an equation (all math leads to equations, it sometimes seems) that lets them calculate the number of partitions for any number.