How a hike led to a math 'Eureka!'

Feb 23, 2011
While on a hike, far from their desks and daily distractions, the mathematicians noticed patterns in the woods that solved their problem. Credit: Carol Clark.

Where do “eureka” moments come from? Emory mathematician Ken Ono found his on a hiking trail in north Georgia.

He and post-doctoral fellow Zach Kent were on the way to Tallulah Falls last October when the patterns they noticed in the trees, the leaves and the switchbacks on the trail suddenly revealed the mystery of the fractal repeating structure for partition numbers.

“We realized the process of these numbers folding over on themselves is very much like what you see in the woods,” Ono says. “It was kind of a poetic moment,” he recalls of looking out on a mountainous valley, knowing that nature had helped them crack a mystery that had baffled some of the greatest minds in math.

“It’s been, honestly, my lifelong passion, this one question of the divisibility properties of these numbers,” Ono says.

This video is not supported by your browser at this time.

Last year, the American Institute of Mathematics and the National Science Foundation funded a team led by Ono to tackle the problem. Ono, Kent and Amanda Folsom spent months building a theory to explain these divisibility properties, developing a framework that seemed to match the data.

“The problem for a theoretical mathematician is you can observe some patterns, but how do you know these patterns go on forever? We were, frankly, completely stuck. We were stumped,” Ono says.

The hike had been intended as simply a way to enjoy a beautiful day. “Going into the woods, escaping from day-to-day tasks, is actually vital for me and my work,” Ono says. “It gives me an opportunity to really focus on really difficult little questions that may fit into a bigger theory.”

So what is an “aha” moment? “The way I see it, it’s not something that happens to you instantly,” Ono says. “It just happens to be the moment that you realize the fruits of all your hard work.”

Explore further: Researchers help Boston Marathon organizers plan for 2014 race

add to favorites email to friend print save as pdf

Related Stories

New math theories reveal the nature of numbers

Jan 20, 2011

For centuries, some of the greatest names in math have tried to make sense of partition numbers, the basis for adding and counting. Many mathematicians added major pieces to the puzzle, but all of them fell ...

Fern's hunger-busting properties supported by research

Nov 15, 2010

Professor Roger Lentle, from the Institute of Food, Nutrition and Human Health at the Massey University, led a team that studied how an extract of the mamaku fern influenced stomach activity. Maori traditionally ...

Recommended for you

Newlyweds, be careful what you wish for

8 hours ago

A statistical analysis of the gift "fulfillments" at several hundred online wedding gift registries suggests that wedding guests are caught between a rock and a hard place when it comes to buying an appropriate gift for the ...

Can new understanding avert tragedy?

11 hours ago

As a boy growing up in Syracuse, NY, Sol Hsiang ran an experiment for a school project testing whether plants grow better sprinkled with water vs orange juice. Today, 20 years later, he applies complex statistical ...

Crowd-sourcing Britain's Bronze Age

11 hours ago

A new joint project by the British Museum and the UCL Institute of Archaeology is seeking online contributions from members of the public to enhance a major British Bronze Age archive and artefact collection.

Roman dig 'transforms understanding' of ancient port

11 hours ago

(Phys.org) —Researchers from the universities of Cambridge and Southampton have discovered a new section of the boundary wall of the ancient Roman port of Ostia, proving the city was much larger than previously ...

User comments : 0

More news stories

Newlyweds, be careful what you wish for

A statistical analysis of the gift "fulfillments" at several hundred online wedding gift registries suggests that wedding guests are caught between a rock and a hard place when it comes to buying an appropriate gift for the ...

Can new understanding avert tragedy?

As a boy growing up in Syracuse, NY, Sol Hsiang ran an experiment for a school project testing whether plants grow better sprinkled with water vs orange juice. Today, 20 years later, he applies complex statistical ...

Roman dig 'transforms understanding' of ancient port

(Phys.org) —Researchers from the universities of Cambridge and Southampton have discovered a new section of the boundary wall of the ancient Roman port of Ostia, proving the city was much larger than previously ...

Crowd-sourcing Britain's Bronze Age

A new joint project by the British Museum and the UCL Institute of Archaeology is seeking online contributions from members of the public to enhance a major British Bronze Age archive and artefact collection.

Hackathon team's GoogolPlex gives Siri extra powers

(Phys.org) —Four freshmen at the University of Pennsylvania have taken Apple's personal assistant Siri to behave as a graduate-level executive assistant which, when asked, is capable of adjusting the temperature ...

Better thermal-imaging lens from waste sulfur

Sulfur left over from refining fossil fuels can be transformed into cheap, lightweight, plastic lenses for infrared devices, including night-vision goggles, a University of Arizona-led international team ...