Article posted: 4/29/2013 12:28 PM

# Tough math problem has to do with the shape of the universe

 "What is the hardest math problem in the world?" asked students in Amy Mueller's fourth-grade class at the Hoover Math & Science Academy, Schaumburg.   Mark Black | Staff Photographer
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By Hope Babowice

"What is the hardest math problem in the world?" asked students in Amy Mueller's fourth-grade class at the Hoover Math & Science Academy, Schaumburg.

In the early 1900s, French mathematician Henri Poincaré wondered about the shape of the three-dimensional universe we live in.

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The Schaumburg Township District Library suggests these adult-level book titles and websites about complex math problems:

• "Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World" by George Szpiro.

• "Elementary Topology: A Combinatorial and Algebraic Approach" by Donald W. Blackett.

The following websites have much more information — including discussion of the solution to the conjecture:

• The Poincaré conjecture: www.math.unl.edu/~mbrittenham2/ldt/poincare.html

• The Clay Mathematics Institute: www.claymath.org/millennium/Poincare_Conjecture

• Dr. Perelman awarded Millennium prize: www.claymath.org/millennium

Keith Devlin, executive director of the H-STAR Institute at Stanford University, helped to explain what is one of the world's hardest math problems — the Poincaré conjecture.

"Is it possible, Poincaré asked, to understand the shape of the universe from the inside?" Devlin wrote. "He proposed a way to do it — mathematically, but not in reality — by repeatedly looping a long string through space and trying to tighten it down to one point. This could determine that the universe is 'simply-connected' like a sphere, which would allow the loop to be tightened to one point.

"If it were 'multiply-connected' like a doughnut or pretzel shape, some loops could not be shrunk to a point because they wind around one of the holes. (Think of the different ways a loop can be placed on the inner tube of a tire. If the loop wraps around the tube, you cannot shrink it to a point.)

"Poincaré conjectured, or made a well-researched guess, that the loop trick would, in principle, enable us to determine the shape of our universe."

About 15 years ago, experts from The Clay Mathematics Institute in Cambridge, Mass., collaborated with mathematicians worldwide to identify seven of the world's hardest math questions.

Sommer Gentry, a math professor at the U.S. Naval Academy in Baltimore, described another chief math problem.

"One of the hardest unsolved math problems is called P versus NP, and it asks whether there is any fast way that computers can find answers to questions like: What are all the prime factors of a large number? The Clay Mathematics Institute has offered a \$1 million prize for anyone who solves the P versus NP problem."

Two years after the Clay Millennium prize was announced, Russian mathematician Grigory Perelman solved the Poincaré conjecture, 100 years after it was formulated. That leaves six of the world's hardest math problems for teams or individuals to resolve.

Math adds into almost everything we do. There's almost no time during the day when we haven't used math — like when we check our computers, which were programmed using an algorithm to measure ingredients needed for a recipe, or when we calculate out how much money is needed to purchase a video game that was designed using math.

Math is all about patterns, Gentry said, and noticing that problems that seem different can actually be similar or the same.

Gentry has developed a mathematical approach to matching kidney donors to patients in need of a new kidney.

"The same math that I use to help people get kidney transplants is used in chemistry to understand the locations of double bonds like those in benzene, an organic chemical compound."

Math fans might be interested in the American Mathematical Society, which posts information about high school-level summer math camps, math news articles and ideas for careers in math. Check out the organization's website at www.ams.org.

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