For 19 years, both novice and renowned mathematicians from all over the world have tried their hand at solving seven of mathematics’ most difficult problems, each of which comes with monumental bragging rights and a $1 million prize from the prestigious Clay Mathematics Institute.
Only one of these problems, which collectively are known as the Millennium Prize Problems, has been solved. Florida Polytechnic University junior Alan Longfellow is dedicating himself to solving the second: the Navier-Stokes Equation.
“These equations have an immense importance for science and engineering, but the fact is when you have an equation that hasn’t been solved and we’re using outdated and clunky methods instead, someone should solve it,” said Longfellow, who graduated high school from The Vanguard School in Lake Wales, Florida. “If I have the determination and the willpower, then it’s my duty to solve it.”
Since beginning his mission a year ago, Longfellow dedicates several hours every week to working on his solution to the Navier-Stokes Equation. It is a series of problems developed in the 19th century and concerns the motion of viscous fluid substances. He said a solution would mean a transformation in the ability to effectively design aircraft and other vehicles. A solution also would be helpful in modeling weather, studying blood flow, and analyzing pollution.
“All these companies that make airplanes, missiles, fighter jets, boats, ships, aircraft carriers – anything where fluid dynamics are involved – these equations are the crux of how it all works,” Longfellow said. “If one were to solve these equations and get an actual solution so you don’t have to make it up as you go, it will save money and they will innovate more than ever before.”
He said he has a good chance at solving the problem because of his academic background. Longfellow is a mechanical engineering major who hopes to one day work in aerospace for a company like Boeing or Lockheed Martin.
“The people who (are trying to) solve these are mathematicians, not engineers. They need an engineer to do this,” he said.
Longfellow is aware that the difficulty of the problem likely means he will need to continue working on it for years to come. However, he is confident in his ability and believes the skills he’s learning at Florida Poly will help him along the way.
“I don’t feel validated unless I’m pushed – hard. I push myself, and Florida Poly has shown me how to do that,” Longfellow said. “Even if I don’t win the prize, the fact that I attempted to do so and that I have the confidence to try comes from the fact that I’m at Florida Poly and not at other schools.”
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