Famous 40-Year-Old Math Problem Solved

Nov 23, 2005

For some, spending more than three years working to solve a more than 40-year-old math problem sounds like a nightmare. For University of Missouri-Columbia mathematics professor Steve Hofmann, solving a problem posed by one of the most famous mathematicians in the second half of the 20th Century has been a dream since his college days.

The major mathematical accomplishment is earning him significant recognition. Hofmann has a speaking invitation at this summer’s meeting of the International Congress of Mathematicians in Madrid, Spain, which takes place only once every four years.

“It’s a problem that has interested me since I was a graduate student,” Hofmann said. “It was one of the biggest open problems in my field and everybody thought it was too hard and wouldn’t be solved. I had toyed with it for years and then put in three years of very serious work before hitting the key breakthrough.”

The problem goes back to two papers written by Tosio Kato, University of California-Berkley, in 1953 and 1961. It turned out to be quite difficult and became known as the “Kato Conjecture” in mathematical circles. The one dimensional version of the problem was solved 20 years later.

“I think I was the last person working on it,” Hofmann joked. “I think everyone else had given up.”

Hofmann admits explaining the problem is difficult because it is rather technical. Its solution applies to the theory of waves propagating through different media, such as a seismic wave traveling through different types of rock. Hofmann said the solution allows mathematicians to better describe the behavior of waves traveling through a medium which itself changes over time.

“To work on a problem for three years and finally crack it open feels fantastic!” Hofmann said. “It’s the reason mathematicians work on problems – for moments like that.”

Hofmann’s work is funded by the National Science Foundation. The solution to the “Kato problem” is detailed in a series of papers published with his research collaborators Pascal Auscher, Michael Lacey, John Lewis, Alan McIntosh and Philippe Tchamitchian.

Source: University of Missouri-Columbia

Explore further: Mapping the world's linguistic diversity—scientists discover links between your genes and the language you speak

Related Stories

Former federal agent pleads guilty to stealing bitcoins

1 hour ago

A former undercover federal agent pleaded guilty to extortion and related charges after acknowledging he channeled more than $700,000 in digital currency from the Silk Road online drug bazaar he was investigating.

Cities, regions, demand bigger climate say

2 hours ago

Leaders of city and regional governments gathered Wednesday in the French city of Lyon, in the grips of a western European heatwave, to demand a bigger stake in the global push to curb global warming.

Hewlett-Packard moves forward with plan to split in two

2 hours ago

Hewlett-Packard is moving forward with plans to split into two companies, filing paperwork to create a new entity that will sell commercial technology, while a separate spinoff will sell personal computers and printers.

Recommended for you

Lady, you're on the money

Jul 03, 2015

So far, women whose portraits appear on U.S. money have been a party of three. Excluding commemorative currency, only Sacagawea, Susan B. Anthony and Helen Keller appear on coins in general circulation, according ...

Old World monkey had tiny, complex brain

Jul 03, 2015

The brain hidden inside the oldest known Old World monkey skull has been visualized for the first time. The creature's tiny but remarkably wrinkled brain supports the idea that brain complexity can evolve ...

User comments : 0

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.