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: Egypt archaeologists find ancient writer's tomb

add to favorites email to friend print save as pdf

Related Stories

Roman dig 'transforms understanding' of ancient port

7 minutes 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 ...

First radar vision for Copernicus

17 minutes ago

Launched on 3 April, ESA's Sentinel-1A satellite has already delivered its first radar images of Earth. They offer a tantalising glimpse of the kind of operational imagery that this new mission will provide ...

New approach needed to deal with increased flood risk

33 minutes ago

Considering the impacts of climate change on flood risk may not be effective unless current risk is managed better, according to new research from the University of Bristol published today in the Journal ...

Robotics goes micro-scale

38 minutes ago

(Phys.org) —The development of light-driven 'micro-robots' that can autonomously investigate and manipulate the nano-scale environment in a microscope comes a step closer, thanks to new research from the ...

Recommended for you

Egypt archaeologists find ancient writer's tomb

Apr 19, 2014

Egypt's minister of antiquities says a team of Spanish archaeologists has discovered two tombs in the southern part of the country, one of them belonging to a writer and containing a trove of artifacts including reed pens ...

Study finds law dramatically curbing need for speed

Apr 18, 2014

Almost seven years have passed since Ontario's street-racing legislation hit the books and, according to one Western researcher, it has succeeded in putting the brakes on the number of convictions and, more importantly, injuries ...

User comments : 0

More news stories

Clippers and coiners in 16th-century England

In 2017 a new £1 coin will appear in our pockets with a design extremely difficult to forge. In the mid-16th century, Elizabeth I's government came up with a series of measures to deter "divers evil persons" ...

Making graphene in your kitchen

Graphene has been touted as a wonder material—the world's thinnest substance, but super-strong. Now scientists say it is so easy to make you could produce some in your kitchen.