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: The stapes of a neanderthal child points to the anatomical differences with our species

add to favorites email to friend print save as pdf

Related Stories

Italian olive tree disease stumps EU

4 hours ago

EU member states are divided on how to stop the spread of a disease affecting olive trees in Italy that could result in around a million being cut down, officials said Friday.

Festo has BionicANTs communicating by the rules for tasks

4 hours ago

Germany-based automation company Festo, focused on technologies for tasks, turns to nature for inspiration, trying to take the cues from how nature performs tasks so efficiently. "Whether it's energy efficiency, ...

Jury decides Silicon Valley firm did not discriminate

4 hours ago

A jury decided Friday that a prestigious venture capital firm did not discriminate or retaliate against a female employee in a case that shined a light on gender imbalance and working conditions for women ...

Intel in talks with Altera on tie-up

4 hours ago

US tech giant Intel is in talks with rival Altera on a tie-up to broaden the chipmaker's product line amid growth in Internet-connected devices, the Wall Street Journal reported Friday.

Recommended for you

Destroyed Mosul artefacts to be rebuilt in 3D

Mar 27, 2015

It didn't take long for the scientific community to react. Two weeks after the sacking of the 300 year-old Mosul Museum by a group of ISIS extremists went viral on Youtube, researchers from the ITN-DCH, IAPP ...

Boys plagiarise more than girls at school

Mar 27, 2015

Research by the University of the Balearic Islands has analysed the phenomenon of academic plagiarism among secondary school students. The study, published in the journal Comunicar, confirms that this practi ...

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.