Nav: Home

Mathematicians deliver formal proof of Kepler Conjecture

June 16, 2017

A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler Conjecture, which is the definitive resolution of a problem that had gone unsolved for more than 300 years. The paper is now available online through Forum of Mathematics, Pi, an open access journal published by Cambridge University Press. This paper not only settles a centuries-old mathematical problem, but is also a major advance in computer verification of complex mathematical proofs.

The Kepler Conjecture was a famous problem in discrete geometry, which asked for the most efficient way to cram spheres into a given space. The answer, while not difficult to guess (it's exactly how oranges are stacked in a supermarket), had been remarkably difficult to prove. Hales and Ferguson originally announced a proof in 1998, but the solution was so long and complicated that a team of a dozen referees spent years working on checking it before giving up.

Explains Henry Cohn, editor of Forum of Mathematics, Pi: "The verdict of the referees was that the proof seemed to work, but they just did not have the time or energy to verify everything comprehensively. The proof was published in 2005, and no irreparable flaws were ever identified, but it was an unsatisfactory situation that the proof was seemingly beyond the ability of the mathematics community to check thoroughly. To address this situation and establish certainty, Hales turned to computers, using techniques of formal verification. He and a team of collaborators wrote out the entire proof in extraordinary detail using strict formal logic, which a computer program then checked with perfect rigor. This paper is the result of their completed work."

Thomas Hales is the Mellon Professor of Mathematics at the University of Pittsburgh. His research spans discrete geometry, representation theory, motivic integration, and formal theorem proving.

Open access article: A formal proof of the Kepler conjecture.

Cambridge University Press

Related Mathematics Articles:

People can see beauty in complex mathematics, study shows
Ordinary people see beauty in complex mathematical arguments in the same way they can appreciate a beautiful landscape painting or a piano sonata.
Improving geothermal HVAC systems with mathematics
Sustainable heating, ventilation, and air conditioning systems, such as those that harness low-enthalpy geothermal energy, are needed to reduce collective energy use and mitigate the continued effects of a warming climate.
How the power of mathematics can help assess lung function
Researchers at the University of Southampton have developed a new computational way of analyzing X-ray images of lungs, which could herald a breakthrough in the diagnosis and assessment of chronic obstructive pulmonary disease (COPD) and other lung diseases.
Mathematics pushes innovation in 4-D printing
New mathematical results will provide a potential breakthrough in the design and the fabrication of the next generation of morphable materials.
More democracy through mathematics
For democratic elections to be fair, voting districts must have similar sizes.
More Mathematics News and Mathematics Current Events

Best Science Podcasts 2019

We have hand picked the best science podcasts for 2019. Sit back and enjoy new science podcasts updated daily from your favorite science news services and scientists.
Now Playing: TED Radio Hour

Rethinking Anger
Anger is universal and complex: it can be quiet, festering, justified, vengeful, and destructive. This hour, TED speakers explore the many sides of anger, why we need it, and who's allowed to feel it. Guests include psychologists Ryan Martin and Russell Kolts, writer Soraya Chemaly, former talk radio host Lisa Fritsch, and business professor Dan Moshavi.
Now Playing: Science for the People

#537 Science Journalism, Hold the Hype
Everyone's seen a piece of science getting over-exaggerated in the media. Most people would be quick to blame journalists and big media for getting in wrong. In many cases, you'd be right. But there's other sources of hype in science journalism. and one of them can be found in the humble, and little-known press release. We're talking with Chris Chambers about doing science about science journalism, and where the hype creeps in. Related links: The association between exaggeration in health related science news and academic press releases: retrospective observational study Claims of causality in health news: a randomised trial This...