Hilbert problem solved?

In 1900, the great mathematician David Hilbert listed 23 outstanding problems in mathematics and challenged his colleagues to solve them. Three of those problems remain unsolved today, but according to this report, one of them may have been conquered.

Elin Oxenhielm, a 22-year-old mathematics student at Stockholm University, may have solved part of one of the science's great problems. Next week an article will be published revealing her solution for part of Hilbert's 16th problem, Swedish news agency TT reports.

The set of 23 problems was put forward by Prussian mathematician David Hilbert in 1900 as challenges for the 20th century. Three remain unsolved, numbers 6,8 and 16.

Oxenhielm's solution pertains to a special version of the second part of problem 16, the 'boundary cycles for polynomial differential equations'.

The mathematical journal Nonlinear Analysis, published by Elsevier, has examined and endorsed Oxenhielm's solution and will publish it in their next issue.

Oxenhielm believes her method can be used to unlock the mystery of the entire 16th problem, newspaper Expressen reports.

I confess that I am unfamiliar with this problem as well as with problem #6, which has to do with the axioms of physicis. Problem #8 is the famous Riemann Hypothesis, which has to do with prime numbers. You can read all about these famous historical problems here and about David Hilbert here. Some recent references on this problem are here.

More interestingly, Problem 16 has a connection to the Taniyama-Shimura Conjecture, which was used by Andrew Wiles to prove Fermat's Last Theorem. Stephen Smale, who proved part of the famous Poincare Conjecture, also made some advances on this problem.

I imagine that we'll be hearing more about this shortly. Via Slashdot.

Posted by Charles Kuffner on November 26, 2003 to Technology, science, and math | TrackBack