A mathematics journal has withdrawn a paper that claimed to crack one of the discipline's great mysteries after reviewing and accepting the work and publishing it online. On 18 November, Nonlinear Analysis published a paper by Elin Oxenhielm - a postgraduate student in mathematics at the University of Stockholm, Sweden - which presented itself as a solution to the second part of Hilbert's sixteenth problem, one of a set of challenges laid out by German mathematician David Hilbert in 1900.If a solution were validated, mathematicians agree, it would be a significant step towards a complete solution to the problem. Oxenhielm predicts just that: "We could find one in a year or so, if we're lucky," she says.

The work was described in a 24 November press release from Oxenhielm and covered in several media outlets including the BBC. But the paper immediately came under fire from mathematicians. "It's completely inadequate - I can't imagine who would have thought it was a proof," says John Mather of Princeton University, New Jersey.

Critics include Oxenhielm's supervisor, Yishao Zhou, who put a statement on her website saying: "The paper is incomplete and contains serious mistakes."

Hilbert specified 23 problems that he said should drive mathematical research. Solving any one of them is almost guaranteed to make a mathematician's name, and by 2000 all but three had been solved.

The sixteenth, the problem of the topology of algebraic curves and surfaces, deals with the territory where geometry meets algebra. Its second part involves showing that the number of periodic solutions to a differential equation is finite.

Such periodic solutions are also known as limit cycles - stable, oscillating trajectories to which a system will return if perturbed. Limit cycles are common in nature, and a proof of the second part could lead to a better understanding of heartbeats, animal movements and the kind of runaway vibrations that can shake a structure to bits.

Oxenhielm formulated her proof using 'describing functions' - which can predict roughly the presence of limit cycles in nonlinear equations.


View: Full Article | Source: Nature.com

I just read the full article and I wonder if some mathematicians didn't understand her new approach or if she really made some errors.

Having a PhD myself, I know how incompetent some so-called professors can be. How can that happend ? Simple, a professor has a bunch of research monkeys called PhD students that work hard to prove themselves, he just cosigns and gets credit for their work. After many years of this treatement, some of them become more managers that researchers.

I really hope for her that she didn't make a mistake otherwise she can forget her academic career...

TheLight