A 22-year-old student at Stockholm University, Elin Oxenhielm, may have solved part of one of mathematics' greatest unsolved problems. Called Hilbert's problem 16, it has confounded workers for over a century. But in a few hours of inspiration she may have seen the light. Her solution is to be published in a maths journal. Her research into so-called planar polynomial vector fields may have practical applications for computer simulations in science and economics. "I solved it before I knew its significance," Elin Oxenhielm told BBC News Online. "It took a few months of thinking about it at first, but then the solution came remarkably quickly," she says. Her breakthrough comes a century after the problem was posed by Prussian mathematician David Hilbert. In 1900 he gave a lecture in Paris where he laid down the 23 greatest problems for maths in the 20th century. They were a varied selection that had confounded the greatest mathematical minds of the age. Couched in language that only mathematicians appreciate, they included such questions as: can the continuum of numbers be regarded as a well ordered set, and can space be constructed by congruent polyhedra? Over a century later only three of Hilbert's problems remain unconquered, numbers six, eight and 16.
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