poincaré conjecture solved?
news round the world report this morning that the poincaré conjecture, a complex one hundred years old problem concerned with the study of shapes, spaces and surfaces and one of the toughest problems in maths, may have been solved by russian scientist dr grigori perelman, of the steklov institute of mathematics.the problem, was devised by henri poincaré, french mathematician and physicist, and tries to understand the shapes of spaces, including three-dimensional and four-dimensional space-time.
«once you go into four dimensions, you are talking about spaces you can't visualise. the easiest way to visualise this is by studying what happens one dimension down - with two-dimensional surfaces» said dr devlin, executive director of stanford's centre for the study of language and information. but poincaré found that generalising this method from two-dimensional surfaces to three-dimensional ones is not as simple as it sounds, because the objects they cover exist in higher dimensions. so he formulated the conjecture to see if what applied in two dimensions also applied for three.
«one of the odd things about this conjecture is that if you go even higher in dimensions - four, five, six manifolds, the poincaré conjecture is true as it is for two manifolds (dimensions)» said dr devlin. «but it fails for three manifolds. the one case that is really of interest in physics is the one case in which it fails.»
he added that it was impossible to anticipate where the poincaré conjecture might have its most profound implications. and this being one of the announced seven millennium problems in maths, it qualifies for the $1m offred by the to anyone who could solve one of them.
sources: google news, the beeb and mathworld.
