Update: Carl Cowen and Eva Gallardo have now after discovering a gap in its logic that meant it did not prove the invariant subspace problem to be true. They are working to bridge the gap and hope to resubmit the paper to a journal in March
Original article, published 31 January 2013
Would a basketball spinning on a fingertip behave the same way in an infinite number of dimensions? The question has flummoxed mathematicians for 80 years, but now it looks as if the answer is yes 鈥� a find that could have implications for quantum theory.
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The invariant subspace problem was studied in the 1930s by John von Neumann, a pioneer of operator theory, the mathematics behind quantum mechanics. The problem asks whether carrying out certain changes, or operations, will always leave part of an object unaltered, or invariant. In the case of the basketball, the operation is rotation. In three dimensions, the sphere鈥檚 rotational axis remains unchanged, but you can鈥檛 take that for granted in infinite dimensions.
On 25 January, a solution was unveiled at a meeting of the Royal Spanish Mathematical Society in La Coru帽a. of the Complutense University of Madrid in Spain and of Purdue University in West Lafayette, Indiana, said they have proved that part of the object will always be unaltered.
No great prize rests on the proof, but, if it is correct, the method of solving it should enable innovations in operator theory, says of the University of Seville. 鈥淥perator theory is the language of quantum mechanics,鈥� he adds.
