![]() (There are lots of different vector spaces with different numbers of dimensions and various rules.) If you haven’t, we can think of a vector as an arrow with a length and a direction, living in a particular vector space. If you’ve ever taken a first-year university course in linear algebra, you will have come across things called vectors, matrices and eigenvectors. But what about the invariant subspace problem itself? (Image credit: The original uploader was Stako at Polish Wikipedia., Public domain, via Wikimedia Commons) What's an invariant subspace? In 1972, Per Enflo (right) collected the prize of a live goose from Polish mathematician Stanislaw Mazur (left) for solving a particularly difficult problem. Polish mathematician Stanisław Mazur had in 1936 promised a live goose to anyone who solved his problem – and in 1972 he kept his word, presenting the goose to Enflo. Aside from his work on the invariant subspace problem, Enflo solved two other major problems – the basis problem and the approximation problem – both of which had remained open for more than 40 years.īy solving the approximation problem, Enflo cracked an equivalent puzzle called Mazur’s goose problem. He is a renowned concert pianist who has performed and recorded numerous piano concertos, and has performed solo and with orchestras across the world.Įnflo is also one of the great problem-solvers in a field called functional analysis. Per Enflo: mathematics, music, and a live gooseīorn in 1944 and now an emeritus professor at Kent State University, Ohio, Enflo has had a remarkable career, not only in mathematics but also in music. He is almost 80, has made a name for himself solving open problems, and has quite a history with the problem at hand. However, the author of this short note, Swedish mathematician Per Enflo, is no ambitious up-and-comer.
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