Has a mathematician solved the ‘invariant subspace problem’? And what does that even mean? Premium

A new paper purports to contain the final piece of a mathematical jigsaw puzzle: the invariant subspace problem

Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title On the invariant subspace problem in Hilbert spaces. The paper is just 13 pages long and its list of references contains only a single entry.

The paper purports to contain the final piece of a jigsaw puzzle that mathematicians have been picking away at for more than half a century: the invariant subspace problem.

Famous open problems often attract ambitious attempts at solutions by interesting characters out to make their name. But such efforts are usually quickly shot down by experts.

However, the author of this short note, Swedish mathematician Per Enflo, is no ambitious up-and-comer. He is almost 80, has made a name for himself solving open problems, and has quite a history with the problem at hand.

Born 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 a renowned concert pianist who has performed and recorded numerous piano concertos, and has performed solo and with orchestras across the world.

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