Mistake found in invariant subspace proof

[ot]

Some context: the Invariant Subspace Problem is an important open problem in functional analysis [1]. There is a MathOverflow thread discussing its significance [2].

For those not familiar with functional analysis, it is basically a generalization of basic linear algebra fact that, in complex finite-dimensional vector spaces, every matrix (or to be more precise, every linear operator) has at least one eigenvector.

Cowen and Gallardo announced [3] that they proved the theorem in December, but apparently the proof is wrong, so the problem is still open.

[1] http://en.wikipedia.org/wiki/Invariant_subspace_problem

[2] http://mathoverflow.net/questions/48908/is-the-invariant-sub...

[3] http://aperiodical.com/2013/01/the-invariant-subspace-proble...

[user24]

> For those not familiar with functional analysis, it is basically a generalization of basic linear algebra fact that, in complex finite-dimensional vector spaces, every matrix (or to be more precise, every linear operator) has at least one eigenvector.

Oh, thanks for the clarification.

[j2kun]

This is one of the worst things that can happen to a paper of yours, the only worse thing being that it is published before you have to retract it.

[gfodor]

I'd say it'd be worse if someone else found the bug.

[JackFr]

I find it interesting that the phrase was 'a gap was discovered', rather than 'we discovered a gap' or 'Prof. X discovered a gap.'

Assuming they are able to prove it, would that rate a footnote 'We are indebted to Prof. X for pointing out ....'?

And also is there a protocol or custom about how long other guys will give them to try to fix it before they try themselves?

[user24]

That's likely just the academic register. I wrote my dissertation saying "we found that..." when really it should have been "I found that...".

Getting the academic tone right in essays/thesis/papers is important and indeed becomes second nature after a while.

[speeder]

Impressive that they admitted the mistake instead of going on full defense and blame something else.

[jgrahamc]

Who could they have blamed? It's a proof: either it holds up to examination or it doesn't.

[jonjacky]

Another recent example: Edward Nelson of Princeton retracted his claim of having a proof of the inconsistency of Peano Arithmetic. Replying to Terence Tao, he wrote: "You are quite right, and my original response was wrong. Thank you for spotting my error. I withdraw my claim."

http://m-phi.blogspot.com/2011/10/nelson-withdraws-his-claim...

http://m-phi.blogspot.com/2011/10/inconsistency-of-pa-and-co...

[psionski]

I came here to say just that :) Good thing we have set the right expectations in the software industry - everything can be explained by "it's a computer, duh" because users expect everything to be full of bugs anyways :)