There’s a new preprint on arXiv, Counterexample to the Hodge Conjecture, by Kim and Roush, that proposes a counterexample to the Hodge conjecture, one of the Clay Mathematics Institute’s 7 Millenium Problems. It’s a bold claim, and the 12-page paper looks like it would be easy for an expert (which I am not) to follow, so we’ll probably hear a definite verdict relatively soon. Interestingly, part of the argument involves a computer calculation.

Via Peter Woit.

**Update.** The authors have withdrawn their claim of a counterexample.