D. B. A. Epstein, V. Markovic, The Logarithmic Spiral: A Counterexample to the K = 2 Conjecture, Annals of Mathematics, Second Series, Vol. 161, No. 2 (Mar., 2005 ...

Arithmetic Geometry and Manin's Conjecture Publication Trend The graph below shows the total number of publications each year in Arithmetic Geometry and Manin's Conjecture.

We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with ...

It would take another year and a half for them to assemble a true counterexample to the periodic tiling conjecture.

But they’re related. Greenfeld and Tao planned to come up with a discrete counterexample to the conjecture that they could then modify to work in the continuous case as well.