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 ...

This is a preview. Log in through your library . Abstract Consider first-passage percolation on the square lattice. Hammersley and Welsh, who introduced the subject in 1965, conjectured that the ...

Sometimes a counterexample to one conjecture shows the way to disprove other conjectures. In my case, it's more of a proof of concept: I can't see how my counterexample could directly lead to ...

Gardam’s discovery of a counterexample to the unit conjecture is oddly reassuring, Kropholler said, because it suggests that this hard work was really needed. “At the very basic core there was always ...

But they were wrong. Last month, a trio of mathematicians announced a counterexample, disproving the conjecture. The result offers fresh guidance on how to approach related problems in physics ...

At just 17, homeschooled Bahamas teen Hannah Cairo upended the 40-year-old Mizohata-Takeuchi conjecture, coming up with a ...

Hollom found a counterexample to this version of the conjecture. He created a small hypergraph whose edges each connected three vertices: Gladkov came across the paper and realized it was just what ...

Mathematicians have solved a decades-old problem in knot theory, discovering that linking two knots together can actually produce a knot that is easier to untie – the opposite of what was expected ...