Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.

Do you know what the dominant word of the day is? It’s conjecture. Mr. Dictionary says that conjecture is an opinion or conclusion formed on the basis of incomplete information. Sounds reckless and ...

What is the optimal way to cut a convex bounded domain K in Euclidean space (ℝⁿ, | · |) into two halves of equal volume, so that the interface between the two halves has least surface area? A ...

This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

Forecasting: the job or activity of judging what is likely to happen in the future, based on the information you have now Guesswork: the process of making a guess when you do not know all the facts ...

The Royal Commission into Black Saturday has been told theories about what caused a power line to fail and allegedly start the Kilmore fire are "mere conjecture". Engineers engaged by Victoria Police ...