One of the oldest unsolved problems in mathematics is also among the easiest to grasp. The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

We present a numerical method for finding extreme examples of identities related to the uniform abc-conjecture for algebraic number fields. Journal Information This journal, begun in 1943 as ...

Experienced mathematicians warn up-and-comers to stay away from the Collatz conjecture. It’s a siren song, they say: Fall under its trance and you may never do meaningful work again. The Collatz ...

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 ...

Nearly 40 years after it was proposed, mathematicians have settled one of the most profound questions in the study of general relativity. In a paper posted online last fall, mathematicians Mihalis ...