The original version of this story appeared in Quanta Magazine. The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the ...

In the literature there has been considerable attention given to the exploration of relationships between certain diophantine equations and class numbers of quadratic fields. In this paper we provide ...

Let (X, μ) be a probability measure space and $T_{1},\ldots ,T_{n}$ be a family of commuting, measure preserving invertible transformations on X. Let $Q(m_{1},\ldots ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

A series of unsolved puzzles in number theory called Diophantine problems date back to 3,700 years ago. Over the years mathematicians have whittled away at them, and recent work has made significant ...

In Douglas Adams' sci-fi series "The Hitchhiker's Guide to the Galaxy," a pair of programmers task the galaxy's largest supercomputer with answering the ultimate question of the meaning of life, the ...

For decades, a math puzzle has stumped the smartest mathematicians in the world. x 3 +y 3 +z 3 =k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as ...

The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the eminent mathematician David Hilbert announced a list of 23 key ...

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics. Mathematical ...