The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up ...

Hannah Cairo found herself stuck on a problem that wouldn’t leave her mind. It wasn’t a regular homework assignment—it was a ...

In this way, they were finally able to prove the Kakeya conjecture in three spatial dimensions, showing that the volume covered by the needle is always three-dimensional.

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 t ...

“Some conjectures are motivated by substance, and other conjectures are motivated by wishful thinking,” he said. The bunkbed conjecture seemed like the latter.

Yale professor Sam Raskin led a team to prove the geometric Langlands conjecture, solving a major part of one of math’s most sweeping paradigms.

Unexpectedly, three mathematicians have now shown that a well-known hypothesis in probability theory called the bunkbed conjecture falls into this category. Read Full Article » ...

The conjecture — which is about the different ways you can navigate the mathematical mazes called graphs when they’re stacked on top of each other like bunk beds — seemed natural, even self-evident.

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Mathematicians are celebrating a 1000-page proof of the geometric Langlands conjecture, a problem so complicated that even other mathematicians struggle to understand it. Despite that, it is hoped ...

The Simplest Math Problem Could Be Unsolvable The Collatz conjecture has plagued mathematicians for decades—so much so that professors warn their students away from it ...