Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

Mathematics often helps us to think about issues that don’t seem mathematical. One area that has surprisingly far-reaching applications is the theory of sets. Sets are one of the most basic objects in ...

Get set theory explained in a clear and complete way, covering everything you need to know from basic definitions to key ...

The relationship between a thin liquid film or drop of liquid and the shape of the surface that it wets is explained with a new simplified mathematical formula. Understanding the precise interaction ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

Hidden Fibonacci numbers, a new shape and the search for a grand unified theory of mathematics are among our choices for most ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently ...

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...