philosophy of mathematics

Proof is the essence of mathematics. But is the standard of proof in research maths really as high as mathematicians would like to believe?

If you can prove that a statement can't possibly be false, does this mean it's true?

Can physics do for maths what maths has done for physics?

Do we live in a matrix? What does physics tell us about reality? Are reality and information one and the same? Do things only exist if they are perceived? Find out some the answers to these fascinating questions.

How understanding why something is impossible can often lead to deeper understanding, contemplations of philosophy and even new mathematics.

Will computers ever replace human mathematicians?

What are mathematical proofs, why do we need them and what can they say about sheep?

Books, brains, computers — information comes in many guises. But what exactly is information?

Mathematics is incredibly good at describing the world we live in. So much so that some people have argued that maths is not just a tool for describing the world, but that the world is itself a mathematical structure. Does his claim stand up to scrutiny?

Most of us have a rough idea that computers are made up of complicated hardware and software. But perhaps few of us know that the concept of a computer was envisioned long before these machines became ubiquitous items in our homes, offices and even pockets.

Are number, space and time features of the outside world or a result of the brain circuitry we have developed to live in it? Some interesting parallels between modern neuroscience and the mathematics of 19th century mathematician Bernard Riemann.

On the face of it the Universe is a fairly complex place. But could mathematics ultimately lead to a simple description of it? In fact, should simplicity be a defining feature of a "theory of everything"? We ponder the answers.