philosophy of mathematics

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.

In this, the second part of this series, we look at a mathematical notion of complexity and wonder whether the Universe is just too complex for our tiny little minds to understand.

Paraconsistent mathematics is a type of mathematics in which contradictions may be true. In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean?
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