## Logically speaking...

In some sense, all of maths should come under the label "logic", and in this collection of articles we try to explain why. We look at logic in the broadest possible sense, bringing together articles on the basics of mathematical logic, its role in computer science and the philosophy of maths, and on how it's being used in applications. We've grouped the articles into three categories:

- Understand the basics: Learn the basic concepts with these gentle introductions to mathematical logic.
- See the bigger picture: Discover logic in action across maths, computer science and the real world.
- Pushing the boundaries: Take a trip to the edges of maths and explore the limits of mathematical logic.

These *Plus* articles accompany a Teacher feature and Post 16 feature on our sister site NRICH, where you can try out some logical reasoning for yourself and have a go at developing convincing arguments!

### Understand the basics

Maths in a minute: Truth tables — Introducing an indispensable tools of mathematical logic

Maths in a minute: Boolean algebra — Meet the algebra of logic!

A bright idea — What do computers and light switches have in common? This article illuminates the connection between light bulbs, logic and binary arithmetic.

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

Something from nothing? — If you can prove that a statement can't possibly be false, does this mean it's true?

### The bigger picture

Snakes and adders — How logic allows your computer to perform complex tasks when fed on a diet of just 0s and 1s.

Maths in a minute: Simplifying circuits — An example of how the brilliant Claude Shannon used Bollean algebra to simplify circuit design.

Spaceships are doing it for themselves — A news story exploring how intelligent spacecraft with human-like reasoning capabilities can make important decisions for themselves.

Meet Claude Shannon — You may not have heard his name, but you're making use of his work many times over every single day. Claude Shannon is hailed by many as the father of the information age.

Constructive mathematics —
If you like maths because things are either true or false, then you'll be worried to hear that in some quarters this basic concept is hotly disputed. This article looks at *constructivist mathematics*, which holds that some things are neither true, nor false, nor anything in between..

### Pushing the boundaries

The hardest logic puzzle ever — Try your brain at this tricky, but lovely, riddle!

Mathematical mysteries: The Barber's Paradox — Suppose you walk past a barber's shop one day, and see a sign that says "Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else." Ask yourself - does the barber shave himself?

Picking holes in mathematics — When Kurt Gödel published his *incompleteness theorems* in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. But maths still stands, and the unprovable statements logicians might be about to enter the mainstream.

Mathematics for aliens — Is the logic of mathematics universal and could it help us to communicate with aliens?