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Maths in a minute: Gödel's incompleteness theorems
Find out about these important results that destroyed a mathematical dream.
Content about “ logic
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Maths in a minute: Peano arithmetic
How would you explain the natural numbers to an alien devoid of a number instinct? You could try Peano arithmetic...
Collection
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.
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Maths in a minute: Truth tables
Introducing an indispensable tool of mathematical logic.
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Something from nothing?
If you can prove that a statement can't possibly be false, does this mean it's true?
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George Boole and the wonderful world of 0s and 1s
The story of George Boole is an extraordinary example of collaboration across the centuries.
Collection
Happy birthday, George Boole!
Modern computers wouldn't be possible without George Boole, who died before light bulbs even came on the market. We celebrate his 200th birthday with a look at the man and his work.
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Why we want proof
What are mathematical proofs, why do we need them and what can they say about sheep?
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Is the Universe simple or complex?
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.
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This is not a carrot: Paraconsistent mathematics
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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The philosophy of applied mathematics
We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy.
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Picking holes in mathematics
In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics?