Back in Chapter 8, we introduced the weak arithmetic Q, and soon saw that it is boringly incomplete. Then in Chapter 10 we introduced the much stronger first-order theory PA, and remarked that we ...

Deciphering the EUs new regulation of organic wine from 8 March 2012, is as confusing as understanding Gödel's Incompleteness Theorem or the Laws of Cricket. It relies on the normal rules of ...

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Maths is meant to be certain, either right or wrong. Turns out, it's not that simple. For Gödel's theorem has proved that there are "undecidable" theories, which one can neither prove nor disprove.

Topics include propositional logic, boolean algebras and rings, first-order logic and systems of deduction. Time permitting, we will touch on Tarski's notion of model, and the completeness and ...

Evolution theory suggests that conscious perceptions of the world are tuned to fitness to promote survival. Quantum mechanics ...

If by 'great' we mean 'heroic', then Andrew Wiles' proof of Fermat's Theorem deserves mention. But for sheer intellectual surprise, and alarming insight, it is hard to think of any result that ...

Bill Whitaker: So tell me, what was this bonus question? Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a ...

An understanding of how to use Pythagoras’ theorem to find missing sides in a right-angled triangle is essential for applying the theorem in different contexts. (3,1) is the coordinate that is 3 ...

Pythagoras’ theorem is a statement that is true for all right-angled triangles.It states that the area of the square on the hypotenuse close hypotenuseThe longest side of a right-angled triangle ...

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