ideaPlanned
Truth Table Builder
Planned tool for propositions, logical connectives, equivalence and valid arguments.
Beauty in maths topic
Logic, Proof and Paradoxes
Logic, proof and paradoxes sit close to the foundations of mathematics: what counts as a valid argument, and what happens when intuition breaks.
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live pages
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prototype tools
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planned ideas
What this area includes
Truth tables and logical connectives
Direct proof, contradiction, induction and counterexamples
Paradoxes involving infinity, sets and probability
Hilbert Hotel, countability and different sizes of infinity
Connections to computing, cryptography and mathematical philosophy
Questions to explore
What makes an argument valid?
How can a statement be surprising but still true?
Where does intuition fail, and how does proof help?
Planned directions
These ideas are not built yet, but they show where this topic could grow next.
ideaPlanned
Proof Strategy Lab
Planned guide to direct proof, contradiction, induction and counterexample hunting.
ideaPlanned
Paradox Gallery
Planned collection of Russell-style, infinity and probability paradoxes that sharpen mathematical thinking.
ideaPlanned
Hilbert Hotel and Infinity
Planned exploration of countability, infinite sets and why infinity behaves unlike ordinary number.
ideaPlanned
GCSE Exam Question Deconstructor
Planned tool that breaks exam-style questions into what is given, what is asked and which method might help.
ideaPlanned
Further Maths Proof and Induction
Planned practice space for induction, contradiction, divisibility and proof structure.
Connected topics
themeLive
Beauty in Maths
A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.
themeLive
Game Theory and Decisions
Strategy, cooperation, competition, voting, incentives and mathematical decision making.
themeLive
Number and Structure
Irrational numbers, ratios, exactness, approximation and hidden structure.
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Cryptography and Secret Messages
Codes, ciphers, primes, modular arithmetic, public keys and secure communication.
How to use this section
Use this section to slow thinking down: make a claim, test it, search for a counterexample, then decide what has actually been proved.