Proof

10 cards. Each one is a 40-second story with a five-minute read behind it.

1. How to use a single counter example to dismantle a mathematical statementIn mathematics, you don't need an exhaustive list to prove a rule wrong. This video demonstrates the power of the counter example, showing how one solitary exception can invalidat…
2. How do we move from a loose idea to a universal truth?Mathematical proofs can feel intimidating, but they are the foundation of certain knowledge. This video explores the transition from intuition to formal certainty, offering a reca…
3. Moving from intuition to rigor: how to construct a mathematical proofUnderstanding a finished proof is different from knowing how to build one. This video deconstructs the internal logic of mathematical reasoning, guiding you through the transition…
4. Why the binomial coefficient is a cornerstone of modern mathematicsThe formula for n choose k appears across countless mathematical fields. This video explores a sophisticated combinatorial explanation of why this specific calculation works, movi…
5. The five geometric rules that define identical trianglesGeometry relies on specific criteria to prove that two triangles are perfectly identical. This video breaks down the five core methods—SSS, SAS, ASA, AAS, and HL—using two-column …
6. Mastering the logic of algebraic proofLearn how to navigate typical GCSE-style algebraic proof questions by translating mathematical language into precise algebraic expressions.
7. Mastering the art of proving algebraic identitiesLearn the systematic method for proving algebraic identities by manipulating one side of an equation until it matches the other, using essential algebraic techniques.
8. How do mathematicians prove what is true?Explore the fundamental mechanics of mathematical proofs and understand the common hurdles faced by university students when transitioning into rigorous academic mathematics.
9. Mastering the logic behind triangle congruence and geometric proofsLearn the step-by-step mechanics of completing two-column proofs and demonstrating that two triangles are identical in shape and size.
10. A note in a book margin took mathematicians 358 years to prove.Around 1637 Pierre de Fermat scribbled in the margin of a book that he had a marvellous proof, too large to fit, that one simple-looking equation has no whole-number solutions. No…

All of Science Open the feed Latest A–Z