Results to Favorite Proof:

What's your name/twitter? | Name of proof | Link to proof somewhere online... | Why do you like this proof? | Additional testaments of love for this proof | Additional testaments of love for this proof | ... | ||||||||||
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@dandersod | Euclid's Proof of Infinte Primes | link | Love proof by contradiction. Simple, powerful, easy to understand. | From the book | ||||||||||||

@sophgermain | Why square root of 2 is irrational | link | It's the first proof i show students and it's simple. | |||||||||||||

@nik_d_maths | Induction for sum of squares | link | Proof by induction is fun, and this involves enough algebra for students to feel they have done something, while being short enough to use early on | I love induction? | ||||||||||||

@stwwilkinson | Uncountability of the real numbers (Cantor) | link | very simple to explain, yet challenges a lot of intuitive notions about infinity | The set up for this proof -- the countability of the rational numbers -- is also mind blowing. | ||||||||||||

@MrHonner | Midline of a Triangle | link | Elementary, but powerful idea in geometry; several different ways to think about why it's true | Great way to demonstrate the power of coordinate geometry for proof | Leads to beautiful results like Varignon's Theorem | |||||||||||

@Moko58 | Product of 2 odd number is an odd number | link | Even beginners can attempt this proof. | this is a great proof. | ||||||||||||

@mpershan | Incompleteness of axioms of arithmetic | link | It's problably the hardest mathematical idea that I even sort of understand, which is definitely part of why I like it, but the self-referential sentence is brilliant and all sorts of cool things follo wform it. | |||||||||||||

@mathymcmatherso | Geometric Proof of the Pythagorean Theorem | link | Has a visual and algebraic component that go hand-in-hand. Personally: most convincing and direct proof of pythagorean theorem I've ever seen | |||||||||||||

@j_lanier | There exists an irrational number that when raised to an irrational power results in a rational number. | link | I like this proof because it is simple; it yields a positive result, rather than a "there exists no..."; and it's concrete but so delightfully non-constructive--we find out that there exists such a thing without having a single example of it! So cheeky. | I can't promise that it's my favorite ever, but it's a dang neat proof. | ||||||||||||

@DanielPearcy | Can't pick between irrationality of root(2), infinitely many primes, uncountability of reals | Looks like I'm a sucker for proof by contradiction. | Funnily enough I don't know many recent (last 100 years) proofs | |||||||||||||

A pretty common theme: Simplicity in presentation or Visual Component.

<snark>Note: No 2 column geometry proofs are found in this list.</snark>