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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

5 votes

Important open exposition problems?

This is an interesting question. Responding sideways, I can give a closed exposition problem, namely the Kepler conjecture. Here is a talk by Thomas Hales: Lessons learned from the Formal Proof of t …
1 vote

Excellent uses of induction and recursion

I came across this one browsing old questions under the logic tag. Here's proof of the Principle of Induction: https://openmathematics.org/#induction The GitHub repository URL is available in the …
2 votes

What is Realistic Mathematics?

Update: Having read below a second time, I think you should change your usage from 'realistic mathematics' to 'empirical mathematics'. I think this is much more apt, plus it has the advantage that …
James Smith's user avatar
3 votes

An example of a beautiful proof that would be accessible at the high school level?

The most success I have ever had teaching proofs at secondary school level is with the Peaucellier–Lipkin linkage. The proof relies on nothing more than basic geometry, namely similar triangles, but t …