I like to ask for beautiful mathematical theorems with short proof. A proof is short in my sense if it is at most one page assuming basic notations and very basic results a second year student will know and understand. I do not like to discuss what beauty means...I have now written down a script with 107 such theorems (in my sense) and their proof and I have ideas for another 20. One the one hand I would be very thankful for theorems I have yet not considered. On the other hand I like to see if there is some consensus which theorems with a short proof are beautiful.

I like to ask for beautiful mathematical theorems with short proof. A proof is short in my sense if it is at most one page assuming basic notations and very basic results a second year student will know. I do not like to discuss what beauty means...I have now written down a script with 107 such theorems (in my sense) and their proof and I have ideas for another 20. One the one hand I would be very thankful for theorems I have yet not considered. On the other hand I like to see if there is some consensus which theorems with a short proof are beautiful.