By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant.
The Wallace-Bolyai-Gerwien theorem shows that any two polygons with equal area must admit a dissection into finitely many pieces where one is allowed to arbitrarily rotate and translate the pieces to go from one polygon to the other. The problem about whether a hinged dissection exists remained open until 2007. You can read the paper here, which presents a method which always works to find a hinged dissection.”
MY BRAIN CAN’T HANDLE THIS
Ask yourselves, what problem have you solved, ever, that was worth solving, where you knew all of the given information in advance? Where you didn’t have a surplus of information and had to filter it out, or you didn’t have sufficient information and had to go find some?
If you joined us late, that scoreboard is correct
—THE BBC COMMENTATOR JUST NOW (via manuelfrickinneuer)