Mathematics
The Construction of the Real Numbers via Dedekind Cuts
Quick fact
A Dedekind cut is a way to 'fill the gaps' in the rationals by dividing them into two infinite sets—every rational is either in the 'left' set or the 'right' set, and the cut itself represents a real number.
Why this is interesting
You've used numbers like √2 and π, but have you ever wondered what they really are? The rational numbers have gaps, so how can we fill them to create the continuous number line?