Mathematics
Knots and the Alexander Polynomial
Quick fact
The Alexander polynomial was introduced by J. W. Alexander in 1928 and was the first knot invariant that could distinguish knots that share the same fundamental group, such as the granny knot and the square knot.
Why this is interesting
You've probably tied a knot in a shoelace and know it's hopelessly tangled. But how can a mathematician prove that two knots are truly different, even if they look almost identical?