Daylight is polarized, the strength being greatest at points in the sky at right angles to the sun,
and zero at four points: above and below the sun and anti-sun. The zero-polarization points
are 'fingerprint' singularities, around which the polarization direction makes a half-turn.
Using elementary singularity theory, the polarization pattern across the whole sky can be
described in a way that fits recent observations with an accuracy comparable to that of
conventional elaborate multiple-scattering calculations. This recent work is a contribution
to a story that started in 1817 and has been central to our understanding of polarized light.