foundations

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

Practical Engineering explains why San Francisco's Millennium Tower is sinking and tilting, covering how geology and foundation design (friction piles in the Colma Formation) affect skyscrapers. It also covers the fix being attempted.