The institute behind the Millennium Prize Problems, with free lecture videos, published proofs, historical mathematics archives and details of its research programmes.
Why I recommend it: Free access to serious mathematics — the lecture library alone is worth bookmarking if you are studying or teaching math.
Every open XPRIZE challenge with its prize purse, deadlines and entry requirements — multi-million-dollar competitions in health, climate, education and AI.
Details: Free to enter and open to teams anywhere — a real route to funding if you have a technical idea and a team.