I want to build a website that takes every open problem from Wikipedia's list of unsolved problems in mathematics and makes them browsable, searchable and genuinely useful. It should be a static site with no backend and no accounts, where everything a person writes stays in their own browser and works offline.
The problem data should be generated by a script that parses the source article rather than typed by hand, along with a second script that pulls each problem's own article intro. I want a landing page that shows the fields visually, a featured problem of the day, and collections built from rules over the data so they can't go stale. Browsing should support ranked search, filters by field and status, several sort orders, and the whole state kept in the URL so views are shareable. Each problem gets a detail page with its statement, citations and related problems with the reason they're related.
People should be able to track their own progress on a problem and keep a private journal with LaTeX notes, images, version history, JSON export and import, all optionally encrypted with a passphrase.
Finally, add a lab where the mathematics actually computes live, things like Collatz orbits, a prime sieve with Goldbach decompositions, the Riemann zeta zeros and Robin's inequality, with real tests checking the numbers against published values. Also a hand written glossary and a quiz as plain static pages.