Paradoxes have always fascinated me. They seem to be true entities, just waiting for resolution (not a disproof) of some sort.
The website Some Paradoxes offers a useful anthology of paradoxes. The creator and maintainer--Geoff Wilkins--claims the website recives more than 3500 visits each day. I note also that Geoff is the Co-ordinator of the Hope Projects, an independent charitable company in Birmingham, England, that works with destitute asylum-seekers in the West Midlands.
Not knowing your experience with Paradoxes, I suggest you begin by sampling the following:
Along the way, I expect youy have browsed other paradoxes as well (given the visual set-up of the website).
- Introduction for some background
- Happiness or a Ham Sandwich Proof
- The Liar Paradox
- Hilbert's Hotel Paradox
- The Barber Paradox
- Interesting and Uninteresting Numbers
- Some of the visual paradoxes such as the Necker Cube or Penrose Triangle
Unfortunately, the website does not include some of the greatest mathematical paradoxes, such as the Banach-Tarski Paradox, Gabriel's Horn, or Simpson's Statistical Paradox. So, explore this website as a start and search for other paradoxes in texts or lurking on-line.