Open Problems

These are open problems that I've encountered in the course of my research. Not surprisingly, almost all the problems are geometric in nature. A name in brackets is the first person to describe the problem to me; this may not be original source of the problem. If there's no name, either I thought of the problem myself (although I was certainly not the first to do so), or I just forgot who told me.

Problems in bold are described in more detail than the others, and are probably easier to understand without a lot of background knowledge.

If you have any ideas about how to solve these problems, or if you have any interesting open problems you'd like me to add, please let me know. I'd love to hear them!

Caveat lector!

This web page and its children have not been significantly updated since 2001. Many of the problems listed on this page have been partially or even completely solved since then. Please do not cite these pages as evidence that a problem is still open; that makes no more sense than citing a paper published in 2001!

Existence Problems: Does Object X exist?

Combinatorial Problems: How complex is Object X?

Algorithmic Problems: How fast can Problem X be solved?

Other People's Problems

Recommended Books

We should try to love the questions themselves, like locked rooms and like books that are written in a very foreign tongue.
- Rainer Maria Rilke
Problem solving is hunting. It is savage pleasure, and we are born to it.
- Thomas Harris, The Silence of the Lambs
If you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions - for the fun of it - then one day you'll turn around and discover that nobody actually did that one! And that's the way to become a computer scientist.
- Richard Feynmann, Feynmann Lectures on Computation

Open Problems - Jeff Erickson ( 09 Apr 2001