Asking Questions

These pages are full of questions, but there aren't nearly so many answers! That is because asking questions is central to doing mathematics.

All mathematicians know that questions pile up much faster than nicely proved answers. Doing mathematics involves asking questions, thinking about questions, and relating questions to one another.

When you do mathematics, you will have many questions of your own. Send in your questions. Read the mail to see what questions other people are asking. Perhaps you can answer them.

Here are some questions to get you started. Some are easy and some are hard.

Can every link be arranged into a nice orderly pile of closed circular braids?
Is is possible to draw the graph described in the Three For the Money problem?
Why does every complete graph have a diameter of 1?
How many colors will it take to color the map of Swirltown?
How much is infinity plus one?
Does every graph with an eulerian circuit also have a hamiltonian circuit?
How useful are the notions of crossing number, link number, and braids for classifying knots?
What is the smallest map you can draw that requires 4 colors to color it?
How do you begin to figure out whether the student named Connie is a Bright or a Brave in the play A Usual Day at Unusual School?
If your ticket says abbabbabba will Machine 1 award you a prize?
Can you draw a finite state machine that looks different from Machine 1, but behaves exactly the same?
When all of the Continuum Tour Busses showed up at the Hotel Infinity, do you think that George would have found a room for everyone if he had been able to continue with his plan?
When you have solve the Ice Cream Stands Problem for a graph by finding a dominating set how can you be sure that your solution requires the smallest possible number of ice cream stands?

When you are thinking about a mathematical object and the properties that it has, often questions come to mind that have to do with maximality and minimality.