On October 12th, I saw a post by Dan Christensen on Google+ about a list of five open problems posed by the mathematician John Conway that have monetary rewards associated with them. In particular, Conway is offering $$1,000$ for solutions (either positive or negative) to any of the problems. Here are the five problems (as stated by Conway):
Update: Problem 5 has been solved! 13532385396179 is a counterexample. To learn more, check out the Aperiodical and the following video from Numberphile:
If you solve one of these, you can reach Conway by sending snail mail (only) in care of the Department of Mathematics at Princeton University.
Around the same time that I stumbled onto these problems, I was brainstorming ideas for a couple of upcoming talks that I was slated to give (one for undergraduates and one for high school students). I decided that discussing open problems with monetary rewards with an emphasis on Conway’s problems would likely make for a nice talk. Here is the abstract that I settled on for both talks.
There is a history of individuals and organizations offering monetary rewards for solutions, either in the affirmative or negative, to difficult mathematically-oriented problems. For example, the Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. A correct solution to any of the problems results in a $$ $1,000,000 prize being awarded by the institute. To date, only one of the problems has been solved (the Poincaré Conjecture was solved by Grigori Perelman, but he declined the award in 2010). These are hard problems! The renowned mathematician John Conway (Princeton) maintains a list of open problems and for each problem on the list, he is offering $$ $1000 to the first person that provides a correct solution. In this talk, we will explore a few of Conway’s problems, and in the unlikely event we come up with a solution, we’ll split the money.
On Friday, October 24, 2014, I gave a talk during the Friday Afternoon Mathematics Undergraduate Seminar (FAMUS) at NAU. Speaking at FAMUS is always fun and my talk seemed to be well-recieved.
After having a practice run during FAMUS, I was able to improve the slides I intended to use during my talk at the 2014 NAU High School Math Day, which took place a few days later on Tuesday, October 28, 2014. Here are my slides:
I had a blast presenting to the high school students. It cracked me up that there were a few students that immediately started obsessing over the Sylver coinage problem and likely didn’t hear a word I said after that. My goal was to give an engaging and high energy talk. I also slid in some humor and I was happy that everyone laughed when they were supposed to. Interestingly, the thing I said that the students thought was the funniest was something that I didn’t intend to be humorous. When I stated that “If you solve one of these, you can reach Conway by sending snail mail (only) in care of the Department of Mathematics at Princeton University,” the audience burst into laughter. Requiring snail mail seemed so ridiculous to them, they thought it was a joke.
As a side note, I used mtheme (available for free on GitHub) together with beamer/LaTeX to generate my slides. I’m really happy with the look of mtheme and thrilled to get away from the standard beamer themes.
Mathematics & Teaching
Northern Arizona University
MAT 123: First Year Seminar
MAT 136: Calculus I
MAT 526: Combinatorics
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