Bang and Whimper

In the past few days, I’ve seen a couple of good little math problems posted on Twitter. I follow a number of mathematicians, including James Tanton (@jamestanton), who pretty regularly posts math problems that are sometimes easy enough that I have a fair chance of solving them (though he almost never provides any solutions, so it’s sometimes hard to tell if I’ve gotten it right). A couple of days ago, he asked a simple question:

This is not a terribly difficult problem to solve as long as you can sum a particular doubly-infinite series, but summing that series is probably the most interesting part of the problem.

Nothing says “fun and exciting” to me quite like videos about math and mathematicians. And lately, I’ve been experiencing a lot of fun and excitement watching the two videos linked below. Both are chopped into several pieces, all of which are linked below. The first is a fantastic lecture on “The Importance of Mathematics” by Timothy Gowers, a professor of mathematics at Cambridge University. In this lecture, he gives some surprisingly simple but elegant illustrations for non-mathematicians of the beauty and aesthetic charm of some good mathematics. It is a rather rewarding lecture, and is currently available on YouTube in eight (8) parts:

1. Timothy Gowers, “The Importance of Mathematics”, Part 1
2. Timothy Gowers, “The Importance of Mathematics”, Part 2
3. Timothy Gowers, “The Importance of Mathematics”, Part 3
4. Timothy Gowers, “The Importance of Mathematics”, Part 4
5. Timothy Gowers, “The Importance of Mathematics”, Part 5
6. Timothy Gowers, “The Importance of Mathematics”, Part 6
7. Timothy Gowers, “The Importance of Mathematics”, Part 7
8. Timothy Gowers, “The Importance of Mathematics”, Part 8

The second video I recently watched and enjoyed is a short documentary about Andrew Wiles’ proof of Fermat’s Last Theorem. Watch the introduction, see Professor Wiles almost break down in describing his discovery, and be hooked. This video is also available on YouTube in five parts:

1. UKTV Documentary, “Fermat’s Last Theorem”, Part 1
2. UKTV Documentary, “Fermat’s Last Theorem”, Part 2
3. UKTV Documentary, “Fermat’s Last Theorem”, Part 3
4. UKTV Documentary, “Fermat’s Last Theorem”, Part 4
5. UKTV Documentary, “Fermat’s Last Theorem”, Part 5

NP: Modest Mouse, Neverending Math Equations