Last week was a very big week for mathematics.
First of all, Bill Clinton made arithmetic the centerpiece of his speech at the DNC. While it may not be new to let arithmetic affect policy, it has been absent from politics for some time. John Stewart hailed its return saying
I never thought I’d say this but I have missed you so much, math.
That’s the kind of thing we love to hear. The entire video is below. Warning: this plays 11pm on comedy central, and the language reflects that.
If that was all that happened this week, it would still be a big week. But, perhaps even more astonishingly, there’s been a credible, ambitious stab at a huge, unsolved mathematical problem wonderfully known as the abc Conjecture. The conjecture gives certain restrictions on the primes factorizations of numbers involved in the generic addition problem A + B = C. (Hence the conjecture’s name.) What’s so cool about it is that it seems to express a deep and almost distressing relationship between addition and multiplication (via prime factoring) that, for some reason, prevents certain kind of behavior. For example, the incredibly famous Fermat’s Last Theorem follows from the abc conjecture as a corollary. I saw a talk on this in graduate school, which was not too long ago, and the speaker essentially said that we have no idea how to even begin attacking this problem. Now, it may have been solved. The champion is Shinichi Mochizuki, and the details are here. If you want some deeper technicalities, you can find them here.
If that weren’t enough, Paul Lockhart’s new book, which I have been waiting for him to publish for 8 years, back when he gave me a draft that opened up some of the most beautiful mathematical approaches to classic problems I’ve ever seen, has finally been published. You can get a copy here. I’ll blog about this in more detail later, but if you’re interested in math or math ed, do yourself a favor and get yourself a copy now.