by Jonathan Kujawa

Lots of people enjoy a good puzzle. Take Sudoku puzzles. Like many good puzzles, the rules of Sudoku are simple. The challenge is to figure out the implications of each possible move and to use those implications to reason our way to the solution. You probably know how this goes: you try to put a 5 in one box, but that leads to problems down the road when that choice forces you into a situation that violates the rules. The only way out is to relent and admit that 5 must go into a different box.
At its heart, mathematics is a vast Sudoku puzzle. Through reasoning, clever observations, and following the implications wherever they go, we learn new things about the mathematical universe. For example, if xn + yn = zn has a solution where n, x, y, z are integers and n > 2, then certain geometric shapes called elliptic curves must have a unique associated function with special properties that make it a “modular form” [1]. Hard work by Andrew Wiles and many others showed that the relevant elliptic curves cannot be associated to a modular form; hence, we must relent and admit that Fermat’s equation has no solutions.
Mathematicians love nothing better than solving a math problem by conjuring new knowledge out of thin air using nothing but creative reasoning. That creativity and use of the human mind are sadly missing from much of our math education.
The problems of puzzles are very near the problems of life. —Erno Rubik
I was recently reminded of the puzzle-like nature of mathematics. In conjunction with the annual Teachers of Teachers of Math conference hosted by my university, my department hosted a celebration of the life and career of our colleague, Gary Musser. Gary was a long-time faculty member in our department who, sadly, passed away this year. I had the pleasure of chatting with Gary and his wife, Irene, when I first arrived at Oregon State. Although Gary retired several decades ago, he and Irene continued to have a deep interest in the department, in mathematics, and in teaching mathematics. In their honor, the department gives the Gary Musser Award each year to support outstanding prospective elementary or middle school teachers.
Why an award for prospective teachers? Well, while Gary’s PhD thesis was on a highly theoretical and advanced area of mathematics, his professional energies were focused on an even harder problem: how to train school teachers to be effective at teaching children mathematics. This problem is doubly hard. After all, young children need a good educational experience in math, and at the same time, the teachers of young children are often not “math people” themselves. Gary understood the importance of solving this problem. He spent his career having a profound effect on how mathematics is taught in Oregon and across the United States.
One of Gary’s strongest-held beliefs was in the importance of puzzles. Read more »






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