Newswise — Has Williams College mathematician Frank Morgan devised the greatest riddle since that of the Sphinx? Five years after he put it to the test in "The Math Chat Book," Morgan is still waiting for someone, anyone, to give him the right answer in exchange for a $1,000 prize. Morgan says he's gotten a few entries, but no one has come very close at all. (See archives at http://MathChat.org).
Morgan found a much different response - 400 correct answers - when one of his puzzles was featured on NPR's Weekend Edition.
That puzzle - "Find a word, so if you add a letter at the beginning, the meaning becomes plural" - was actually deemed a bit too difficult, so, to give listeners a break, was modified to "put an 'a' at the beginning to make the meaning plural."
"The only thing we're familiar with is add an 's' at the end and make the word plural," said Morgan. "Now here it just says make the meaning plural, so I guess it could be the plural of a synonym." (The answer to this puzzle is at the end of this article.)
Puzzles are Morgan's way of providing what he believes are the two universal needs - ideas and a way to communicate them.
"The hard thing about ideas is, how do you even get started thinking?" said Morgan. "The trouble with a lot of education nowadays is that we get the answers before we have the questions. Puzzles are the questions and that's where real thinking begins, not with the answer, but with the question."
From a mathematician's point of view, puzzles are just math questions and math serves as a method to solve riddles, answer questions, and investigate mysteries. It is a way of problem solving that is applicable to almost anything, including such odd endeavors as the shape of soap bubbles.
Analyzing the shape of soap bubbles, however, gets to the root of what Morgan claims is the secret of math: Take whatever problem you have and replace it with an easier problem.
"Suppose someone said 'What's the ideal shape for an airplane?'" said Morgan. "Well, engineers work on that; that's too hard. I would say, as a mathematician, 'that problem is too hard, but I can approach the same topic by saying 'What shape is a soap bubble?' because that is the simplest shape.' That's what we mathematicians do; we learn principles by studying the simplest problems, answering the simplest questions; and then we try to learn lessons that maybe the engineers can use on their harder problems."
Morgan fears that many people are being robbed of the opportunity to make use of such an elegant problem solving technique because of its misrepresentation during the grade school years.
"You learn arithmetic; that's not really mathematics," said Morgan. "And, you're put in a situation where over time you are bound to have an experience in math class that makes you feel stupid, it's almost like in 'Clockwork Orange,' teaching him to hate music. That's not how it's supposed to be at all. Math is supposed to be a fun game."
Morgan is doing all he can to rectify the situation through puzzles, which serve as his way of translating the truth of mathematics into a form that most people are familiar with and can apply to their everyday experience.
"It's the universal activity, just another form of it," said Morgan. "It's all of life, that's what everybody does all the time."
Frank Morgan is currently working on his second book about Real Analysis, the theory behind calculus, teaching a topology tutorial, and teaching a course on investment mathematics, which has never been taught at Williams College before.
The answer to Morgan's NPR puzzle is "yes" as in "the ayes have it." The answer to his Math Chat riddle remains a mystery locked in Morgan's mind unless some reader is able to answer the riddle (http://www.maa.org/news/quest.html). In that case, the reader will be $1,000 richer.
Williams College is consistently ranked one of the nation's top liberal arts colleges. The college's 2,000 students are taught by a faculty noted for the quality of their teaching. The achievement of academic goals includes active participation of students with faculty in research. Admission decisions are made regardless of a student's financial ability, and the college provides grants and other assistance to meet the demonstrated needs of all who are admitted. Founded in 1793, it is the second oldest institution of higher learning in Massachusetts. The college is located in Williamstown, Mass. To visit the college on the Internet: http://www.williams.edu
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