More recreational math reading suggestions

Georgia Tech Computer Science Prof. Dick Lipton has a blog which our more advanced math circle students may enjoy: Gödel's Lost Letter and P=NP.

AAMC Advisor Prof. Krishnamoorthy recommends the blog and, in particular, this post discussing some of Prof. Lipton's favorite books.

Prof. Moorthy is currently reading and enjoying one of the books on Prof. Lipton's list, The Honors Class: Hilbert's Problems and Their Solvers by Ben Yandell.

I (Mary) especially liked Prof. Lipton's description of the book:

This is a book on the famous list of 23 problems of David Hilbert. What I like so much about this book is the history behind the solutions to the problems. In some cases Hilbert problems were “solved” for decades, yet eventually it was discovered that the solutions were wrong or had gaps. Part of my “hidden” agenda is to remind us all that even the immortals make mistakes, have proofs with gaps, and are human.

I heartily endorse and agree with Prof. Lipton's hidden agenda!

Winter break suggestions

Winter break is a great time for students to discover the joys of recreational math reading. Here are some suggestions which can delight students from middle school through the rest of their lives. The books below are classics. Many should be available in public libraries and/or inexpensively in used copies on the Internet.

Mathematical People and More Mathematical People have many delightful stories of the lives of noted 20th century mathematicians. Anyone who thinks mathematicians lead boring lives is in for a surprise when they read these interviews. Magic card tricks, chess puzzles, juggling, trampolines, and Mad Magazine all figured into the lives and mathematical development of one or more of these colorful characters.

Richard Feynman was a physicist, but his funny autobiographical works (What do you care what other people think? and Surely you are joking, Mr. Feynman.) make many references to his unorthodox mathematical education.

Raymond Smullyan's mathematical logic puzzle books (What is the name of this book? and The Lady or The Tiger and many more treasures along those lines) are also great fun.



Martin Gardner's Aha! Insight and Aha! Gotcha! books are great "entry-level drugs" into his abundant collection of recreational math books. You can see our well-worn copy above--the wear and tear reflects its extensive reading and re-reading over the years.

Alexandra Schmidt, math teacher and MATHCOUNTS coach at Hebrew Academy of the Capital District, recommends The Man Who Counted.

If your library uses the Dewey system, try browsing around 510 or 793. If your library uses the Library of Congress numbering system, try browsing around the QA93 section.

You are likely to find some real treats.

A puzzle celebrating Martin Gardner's 95th birthday

John Tierney of the New York Times begins his feature article on the prolific and always delightful recreational mathematician Martin Gardner with a puzzle:

For today’s mathematical puzzle, assume that in the year 1956 there was a children’s magazine in New York named after a giant egg, Humpty Dumpty, who purportedly served as its chief editor.

Mr. Dumpty was assisted by a human editor named Martin Gardner, who prepared “activity features” and wrote a monthly short story about the adventures of the child egg, Humpty Dumpty Jr. Another duty of Mr. Gardner’s was to write a monthly poem of moral advice from Humpty Sr. to Humpty Jr.

At that point, Mr. Gardner was 42 and had never taken a math course beyond high school. He had struggled with calculus and considered himself poor at solving basic mathematical puzzles, let alone creating them. But when the publisher of Scientific American asked him if there might be enough material for a monthly column on “recreational mathematics,” a term that sounded even more oxymoronic in 1956 than it does today, Mr. Gardner took a gamble.

He quit his job with Humpty Dumpty.

On Wednesday, Mr. Gardner will celebrate his 95th birthday with the publication of another book — his second book of essays and mathematical puzzles to be published just this year. With more than 70 books to his name, he is the world’s best-known recreational mathematician, and has probably introduced more people to the joys of math than anyone in history.

How is this possible?

For the answer to the puzzle and the fascinating story of a mathematical legend, see For Decades, Puzzling People With Mathematics in today's New York Times.

You can also find more great Gardner puzzles on John Tierney's NYT blog here.

As the article notes:

“Many have tried to emulate him; no one has succeeded,” says Ronald Graham, a mathematician at the University of California, San Diego. “Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.”

Happy Birthday indeed! And many happy returns of the day!

The value of NEGATIVE information

The HangMath game, which I showed the NYC Math Circle teachers, is also an opportunity to talk about the importance of "negative information."

In other words, if someone has asked about "2's in the tens column," the game requires the emcee to fill in ALL the 2's in the tens column. An efficient information user should make use of negative information (i.e, the blanks that still remain blank in the ten's column do NOT contain 2's) as well as positive information (the blanks that have been filled in with 2's in the tens column DO
contain 2's.)

Thanks to a tip from Professor Moorthy, here's a link to a new twist on a classic puzzle about drawing inferences from negative information: The Case of the Pinocchio Politicians.

You can find many delightful related puzzles that use this kind of reasoning in Martin Gardner's The Unexpected Hanging and Other Paradoxes. Raymond Smullyan's awesome mathematical logic books also have many such puzzles.