Google Doodle fetes 358-year-old math mystery

Today's Google Doodle celebrates the 410th birth anniversary of one of history's greatest mathematicians —as well as the tantalizing mystery he left behind, which stumped other mathematicians for over three centuries. A visit to the Google homepage today, August 17, will treat viewers to what appears to be a simple, unassuming school blackboard in lieu of the usual Google logo.

Google's Doodle for August 17, 2011, is a tribute to 17th-century mathematcian Pierre de Fermat —and the enduring mystery he left behind.

On the board is the apparently hastily-scribbled equation xⁿ + yⁿ ≠ zⁿ [n>2], accompanied by the following hover text: "I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain." Both are references to 17th century mathematician Pierre de Fermat, whose 410th birthday is being celebrated today. A glib marginal comment Apart from laying the foundations of calculus and modern number theory, Fermat is best known for a small note that he scribbled in the margin of his personal copy of the book Arithmetica by Diophantus:

"It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers," he wrote.

However, Fermat apparently ran out of writing space, and concluded without further elaboration:

"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

The profound simplicity of Fermat's conjecture —formulated as xⁿ + yⁿ ≠ zⁿ [n>2]— piqued the curiosity of generations of mathematicians and historians alike, who sought to find his "marvelous proof". Unfortunately, despite Fermat's glib marginal comment, there is no historical record or documentation of his proof —leaving succeeding generations of mathematicians to independently formulate their own. Did he, or didn't he? In 1995, mathematician Andrew Wiles published a 100-page paper that finally proved Fermat's Last Theorem. The work took him seven years to complete. It took 358 years before this proof was finally found to what the Guinness Book of World Records had called "the world's most difficult math problem" up to that time. "It may well be that Fermat realised that his remarkable proof was wrong, since all his other theorems were stated and restated in challenge problems sent to other mathematicians," explain J J O'Connor and E F Robertson of the Scotland University School of Mathematics and Statistics. And yet, despite the problem's conclusion, mathematicians around the world still wonder: What exactly was Fermat thinking? Did he have a simpler, more elegant proof in mind —or did he inadvertently mastermind one of the biggest pranks in history? — GMA News