What We Learn Along the Way: Fermat’s Last Theorem

In 1637 Pierre de Fermat wrote in the margin of Diophantus’s Arithmetica the statement that would puzzle some of the world’s greatest mathematicians for over three centuries:

It is impossible to write a cube as a sum of two cubes, a fourth power as a sum of two fourth powers, and, in general, any power beyond the second as a sum of two similar powers. For this, I have discovered a truly wondrous proof, but the margin is too small to contain it.

Fermat, celebrated for making such declarations with little confirmation, kept mathematicians scratching their heads and squaring their roots trying to discover proofs for his statements. By the 19^th century, all of Fermat’s theories had been resolved except the one above, a statement that became know as Fermat’s Last Theorem.

We will never know whether Fermat had actually discovered a correct proof of his theorem, but we do know that Andrew Wiles of Princeton University produced a 130-page proof in 1994, 357 years after Fermat wrote his tantalizing marginal note.

Although Fermat’s Last Theorem has not yet been used for practical purposes, many new ideas and numerous practical technological advances developed in solving the problem. Sometimes what we learn along the way to a destination becomes more important than reaching the end of our journey.  

Revised from The Heart of Mathematics by Edward Burger and Michael Starbird

The Holy Spirit

Deep in each of us resides the awareness that something knows we exist. 

The Holy Spirit is with us all the time. But we block it out with fast living, fast cars, fashion, fantasy, Facebook, iPhones, iPads, iTunes, iClouds, twitters and tweets, worries and wastes, greeds and gets. Nonetheless the Holy Spirit is there to comfort us and to guide us.

We can see with our inner eye, feel with our heart, and experience with our mind the Holy Spirit when we release our selfish ambition and vain conceit; when we surrender our desires and cravings; when we dismiss our worries and fears; when replace judging with insight; when we substitute grasping with giving; when we defeat sloth with fruitful living.

You Never Know

Wow!!!!!!! He comes across as the prototypical Wally Cox, if you are old enough to remember the TV character. Indeed, he sort of looks like him. Very modest. Humble. Soft spoken. Invisible in any room. 

Nonetheless, he exhibited something of an unusual quality that caused me to look him up. His curriculum vitae is 67 pages! He's on important federal committees. Advised the President. For some reason what struck me the most something he had written the association of radio spectrum and game theory!?!? He is a deep thinker.

The first time I met him he said he wanted to know more about fractals so I loaned him my math book for non-math majors. 

The second meeting we didn’t talk about how he could have written the book. Instead, I talked about how I wished I had that book as a freshman and had had a professor who inspired me to know more about math. He said he wanted to learn more about chaos theory. I loaned him my book Chaos. A simple book. An elementary book.

Then I read his CV.

Moral: You don’t know what you don’t know.