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Tuesday, September 2, 2014

The Last Theorem

I am reading an interesting book regarding mathematics, Fermat's Enigma; The epic quest to solve the world's greatest mathematical problem by Simon Singh. The book, which I have not finished, recounts the tale of Andrew Wiles, a Princeton professor who has dreamed of solving Pierre de Fermat's famous theorem since the age of 10.

I should state up front that I have no great love or affinity for math. Like many people with my right brained and particular spatial bent, I was an exceedingly good analytic geometry student and an exceedingly poor student of Algebra and Physics.

Having said all that, the book is riveting and I think worth sharing, if nothing else for the historical time line and synopsis it provides. Very well written and informative even for somebody who is not a number's guy.

This book starts off with an introduction to Pythagorus of Samos in the sixth century b.c.e., the man who taught us that the sum of a right angle's squared sides equals the square of the hypotenuse. Pythagorus was a cycladian scholar who gleaned many of his ideas from the ancient Egyptians and Babylonians. Pythagorus work is the foundation for Fermat's last theorem.

But I digress.

Pythagorus had a wealthy patron, Milo of Croton, one of the most powerful and physically strongest men in Greece. The mathematician established a Pythagorean Brotherhood with his help. This collective believed that one could divine the most arcane secrets of the universe by understanding numbers. Spilling the order's mathematical secrets was a crime occasionally punished with death. As you can see, these people took their math very seriously.

They discovered a class of numbers called perfect numbers, numbers whose divisors add up to the number itself. 6 (1, 2, 3) and 28 ( 1, 2, 4, 7, 14) are two examples of perfect numbers. The next two are 496 and 8128. Today computers have tracked perfect numbers to 130,000 digits. Euclid weighed in on the subject of perfect numbers two centuries later but that is a tale for another time.

A man named Cylon had his admission to the brotherhood rejected and plotted and executed a revenge that ended up killing Pythagorus in 510 b.c.e. However the thirst for number logic that Pythagorus championed could not be quenched and the concept of mathematical proof spread though the civilized world.

In the third century b.c.e. Alexandria was now the center of the world's learning. Alexander the Great had conquered Asia Minor, Greece and Egypt and he wanted his namesake city to be the most learned in the world.

After he died and Ptolemy I took the throne, Alexandria became the site of the world's first university. Euclid himself was the first head of the math department.

Scholars from all over the world flocked to the city, known for having the greatest library in the world, the Alexandrian Library. The idea for the library came from an exiled Athenian, Demetrius Phalaerus.

They were so voracious for books that travelers to the city would have their books seized and copied, with the original going to the library! The library was said to have over 600,00 books.

And so the book brings us to one of the most fascinating characters, Diophantes, an Alexandrine of unknown origin who lived somewhere between 150 b.c.e. and 250 c.e. Diophantes was a math whiz and a master of number theory, purportedly also a master riddler.

He compiled the math theorems of his day into a comprehensive thirteen book treatise called Arithmetica.  Only six of the books would survive the coming dark ages. The surviving volumes helped pique the interest of one Pierre de Fermat, one of the heroes of the story.

Alexandria was getting threatened a lot by its neighbors in those days. In 47 b.c.e. Caesar tried to make a salad of the joint and assaulted good Queen Cleopatra and set fire to the Alexandrian fleet. The library was situated near the harbor and hundreds of thousands of rare tomes were lost forever to fire and ash.

Cleopatra and Marc Antony subsequently tried to make things right and restored the library. For the next four centuries everything was copacetic and then disaster struck again.

The Christian Emperor Theodosius ordered all pagan monuments to be destroyed in 389 c.e.. The Alexandrine library was located in the Temple of Serapis. Scholars tried to save the books but as the author states in the book, they were butchered by the angry Christian mob.

The dark ages, as Singh puts it, had begun. Roughly 300 years later, a caliph came by to finish the job. Caliph Omar mandated that all non koranic books be destroyed in 642 and so it was. Greek mathematics and untold repositories of knowledge went literally up in smoke and stayed that was for at least a thousand years. It was only kept alive by a few scant scholars in India and Arabia who practiced in the secret shadows. And yet these keepers of truth also added a very important concept to number theory, the addition of zero.

Arabic symbology gave new life to the ancient greeks' concepts and immensely refined the science of computation. The French scholar Gerbert of Aurillac learned the new way to count from some traveling Moors in the 10th century and he brought the system to France and northern Europe. In 999 he was elected Pope Sylvester II, a fortuitous nomination for science and mathematics.

Pierre De Fermat
Constantinople was sacked in 1453 by the Turks. It now held the last remnant of the famous library. Scholars, fearing destruction of the remaining books, made a concerted effort to recover what they could. And so Arithmetica and Diophantes's surviving texts made its way to France and one Pierre de Fermat.

Unfortunately we see an all too familiar thread running through this mathematical timeline. Belief systems and their adherents, running roughshod over the scientific and rational and plunging us into the dark ages. Where have we heard this one before?

To be continued...

Part 2

1 comment:

Jon Harwood said...

Well all I can say is 666=666. WE'RE ALL DOOMED!