Friday, 22 February 2008

Uncle Petros and Golbach’s Conjecture by Apostolos Doxiadis

Uncle Petros and Golbach’s Conjecture was originally a best selling Greek novel and has now been published over 20 languages so don’t get switched off by the title and subject matter. Forget about it being about maths and in fact think of Moby Dick to place this book. It’s about obsession and pride in chasing the impossible dream. You understand the thrill and terror of chasing impossible dreams.

Right now let’s get the maths out of the way. Golbach’s Conjecture first stated in the 18th century suggests that:

Every even integer greater than 2 can be written as the sum of two primes.

But mathematicians lack proof that in all circumstance it would hold. For example think about Physics where if dealing with the very big or the very small ordinary scientific understanding ceases to work. So could this be the case in Mathematics? Yes over my head as well! But the author is a childhood mathematical genius who submitted original research at 15 before even starting his degree and also an acclaimed film maker and writer. So he both understands the mathematical issues and can write so that we understand and care.

We first meet Uncle Petros in the 1970’s through the eyes of the beloved favourite nephew as a teenager. Petros is dismissed as the family failure that supports him through the family business while he does nothing but read books and plays chess. He leaves his home only once a month to do the books of a charity founded by his father. The beloved favourite nephew is met by a wall of adult silence when he tried to find out what the anger of the family is about. A chance phone call and a subsequent letter lead him to discover that far from a failure Uncle Petros had been a professor of mathematics in the 20’s and 30’s at a prestigious German University. This makes him as obsessive as his Uncle as he struggles to discover the Truth of the family scandal.

He tries to become a mathematician to help him challenge and understand what had obsessed his Uncle. This causes huge family problems- this is a Greek family remember where honouring your family and Father is a top rule in life. He finally manages to get the story of his Uncles obsessive hunt out in the open but at a high personal cost to his own ambitions. It is clear that Uncle Petros is a genius who will never be known as his hopes are dashed in the 30’s by the publication of Kurt Godel’s Theorem. Yes more maths but not much so don’t leave. This solves the problem of completeness by showing that any theory of numbers will contain unprovable propositions. Alan During (him of how do we know a computer has human intelligence- asked before computers were developed- now that’s what being clever is about) then demonstrates that theorists have no idea which proposition is merely hard to prove and which are impossible to prove.

Hence, Uncle Petros has no way of knowing if spending all his life in trying solve the Golbach’s Conjecture is a possible but hard task or impossible task. He gives up, his dreams and hopes ended. The beloved nephew is finding the truth is released from his obsession and so escapes the fate of his Uncle but then realises that a psychological lie has taken place which he needs to lance but this has tragic consequences.

Uncle Petros and Golbach’s Conjecture is highly recommended Greek tragedy in less then 200 pages about theoretical maths and why love and life is about how you answer the Bette Davis Theorem:

Oh, don't let's ask for the moon. We've already got the stars.

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