Although Uncle Petros remained expressionless, I noticed a slight tremor run down his hand.' Who's spoken to you about Goldbach's Conjecture?' he asked. A key plot point to Goldbach's Conjecture is Uncle Petros' deceit in giving his nephew the Sisyphean-task of solving Goldbach's theorem in order to prove his. As their titles suggest, these two novels are about mathematics—or, to be more precise, they are about mathematicians. Neither book makes any serious attempt .
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Uncle Petros and Goldbach's Conjecture () tells the tale of brilliant mathematician Petros Papachristos, who devotes his life to solving a notoriously difficult. Read Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis for free with a 30 day free trial. Read unlimited* books and audiobooks on the web, iPad, . Doxiadis a., Uncle Petros and Goldbach's Conjecture () - Ebook download as PDF File .pdf) or read book online. eBook.
Despite the fact that he never shared even a slight part of the labour and the responsibilities involved in running the factory that the three inherited jointly from my grandfather, Father and Uncle Anargyros unfailingly paid Uncle Petros his share of the profits.
This was due to a strong sense of family, another common legacy. As for Uncle Petros, he repaid them in the same measure. Not having had a family of his own, upon his death he left us, his nephews, the children of his magnanimous brothers, the fortune that had been multiplying in his bank account practically untouched in its entirety. Its starting-point is in a letter written in , contained in the former, wherein the minor mathematician Christian Goldbach brings to the attention of the great Euler a certain arithmetical observation.
The custom of this annual meeting had been initiated by my grandfather and as a consequence had become an inviolable obligation in our tradition-ridden family. We journeyed to Ekali, a suburb of Athens today but in those days more of an isolated sylvan hamlet, where Uncle Petros lived alone in a small house surrounded by a large garden and orchard. The contemptuous dismissal of their older brother by Father and Uncle Anargyros had puzzled me from my earliest years and had gradually become for me a veritable mystery.
The discrepancy between the picture they painted of him and the impression I formed through our scant personal contact was so glaring that even an immature mind like mine was compelled to wonder.
In vain did I observe Uncle Petros during our annual visit, seeking in his appearance or behaviour signs of dissoluteness, indolence or other characteristics of the reprobate. On the contrary, any comparison weighed unquestionably in his favour: the younger brothers were short-tempered and often outright rude in their dealings with people while Uncle Petros was tactful and considerate, his deep-set blue eyes always kindling with kindness.
They were both heavy drinkers and smokers; he drank nothing stronger than water and inhaled only the scented air of his garden. Furthermore, unlike Father, who was portly, and Uncle Anargyros, who was outright obese, Petros had the healthy wiriness resulting from a physically active and abstemious lifestyle.
My curiosity increased with each passing year. From my mother I learned of his daily activities one could hardly speak of an occupation : he got up every morning at the crack of dawn and spent most daylight hours slaving away in his garden, without help from a gardener or any modern labour-saving contraptions — his brothers erroneously attributed this to stinginess.
He seldom left his house, except for a monthly visit to a small philanthropic institution founded by my grandfather, where he volunteered his services as treasurer. His house was a true hermitage; with the exception of the annual family invasion there were never any visitors.
Uncle Petros had no social life of any kind. But such empirical proof is inadequate for mathematics no matter how often it is observed. Hence the importance of the Conjecture if it can be proven abstractly as an invariable condition for any number at all and not just specific numbers. Mathematical logic works backwards from an hypothesis to discover the logic by which the hypothesis can be derived from communally accepted axioms.
This logic can be both positive - if X, then Y etc. This latter form is that of a logical reductio ad absurdam, a contradiction which both affirms and denies a conclusion. Almost everything about religious faith is subject to a reductio ad absurdam. Mathematicians would view such a theological conclusion therefore as meaningless. The difference here is somewhat surprising. Theology relies on fixed axioms from which it the derives its conclusions.
These axioms are given the status of revealed truth and are the dogmatic focus of religious faith. Mathematicians since Godel on the other hand know that the fundamental axioms of their science are somewhat arbitrary. Euclid is not proven wrong but merely shown to be a special case of the more general conditions of Riemann.
This is an illustration as well of a crucial difference in method. Mathematics seeks to continuously extend the generality of its conclusions by discovering more and more inclusive axioms from which to work. Religious faith seeks to fix the axioms in order to preserve, limit and restrict doctrinal conclusions. Put another way: mathematics looks into the abyss of the Incompleteness Theorem and considers it an horizon to be striven toward painfully, incrementally, and with ho chance of complete success.
This takes intellectual and, dare one say it, moral courage. The theologian looks into a similar abyss and considers that the horizon has arrived at his location.
There is nothing to explore, nothing to find beyond the axioms which have been set by tradition. So the faith of the mathematician is not the faith of the religious believer. In fact, the metaphor of scaling a summit does not adequately capture the full impact of a proof.
Once the conjecture is proved, it is not so much the endpoint of an arduous journey but rather the starting point of an even greater adventure. A much more accurate image is that of a mountain pass, the saddle point that allows one to traverse from one valley into another. In fact, this is what makes the Riemann hypothesis so powerful and beloved.
It unlocks many other theorems and insights, and suggests vast generalizations. Mathematicians have been busy exploring the lush valley to which it grants access, even though that valley is still, strictly speaking, hypothetical.
Furthermore, there must be substantial evidence for a conjecture. Niels Bohr famously defined a great truth by the property that its opposite is also a great truth.
But this is definitely not the case for a great conjecture. Since there is generally much circumstantial evidence pointing to its truth, the negation is seen as most unlikely. For instance, the first 10 trillion cases of the Riemann hypothesis have been checked numerically using computers.
Who, at this point, can still doubt its validity? But all this supporting material does not satisfy mathematicians. They demand absolute certainty and want to know why the conjecture is true. Only a conclusive proof can provide that answer. Experience shows that one can easily be fooled. Who would have guessed that the first counterexample involved a number of 30 digits?
It also helps if the challenge can be stated concisely, preferably with a formula containing only a few symbols. A good conjecture should fit on a T-shirt.