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Uncle Petros and Goldbach's Conjecture

h3>Apostolos Doxiadis

Doxiadis, Apostolos;

Uncle Petros and Goldbach's Conjecture [Greek 1992: Theios Petros kai i Eikasia tou GoIbach]

Faber & Faber, 2012, 224 pages

ISBN 057129569X, 9780571295692

topics: |  math | fiction |

A story of mathematicians, told from a fictional viewpoint of a mathematician's nephew. The mathematician in question, Uncle Petros, spends his entire life fruitlessly searching for a proof to a three century old problem.

The author is himself an amateur mathematician and filmmaker, who was admitted to Columbia U mathematics after an original paper at the age of 15.

Petros Papachristos is a mathematician who has devoted his life to proving a 250 year old conjecture:.

	in a letter [to Euler] written in 1742,
	the minor mathematician Christian Goldbach
	brings to the attention of the great Euler
	a certain arithmetical observation.

the Goldbach conjecture states that every even number
greater than two is the sum of two primes.  The story is
narrated from the p.o.v. of Petros's nephew, who has grown
up in the knowledge that his uncle has been a failure.
But when he discovers that his Uncle had been a
well-respected, Cambridge-trained mathematician, the
nephew's image of Uncle Petros changes.


Excerpts


Archimedes will be remembered when Aeschylus is forgotten, because
languages die and mathematical ideas do not. 'Immortality' may be a
silly word, but probably a mathematician has the best chance of
whatever it may mean. - GH Hardy, A Mathematician's Apology

---

Father [with a scowl]: "Son, do you know the secret of Life?"
I: No, I don’t.
F: The Secret of Life is always to set yourself attainable goals. They
   may be easy or difficult, depending on the circumstances and your
   character and abilities, but they should always be at-tai-na-ble! In
   fact, I think I’ll hang your Uncle Petros’ portrait in your room, with
   a caption: EXAMPLE TO BE AVOIDED!" -p.21


What fascinated me was that the kindly, withdrawn and seemingly
unassuming uncle of mine was in fact a man who, by his own deliberate
choice, had struggled for years on end at the outermost boundaries of
human ambition.... While his brothers were studying and getting married,
raising children and running the family business, wearing out their lives
along with the rest of nameless humanity in the daily routines of
subsistence, procreation and killing time, he, Prometheus-like, had
striven to cast light into the darkest and most inaccessible corner of
knowledge. p.21


At last I understood the meaning of the sign at the entrance of Plato’s
Academy : oudeis ageometretos eiseto – ‘ Let no one ignorant of geometry
enter’. The moral of my evening emerged with crystal clarity : mathematics
was something infinitely more interesting than solving second-degree
equations of calculating the volumes of solids, the menial task at which we
laboured at school. Its practitioners dwelt in a veritable conceptual heaven,
a majestic poetic realm totally inaccessible to the un-mathematical
hoi-polloi. p.25


Mathemeticus nascitur non fit - mathematicians are born not made


[after UP explains Euclid's proof that there are an infinite number of
primes]
I: It's so simple.
Uncle Petros : ..sometimes things appear simple only in retrospect."

UP: Never forget it: Mathematicus nascitur non fit – A mathematician is
   born, not made. If you don’t carry the special aptitude in your genes,
   you will labour in vain all your life and one day you will end up a
   mediocrity. A golden mediocrity, perhaps, but an mediocrity
   nevertheless. 31

"He who is fated to drown will never die in bed." p.60

Anybody who claims that scientists – even the purest of pure, the most
abstract, high-flying mathematicians – are motivated exclusively by the
Pursuit of Truth for the Good of Mankind, either has no idea what he’s
talking about or is blatantly lying. Although the more spiritually inclined
members of the scientific community may indeed be indifferent to material
gains, there isn’t a single one among them who isn’t mainly driven by
ambition and a strong competitive urge.  A mathematician’s declared
intention, when embarking on an important research endeavor, may indeed be
the discovery of Truth, yet the stuff of his daydreams is Glory. p.77-8

"You know the popular saying that the three conditions impossible to conceal
are a cough, wealth and being in love? Well, to me there is a fourth:
mathematical gift." 153

Mathematics, Petros had taught me, is a field that acknowledges only its
greatest; this particular kind of natural selection offers failures as the
only alternative to glory. 164

The amalgam of Truth and Beauty revealed through the understanding of an
important theorem cannot be attained through any other human activity, unless
it be (I wouldn’t know) that of mystical religion. … Yes, it had made the
existence of the Ideal slightly more believable, even tangible. 167

On insanity and truth


Kurt G\"odel's insanity -- for unquestionably he is in a certain sense
insane -- is the price he paid for coming too close to Truth in its
absolute form. ... People like him have surpassed the common measure;
they've come to know more than is necessary to man, and for
this hubris they have to pay. - mathematics student and friend Sammy, p.163

The proverbial 'mad mathematician' was more fact than fancy. I came
increasingly to view the great practitioners of the Queen of Sciences
as moths drawn towards an inhuman kind of light, brilliant but
scorching and harsh. Ramanujam, Hardy, Turing, G\"odel and so many
others were too enamoured of the brilliant light: they got too close,
scorched their wings, fell and died. - p.166

Seeing [Uncle Petros] helped me keep alive that part of the self that
most people lose, or forget about, with adulthood -- call it the
Dreamer or the Wonderer or simply the Child Within.  168


deviations from mathematical history

from http://www.tau.ac.il/~corry/publications/articles/Narrative/main3.html
(review with photos of mathematicians, and much mathematical history):
[part 3 of a larger review of narrative in mathematical fiction]

the reliability of the story is further supported by the fact that a
prominent Greek mathematician, who indeed was professor at the great Berlin
school of mathematics, is the advisor of the fictional Petros. There could be
no better choice in terms of coherence and internal logic of the
story. Nevertheless, a factual problem arises here: Carathéodory arrived in
Berlin only in 1918!

Does this deviation from strict historical truth matters in any possible
sense? Most readers will not even be aware of this rather marginal detail, to
begin with, and in any case, this could provide a classical example of poetic
license taken by an author that no reader would bother protesting about. Not
only it provides no sudden reason for giving up suspense of disbelief, but,
as already said, it actually serves very well the plot and plays an actual
role in helping put forward a coherently and convincing story. One might
perhaps claim that the plot should have been conveniently modified on behalf
of historical exactness in this case, but there is no real reason to complain
about the poetic license taken by the author.

Let us look at a second, interesting place where the plot deviates from the
historical record, while providing further support to the plot. In a dialogue
between the narrator and his uncle Petros, reference is made to a famous
lecture presented by David Hilbert at the occasion of the 1900 Paris
International Congress of Mathematicians.

This dialogue is meant to provide a glimpse into the way that absolute
certainty was expected to pervade mathematics at the turn of the twentieth
century, which was also the attitude that guided Petros in his own
mathematical activities. Hilbert is presented as the champion of this view,
as embodied in two famous sayings quoted by the narrator: "Wir müssen wissen,
wir werden wissen" (we must know, we shall know), and "there is no
ignorabimus in mathematics". Thus the narrator says: "Thus spake the great
David Hilbert in the International Congress of 1900. A proclamation of
mathematics as the Heaven of Absolute Truth. The vision of Euclid, the vision
of Consistency and Completeness…"

Well, there are some problems in this description of what Hilbert said at
that opportunity, and the most immediate one concerns the "Wir müssen wissen,
wir werden wissen". These words, later engraved in Hilbert's tombstone,
were not part of the Paris address, but rather of a talk given in 1930 at a
meeting in Königsberg to honour Hilbert on the occasion of being awarded the
honorary citizenship of his native town.


Stranger than fiction

Hilbert also broadcasted a speech in the local radio (which was recorded and
later made available on a 45 record and recently digitalized). It is in that
speech that his famous words appear, as the closing sentence that
encapsulates Hilbert's legendary, unbridled feeling of scientific
optimism. It is a remarkable coincidence that Hilbert gave this speech during
a week in which four mathematical meetings were simultaneously held in
Königsberg. In one of those meetings Kurt Gödel presented for the first time
his first incompleteness theorem. The results developed by Gödel came to
imply a serious blow to the program that Hilbert had been promoting for more
than ten years now to prove the consistency of arithmetic by finitary
methods. But neither in Königsberg in 1930 nor ever thereafter, Hilbert and
Gödel met or listened to each other's talk.

"The story is so dramatic that it resembles fiction", has remarked Gregory
Chaitin commenting this situation. In Königsberg while Hilbert was declaring
"Wir müssen wissen, wir werden wissen", Gödel was speaking about inherent
limitations in mathematical knowledge. We tend naturally to consider a
situation of this kind more likely to be fiction than historical reality.

At any rate, what Hilbert did say in his 1900 speech was not very far away in
spirit from what came to be engraved in his tombstone. He thus said:

This conviction of the solvability of any mathematical problem is a powerful
incentive to the worker. We hear within us the perpetual call: There is the
problem, seek its solution. You can found it by pure reason, for in
mathematics there is no ignorabimus.



Other Reviews

http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/doxiadis.htm--

In the tradition of Fermat's Last Theorem and Einstein's Dreams, a novel
about mathematical obsession.

Petros Papachristos devotes the early part of his life trying to prove one of
the greatest mathematical challenges of all time: Goldbach's Conjecture, the
deceptively simple claim that every even number greater than two is the sum
of two primes. Against a tableau of famous historical figures--among them
G.H. Hardy, the self-taught Indian genius Srinivasa Ramanujan, and a young
Kurt Godel--Petros works furiously to prove the notoriously difficult
conjecture, but suddenly disappears into a solitary existence playing chess
in the Greek countryside.

To his nephew, he is known as the solitary, eccentric Uncle Petros, but when
the young man finds out that his uncle is an esteemed professor of
mathematics, he searches out his uncle's hidden past. Through an adversarial
friendship based on chess and mathematics, he drives the retired
mathematician back into the hunt to prove Goldbach's Conjecture... but at the
cost of the old man's sanity, and perhaps even his life.

Uncle Petros and Goldbach's Conjecture is an intellectual adventure, a story
of proud genius and the exhilaration of pure mathematics. It is about the
search for truth at all costs, and the heavy price of finding it.

Keith Devlin in Math Assocn America MAA Reviews


http://www.maa.org/publications/maa-reviews/uncle-petros-and-goldbachs-conjecture

through the medium of a fictional story, he manages to convey the nature of
pure mathematics, the passion that can drive a mathematician to work for
years on a seemingly irrelevant problem, and the single-minded dedication it
can take to see the project through to its end -- or not, as the case may
be. (Of course, for dramatic effect the obsession displayed by Uncle Petros
is somewhat greater than is the case with any mathematicians I have met --
and that includes Andrew Wiles -- so, as with the hero in the movie Pi, it is
not clear that nonmathematicians who read the book will view mathematics as
an attractive pursuit, or mathematicians as completely sane. But most
nonmathematicians probably think that already anyway.)

In the spirit of Andrew Wiles' assault on Fermat's Last Theorem (the novel
was completed long before Wiles announced his proof, by the way), Uncle
Petros locked himself away in seclusion to work on trying to prove
Goldbach's Conjecture that every even number is the sum of two primes.

---
Apostolos Doxiadis received a Bachelor's Degree in Mathematics from Columbia
University and a Master's Degree in Applied Mathematics from the cole
Pratique des Hautes Etudes in Paris. He has run a number of successful
computer companies, as well as written and directed for screen and stage. The
second of his two feature films, Tetriem, won the prize of the International
Center for Artistic Cinema at the 1988 Berlin International Film
Festival. Doxiadis lives in Athens, Greece.


---blurb
Uncle Petros is a family joke. An ageing recluse, he lives alone in a
suburb of Athens, playing chess and tending to his garden. If you didn't
know better, you'd surely think he was one of life's failures. But his
young nephew suspects otherwise. For Uncle Petros, he discovers, was once a
celebrated mathematician, brilliant and foolhardy enough to stake
everything on solving a problem that had defied all attempts at proof for
nearly three centuries - Goldbach's Conjecture.

His quest brings him into contact with some of the century's greatest
mathematicians, including the Indian prodigy Ramanujan and the young Alan
Turing. But his struggle is lonely and single-minded, and by the end it has
apparently destroyed his life. Until that is a final encounter with his
nephew opens up to Petros, once more, the deep mysterious beauty of
mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel
of intellectual adventure, proud genius, the exhilaration of pure
mathematics - and the rivalry and antagonism which torment those who pursue
impossible goals.


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This article last updated on : 2014 Jul 17