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Category: stories

the secret life of numbers

Just read/glanced through another math-for-the-masses book : [The secret life of numbers](http://www.amazon.co.uk/Secret-Life-Numbers-Pieces-Mathematicians/dp/0309096588/sr=81/qid=1168541999/ref=sr_1_1/203-3776750-7074362?ie=UTF8&s=books) by [George G.
Szpiro](http://www.citebase.org/search?submit=1&author=Szpiro%2C+George+G.). The subtitle made me buy the book : **50 easy pieces on how
mathematicians work and think** Could be fun, I thought, certainly after
reading the Amazon-blurb :

Most of us picture
mathematicians laboring before a chalkboard, scribbling numbers and
obscure symbols as they mutter unintelligibly. This lighthearted (but
realistic) sneak-peak into the everyday world of mathematicians turns
that stereotype on its head. Most people have little idea what
mathematicians do or how they think. It’s often difficult to see how
their seemingly arcane and esoteric work applies to our own everyday
lives. But mathematics also holds a special allure for many people. We
are drawn to its inherent beauty and fascinated by its complexity – but
often intimidated by its presumed difficulty. \”The Secret Life of
Numbers\” opens our eyes to the joys of mathematics, introducing us to
the charming, often whimsical side, of the
discipline.

Please correct me when I’m wrong,
but I found just one out of 50 pieces which remotely fulfills this
promise : ‘Cozy Zurich’ ((on the awesome technical support a lecturer
in Zurich is rumoured to receive)). Still, there are some other pieces
worth reading, 1. ‘A puzzle by any other name’ ((On the
Collatz problem)) 2. ‘Twins, cousins and sexy primes’ ((How
reasearch into the twin primes problem led to the discovery of a
Pentium-bug)) 3. ‘Proving the proof’ ((On Kepler’s problem)) 4.
‘Has Poincare’s conjecture finally been solved’ ((Of course it has
been)) 5. ‘Late tribute to a tragic hero’ ((On Abel’s life and
prize)) 6. ‘God’s gift to science?’ ((Stephen Wolfram
bashing)) to single out a few, embedded in a soup made out of the
usual suspects (knots, chaos, RSA etc.). But, all in all, I fear the
book doesn’t fulfill its promises and once again it demonstrates how
little ‘math-substance’ one is able to put in a book for a general
audience. But let us end with a quote from the preface that I really
like :

Whenever a socialite shows off his flair
at a coctail party by reciting a stanza from an obscure poem, he is
considered well-read and full of wit. Not much ado can be made with the
recitation of a mathematical formula, however. At most, one may expect a
few pitying glances and the title ‘party’s most nerdy guest’. To the
concurring nods of the cocktail crowd, most bystanders will admit that
they are no good at math, never have been, and never will be.
Actually, this is quite astonishing. Imagine your lawyer
telling you that he is no good at spelling, your dentist proudly
proclaiming that she speaks n foreign language, and your financial
advisor admitting with glee that he always mixes up Voltaire with
Moliere. With ample reason one would consider such people as ignorant.
Not so with mathematics. Shortcomings in this intellectual discipline
are met with understanding by everyone.

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shameless

Shamelessly (if that is a proper word in english/american e.? it should
be…) copied from ‘view source’ from Uncertain Principlesdelurk_terr.jpgJanet reminds me that this has
been declared National De-Lurking Week. If you’re in
the habit of reading this blog, but don’t usually comment,
here’s a made-up holiday you can celebrate by leaving a comment
here. You’ll need to put in a name (it needn’t be yours) and
an email address (I promise it won’t be spammed as a result), but
then you can type anything you like (within reason) into the comment
box, and post it here.

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attention-span : one chat line

Never
spend so much time on teaching than this semester and never felt so
depressed afterwards. The final test for the first year course on
grouptheory (60 hrs. going from nothing to Jordan-Holder and the Sylow
theorems) included the following question :

Question :
For a subgroup $H \subset G $ define the normalizer to be the
subgroup $N_G(H) = \{ g \in G~:~gHg^{-1} = H \} $. Complete the
statement of the result for which the proof is given
below.

theorem : Let P be a Sylow subgroup of
a finite group G and suppose that H is a subgroup of G which
contains the normalizer $N_G(P) $. Then …

proof :
Let $u \in N_G(H) $. Now, $P \subset N_G(P) \subset H $
whence $uPu^{-1} \subset uHu^{-1} = H $. Thus, $uPu^{-1} $, being of the
same order as P is also a Sylow subgroup op H. Applying the Sylow
theorems to H we infer that there exists an element $h \in H $ such
that
$h(uPu^{-1})h^{-1} = P $. This means that $hu \in N_G(P) $.
Since, by hypotheses, $N_G(P) \subset H $, it follows that $hu \in H $.
As $h \in H $ it follows that $u \in H $, finishing the proof.

A
majority of the students was unable to do this… Sure, the result was
not contained in their course-notes (if it were I\’m certain all of them
would be able to give the correct statement as well as the full proof
by heart. It makes me wonder how much they understood
of the proof of the Sylow-theorems.) They (and others) blame it on the
fact that not every triviality is spelled out in my notes or on my
\’chaotic\’ teaching-style. I fear the real reason is contained in the
post-title…

But, I\’m still lucky to be working with students
who are interested in mathematics. I assume it can get a lot worse (but
also a lot funnier)

and what about this one :

If you are (like me) in urgent need for a smile, try out
this newsvine article for more
bloopers.

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