Skip to content →

Tag: arty

the secret life of numbers

Just read/glanced through another math-for-the-masses book : [The secret life of numbers]( by [George G.
Szpiro]( 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

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.

Leave a Comment

Krull & Paris

Category-Cafe ran an interesting post The history of n-categories
claiming that “mathematicians’ histories are largely
‘Royal-road-to-me’ accounts”

To my mind a key
difference is the historians’ emphasis in their histories that things
could have turned out very differently, while the mathematicians tend to
tell a story where we learn how the present has emerged out of the past,
giving the impression that things were always going to turn out not very
dissimilarly to the way they have, even if in retrospect the course was
quite tortuous.

Over the last weeks I’ve been writing up
the notes of a course on ‘Elementary Algebraic Geometry’ that I’ll
be teaching this year in Bach3. These notes are split into three
historical periods more or less corresponding to major conceptual leaps
in the subject : (1890-1920) ideals in polynomial rings (1920-1950)
intrinsic definitions using the coordinate ring (1950-1970) scheme
theory. Whereas it is clear to take Hilbert&Noether as the leading
figures of the first period and Serre&Grothendieck as those of the
last, the situation for the middle period is less clear to me. At
first I went for the widely accepted story, as for example phrased by Miles Reid in the
Final Comments to his Undergraduate Algebraic Geometry course.

rigorous foundations for algebraic geometry were laid in the 1920s and
1930s by van der Waerden, Zariski and Weil (van der Waerden’s
contribution is often suppressed, apparently because a number of
mathematicians of the immediate post-war period, including some of the
leading algebraic geometers, considered him a Nazi collaborator).

But then I read The Rising Sea: Grothendieck
on simplicity and generality I
by Colin McLarty and stumbled upon
the following paragraph

From Emmy Noether’s viewpoint,
then, it was natural to look at prime ideals instead of classical and
generic points—or, as we would more likely say today, to identify
points with prime ideals. Her associate Wolfgang Krull did this. He gave
a lecture in Paris before the Second World War on algebraic geometry
taking all prime ideals as points, and using a Zariski topology (for
which see any current textbook on algebraic geometry). He did this over
any ring, not only polynomial rings like C[x, y]. The generality was
obvious from the Noether viewpoint, since all the properties needed for
the definition are common to all rings. The expert audience laughed at
him and he abandoned the idea.

The story seems to be
due to Jurgen Neukirch’s ‘Erinnerungen an Wolfgang Krull’
published in ‘Wolfgang Krull : Gesammelte Abhandlungen’ (P.
Ribenboim, editor) but as our library does not have this book I would
welcome any additional information such as : when did Krull give this
talk in Paris? what was its precise content? did he introduce the prime
spectrum in it? and related to this : when and where did Zariski
introduce ‘his’ topology? Answers anyone?

Leave a Comment

simple group of order 2

The Klein Four Group is an a
capella group from the maths department of Northwestern. Below a link to
one of their songs (grabbed from P.P. Cook’s Tangent Space

Simple Group (of order two)

A Klein Four original by
Matt Salomone

The path of love is never
But mine’s continuous for you
You’re the upper bound in the chains of my heart
You’re my Axiom of Choice, you know it’s true
But lately our relation’s not so well-defined
I just can’t function without you
I’ll prove my
proposition and I’m sure you’ll find
We’re a
finite simple group of order two
I’m losing my
I’m getting tensor every day
without loss of generality
I will assume that you feel the same
Since every time I see you, you just quotient out
The faithful image that I map into
But when we’re
one-to-one you’ll see what I’m about
we’re a finite simple group of order two
Our equivalence
was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
everything is so complexified
When we first met, we simply
My heart was open but too dense
Our system
was already directed
To have a finite limit, in some sense

I’m living in the kernel of a rank-one map
From my
domain, its image looks so blue,
‘Cause all I see are
zeroes, it’s a cruel trap
But we’re a finite simple
group of order two
I’m not the smoothest operator in my
But we’re a mirror pair, me and you,
let’s apply forgetful functors to the past
And be a
finite simple group, a finite simple group,
Let’s be a
finite simple group of order two
(Oughter: “Why not
I’ve proved my proposition now, as you
can see,
So let’s both be associative and free
And by corollary, this shows you and I to be
inseparable. Q. E. D.

Leave a Comment


You don’t
know how lucky you are to be able to begin a LaTeX-document with
something like \documentclass[a4]{amsart}. This simple line
tells the machine what the size of paper is it has to print to, which
part of that paper has to be filled with text, what the design of
titles, sections etc. is (and probably more). Just convince yourself
(for the sake of argument) that you want to produce a readable
mathematical book on paper of dimensions say 6 by 9 inch. How would you
do this? Simple : all you have to do is to adjust certain TeX-parameters
the way you want! Well, that’s exactly what the _neverendingbooks
design department_ has been doing for the last couple of weeks!

The package we would use was easy enough to find. A long time ago, Geert suggested that we
should use the
memoir package
. The fun starts the moment you are foolish enough to
print the manual : 300 pages! After an inspiring account of
book-printing basics over the ages, you are told that you have total
freedom to set your _stock paper size_, how it needs to be
_trimmed_ to get the final result, how you should designs
everything from the title, over abstract, acknowledgement, thanks, table
of contents contents, dedications etc. down to chapter, section and page
styles. In short : ULTIMATE FREEDOM!!!

But, as some of you may
know from experience, there is nothing more frightening to the moderate
autist (and frankly, are there any other mathematicians?) than ultimate
freedom! So, we set up a task-force, had daily brain-storm sessions,
produced numerous trial-prints and eventually came out with something
that came very close to the _better designed book_. Let’s face it
: can you name me _one_ (yeah right, just 1) well-designed
mathematical book? If you don’t believe me, browse through the recent
mathematics-books on amazon (as our design-department
did for a whole week-end, deprived of beverages and other pleasures).
Found anything? Yes?? Please, please let us know! On the other hand, if
you browse through the Art, architecture and
photography section
you will spot several extremely good-looking
books very soon. Well, after a week we succeeded in designing the
_arty-farty-fanshi-wanshi_ (as PD1 would name it, jealous that
she was not in on the fun) mathematical book! And, what did we do with
the labours of all this hard work? NOTHING! We simply dropped the whole
idea (if you are a graphics-designer trying to survive within a
mathematics publishing firm (not easy we know, you have all our
sympathy) and want to do something more fun, contact us and if we can
reach an adequate financial agreement we will be happy to send you our

So, what went wrong? Nothing really, it just dawned on
us that _NeverEndingBooks.org_ should not go for the
better-designed mathematics book. All our (potential) authors can
publish as easily at Oxford University
, the European Mathematical
or, if they have no moral objection, at the AMS. So, why
would they choose us instead of these more established publishing
houses? Just because our books look slightly (well let’s face it : a
lot) better? Probably not. We, at should not go for
the better-designed book, we should not go for the book concept at all,
we should invent something entirely NEW & SEXY & USABLE & DESIRING & (I
hope you get the drift!). Next time, I’ll let you in on the first ideas
of our design-department!

Leave a Comment


The nerd
implimentation of GTD
is based on plain text-files, or more

– all lists in text files, kept in directory
– all documents maintained in Markdown for easy
HTML conversion

I’ve been writing HTML-code since the times
that the best browser around was something called NCSA Mosaic so I’ve never paid too much attention to
before. Here is its main purpose

Markdown is a
text-to-HTML conversion tool for web writers. Markdown allows you to
write using an easy-to-read, easy-to-write plain text format, then
convert it to structurally valid XHTML (or >HTML). Thus, Markdown is
two things: (1) a plain text formatting syntax; and (2) a software tool,
written in Perl, that converts the plain text formatting to

An example of Markdown-code followed by its
HTML-output can be seen at the BlueCloth website and I have
to agree that the Markdown text is very legible. I’ve been playing
around with Markdown for a couple of days now (in fact this post is
written in Markdown as WordPress has a Markdown-plugin) and have found a
few uses for it (more on this another time). Essential sites to visit if
you want to learn some Markdown are : its basic
and in the rare cases that this doesn’t do what you want to
do there is also a full

If you want to use Markdown to write your
HTML-pages you need to be able to convert Markdown to HTML (and
conversely although the uses for this are not immediately clear, but
there are plenty of good reasons!). That’s what the Perl-script does for you (one way) and the
Python-script (to be found here) (the other

To get them working using BBedit
all you have to do is to put them in the _BBEdit Support/Unix
Support/Unix Filters_ directory (to be found in the BBEdit-folder in
_/Applications_). Then, if you have written a Markdown-text, do a
_Select All_ go to the !# menu and look for under _Unix Filters_ and voila, you have valid XHTML
(the other direction is similar).

This is a bit of work and one
would like to do both operations in nearly all Applications using the
_Services Menu_ (in fact, until a few weeks ago I had no clue
that there was something as useful as this menu hidden under the
program-name-menu of any Cocoa-program!). This is best done using HumaneText.service. The
installation is really as siimple as they say on this page (although it
took me a couple of trials before it worked, and I use the Services-menu
rather than the keystroke-shortcuts).

HumaneText works perfectly with TextEdit,
SubEthaEdit and (probably more important to mathematicians) TeXShop and
iTeXMac (the two most common front-ends for (La)TeX under OS X). A
noteworthy exception is BBEdit (hence the above laborious work-around).
Sometimes there are problems with punctuation in the conversion but you
can get around this using SmartyPants.

Leave a Comment