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Category: stories

soaked but hopefull


When more than 20.000 Antwerpees from all etnic and religious
backgrounds defy the pouring rain to march against racism, I’m
(moderately) hopeful about Antwerps future. If you are
interested to know the cause for this demonstration, here is a pretty accurate account of recent
events in Antwerp (and Belgium).

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le travers – april 2006

Here is a
solution to the Intel-Mac schizo-situation of having GAP running on the
Mac-partition, whereas Singular and Maxima had to run on the
WindowsXP-partition (see this post for
the problems) : get and install Sage!

Crete de
l’espinasse : Wednesday 20.17h Alt. 750m. The nearest place having
mobile reception. It takes a walk of 1.25km and a climb of 150m to get a
signal…

Croix
Blanche : Tuesday 14.03h : Alt. 897m : the end of a 6km climb from
450m…

Le
Travers : Monday 19hrs Alt. 604m, 19 C…


Chapelle
St Regis : Sunday 11.45h Alt. 719m. The highest point of the
bicycle-tour : le Travers-Dompnac-Pourcharesse-St Melany-le Travers
(27.2 km).

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why mathematicians can’t write

The Music of the
Primes
will attract many young people to noncommutative geometry a
la Connes. It would be great if someone would spend a year trying to
write a similar pamphlet in favour of noncommutative _algebraic_
geometry, but as I mentioned before chances are not very high as most
mathematicians are unwilling to sacrifice precision and technical detail
for popular success. Still, perhaps we should reconsider this position.
A fine illustration why most mathematicians cannot write books for a
bigger audience is to be found in the preface to the book “The
problems of mathematics” (out of print or at least out of
amazon.com) by the Warwick mathematician Ian Stewart.
Below I quote a fraction from his ‘An interview with a
mathematician…’

(I)nterviewer : … So,
Mathematician : what delights do you have in store for us?
(M)athematician : I thought I’d say a bit about how you can get a TOP
but non-DIFF 4-manifold by surgery on the Kummer surface. You see,
there’s this fascinating cohomology intersection form related to the
exceptional Lie algebra $E_8$, and…
(I) : That’s
fascinating.
(M) : Thank you.
(I) : Is all that
gobbledegook really significant?
(M) : Of course! It’s one of the
most important discoveries of the last decade!
(I) : Can you
explain it in words ordinary mortals can understand?
(M) : Look,
buster, if ordinary mortals could understand it, you wouldn’t need
mathematicians to do the job for you, right?
(I) : I don’t want
the technical details. Just a general feeling for what’s going on.
(M) : You can’t get a feeling for what’s going on without
understanding the technical details.
(I) : Why not?
(M) :
Well, you just can’t.
(I) : Physicists seem to manage.
(M)
: But they work with things from everyday experience…
(I) :
Sure. ‘How gluon antiscreening affects the colour charge of a
quark.’ ‘Conduction bands in Gallium Arsenide.’ Trip over
‘em all the time on the way to work, don’t you?
(M) : Yes,
but…
(I) : I’m sure that the physicists find all the
technical details just as fascinating as you do. But they don’t let them
intrude so much.
(M) : But how can I explain things properly if I
don’t give the details?
(I) : How can anyone else
understand them if you do?

(M) : But if I skip the fine
points, some of the things I say won’t be completely true! How can I
talk about manifolds without mentioning that the theorems only work if
the manifolds are finite-dimensional paracompact Hausdorff with empty
boundary?
(I) : Lie a bit.
(M) : Oh, but I couldn’t do
that!
(I) : Why not? Everybody else does.
(M) : But, I
must tell the truth!
(I) : Sure. But you might be prepared to
bend it a little, if it helps people understand what you’re doing.
(M) : Well…

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music of the primes

Let me
admit it : i was probably wrong in this post to
advise against downloading A walk in the noncommutative
garden
by Alain Connes and Matilde Marcolli. After all, it seems
that Alain&Matilde are on the verge of proving the biggest open
problem in mathematics, the Riemann
hypothesis
using noncommutative geometry. At least, this is the
impression one gets from reading through The music of the
primes, why an unsolved problem in mathematics matters
by Oxford
mathematician Prof.
Marcus du Sautoy
… At the moment I’ve only read the first
chapter (_Who wants to be a millionaire?_) and the final two
chapters (_From orderly zeros to quantum chaos_ and _The
missing piece of the jigsaw_) as I assume I’ll be familiar with most
of the material in between (and also, I’m saving these chapters for some
vacation reading). From what I’ve read, I agree most with the final
review at amazon.co.uk

Fascinating
and infuriating
, October 5, 2004
Reviewer: pja_jennings
from Southampton, Hants. United Kingdom
This is a book I found
fascinating and infuriating in turns. It is an excellent layman’s
history of number theory with particular reference to prime numbers and
the Riemann zeta function. As such it is well worth the reading.
However I found that there are certain elements, more of style than
anything else, that annoyed me. Most of the results are handed to us
without any proof whatsoever. All right, some of these proofs would be
obviously well beyond the layman, but one is described as being
understandable by the ancient Greeks (who started the whole thing) so
why not include it as a footnote or appendix?
Having established
fairly early on that the points where a mathematical function
“reaches sea level” are known as zeros, why keep reverting
to the sea level analogy? And although the underlying theme throughout
the book is the apparent inextricable link between the zeta function’s
zeros and counting primes, the Riemann hypothesis, I could find no
clear, concise statement of exactly what Riemann said.
Spanning
over 2000 years, from the ancient Greeks to the 21st century, this is a
book I would thoroughly recommend.

Books on Fermat’s last
theorem
(and there are some nice ones, such as Alf Van der Poorten’s
Notes on
Fermat’s last theorem
) can take Wiles’ solution as their focal
point. Failing a solution, du Sautoy constructs his book around an
April’s Fool email-message by Bombieri in which he claimed that a young
physicist did prove the Riemann hypothesis after hearing a talk by Alain
Connes. Here’s du Sautoy’s account (on page 3)

According
to his email, Bombieri has been beaten to his prize. ‘There are
fantastic developments to Alain Connes’s lecture at IAS last wednesday.’
Bombieri began. Several years previously, the mathematical world had
been set alight by the news that Alain Connes had turned his attention
to trying to crack the Riemann Hypothesis. Connes is one of the
revolutionaries of the subject, a benign Robespierre of mathematics to
Bombieri’s Louis XVI. He is an extraordinary charismatic figure whose
fiery style is far from the image of the staid, awkward mathematician.
He has the drive of a fanatic convinced of his world-view, and his
lectures are mesmerising. Amongst his followers he has almost cult
status. They will happily join him on the mathematical barricades to
defend their hero against any counter-offensive mounted from the ancien
regime’s entrenched positions.

Contrary to physics,
mathematics doesn’t produce many books aimed at a larger public. To a
large extend this is caused by most mathematicians’ unwillingness to
sacrifice precision and technical detail. Hence, most of us would never
be able to come up with something like du Sautoy’s description of Weil’s
work on the zeta function of curves over finite fields (page 295)

It was while exploring some of these related landscapes that
Weil discovered a method that would explain why points at sea level in
them like to be in a straight line. The landscapes where Weil was
successful did not have to do with prime numbers, but held the key to
counting how many solutions an equation such as $y^2=x^3-x$ will have if
you are working on one of Gauss’s clock calculators.

But,
it is far too easy to criticize people who do want to make the effort.
Books such as this one will bring more young people to mathematics than
any high-publicity-technical-paper. To me, the chapter on quantum chaos
was an eye-opener as I hadn’t heard too much about all of this before.
Besides, du Sautoy accompanies this book with an interesting website musicofprimes and several of
his articles for newspapers available from his homepage are
a good read (in case you wonder why the book-cover is full of joggers
with a prime number on their T-shirt, you might have a look at Beckham in his
prime number
). The music of the
primes
will definitely bring many students to noncommutative
geometry and its possible use to proving the Riemann Hypothesis.

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arXiv trackback wars

If you happen to have a couple of hours to kill, you might have a look at the
arXiv trackback policy debate over at Jacques Distler’s blog Musings. But before you dive into this it is perhaps useful to glance at what went before. Distler did pester (his wording, not mine) the arXiv to add trackbacks from certain weblogs to hep-th postings (i’m not aware of math-papers having trackbacks). So far so good, the more information about a paper the better i’d say, but it seems that not all weblogs’ trackbacks are allowed… A small commitee has the power to divide hep-th people into ‘crackpots’ or ‘active researchers’
(mother nature may very well decide to add all stringtheorists from the second category to the first in a couple of years… but, i’m digressing) and accordingly censor specific blogs and frustrate their authors, Peter Woit’s blog Not Even Wrong being the main victim. The whole trackback-policy is yet another futile academics power-game. Futile because there is an obvious way around it : type into Technorati either the arXiv-number or title or author and you will get all (!) weblog postings mentioning the paper (Technorati even has a slider if you only want to read postings with ‘authority’ rather than all). Perhaps one of the more tech-abled stringtheorists should spend an afternoon to write a
bookmarklet
to perform this trick from any arXiv abstract page…

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Alain Connes on everything

A few
days ago, Ars Mathematica wrote :

Alain Connes and Mathilde Marcolli have posted a
new survey paper on Arxiv A walk in the
noncommutative garden
. There are many contenders for the title of
noncommutative geometry, but Connes’ flavor is the most
successful.

Be that as it may, do
not print this 106 page long paper! Browse through it
if you have to, be dazzled by it if you are so inclined, but I doubt it
is the eye-opener you were looking for if you gave up on reading
Connes’ book Noncommutative
Geometry
…. Besides, there is much better
_Tehran-material_ on Connes to be found on the web : An interview
with Alain Connes
, still 45 pages long but by all means : print it
out, read it in full and enjoy! Perhaps it may contain a lesson or two
for you. To wet your appetite a few quotes

It is
important that different approaches be developed and that one
doesn’t try to merge them too fast. For instance in noncommutative
geometry my approach is not the only one, there are other approaches
and it’s quite important that for these approaches there is no
social pressure to be the same so that they can develop
independently. It’s too early to judge the situation for instance
in quantum gravity. The only thing I resent in string theory is that
they put in the mind of people that it is the only theory that can
give the answer or they are very close to the answer. That I resent.
For people who have enough background it is fine since they know all
the problems that block the road like the cosmological constant, the
supersymmetry breaking, etc etc…but if you take people who are
beginners in physics programs and brainwash them from the very start
it is really not fair. Young physicists should be completely free,
but it is very hard with the actual system.

And here for some (moderate) Michael Douglas bashing :

Physicists tend to shift often and work on the
last fad. I cannot complain because at some point around 98 that fad was
NCG after my paper with Douglas and Schwarz. But after a while when
I saw Michael Douglas and asked him if he had thought more about
these problems the answer was no because it was no longer the last
fad and he wanted to work on something else. In mathematics one
sometimes works for several years on a problem but these young
physicists have a very different type of working habit. The unit of
time in mathematics is about 10 years. A paper in mathematics which is
10 years old is still a recent paper. In physics it is 3 months. So
I find it very difficult to cope with constant
zapping.

To the suggestion that he is the
prophet (remember, it is a Tehran-interview) of noncommutative geometry
he replies

It is flattering but I don’t think
it is a good thing. In fact we are all human beings and it is a
wrong idea to put a blind trust in a single person and believe in
that person whatever happens. To give you an example I can tell you
a story that happened to me. I went to Chicago in 1996, and gave a
talk in the physics department. A well known physicist was there and
he left the room before the talk was over. I didn’t meet this
physicist for two years and then, two years later, I gave the same
talk in the Dirac Forum in Rutherford laboratory near Oxford. This
time the same physicist was attending, looking very open and convinced
and when he gave his talk later he mentioned my talk quite
positively. This was quite amazing because it was the same talk and
I had not forgotten his previous reaction. So on the way back to
Oxford, I was sitting next to him in the bus, and asked him openly
how can it be that you attended the same talk in Chicago and you
left before the end and now you really liked it. The guy was not a
beginner and was in his forties, his answer was “Witten was seen
reading your book in the library in Princeton”! So I don’t want
to play that role of a prophet preventing people from thinking on
their own and ruling the sub ject, ranking people and all that. I
care a lot for ideas and about NCG because I love it as a branch of
mathematics but I don’t want my name to be associated with it as a
prophet.

and as if that was not convincing
enough, he continues

Well, the point is that what
matters are the ideas and they belong to nobody. To declare that
some persons are on top of the ladder and can judge and rank the
others is just nonsense mostly produced by the sociology (in fact by the
system of recommendation letters). I don’t want that to be true in
NCG. I want freedom, I welcome heretics.

But please, read it all for yourself and draw your own conclusions.

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2005 lists : mathematical novels

Mathematical Fiction
is a nice site maintained by Alex Kasman and is an
attempt to collect information about all significant references to
mathematics in fiction. In september I ordered a pile of novels from
this list from Amazon and had an enjoyable read (mostly) since.
I’ve mentioned a couple of books already on this blog and at one
time had the intention of writing about each book I finished. But,
I’m not very good at refereeing/reviewing, so not much came out of
this… Still, the MathFiction list is an excellent way to
discover authors and books you probably wouldn’t encounter
otherwise. So far, I read about 15 novels from the list, focussing on
mystery (rather than SF or any other of the categories the list let you
choose from). Here is a list of the ten I liked most, in order (with
links to the relevant MathFiction page)

  1. In search of Klingsor, by Jorge Volpi
  2. Popco, by Scarlett Thomas
  3. Lord Byron’s novel ‘The Evening Land’, by John
    Crowley
  4. The Oxford Murders, by Guillermo Martinez
  5. Nymphomation, by Jeff Noon
  6. The fractal murders, by Mark Cohen
  7. Improbable, by Adam Fawer
  8. Calculating God, by Robert J. Sawyer
  9. The wild numbers, by Philibert Schogt
  10. Signal to noise, by Eric S. Nylund

If you
are interested in the lives of mathematicians and physicists living
around 1940, buy the first one. If not, try the second one and read more
about the author here, including her
neverending
interview

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Jacobian conjecture remains open

Lately some
papers were posted on the arXiv
claiming to solve the plane Jacobian conjecture. Fortunately, T.T. Moh took
the time to crack these attempts and posted the mistakes they made also
on the arXiv : Comment on a Paper by
Yucai Su On Jacobian Conjecture
and Comment on a Paper by
Kuo, Parusinski and Paunescu On Jacobian Conjecture
. Both papers are
only 2 pages long but are fun reading.

This note
was written on Oct 10, 2005 and was sent to the authors. At once
they replied to insist that they are correct, which was natural.
After a month we checked the website of Parusinski,
and found that a new sentence ”The proof contains some gaps in
section 7” by the authors without mentioning any objection by
us.

So, the plane Jacobian conjecture remains
open, at least for now..

As for Kuo and his
collaborators, we believe that they have a good taste of
mathematics, and wish that they will push the analytic method deeper
to solve the Jacobian Conjecture.

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teaching mathematics

Tracking an email address from a subscribers’ list to the local news bulletin of a tiny village somewhere in the French mountains, I ended up at the Maths department of Wellington College.

There I found the following partial explanation as to why I find it increasingly difficult to convey mathematics to students (needless to say I got my math-education in the abstract seventies…)

“Teaching Maths in 1950:

A logger sells a truckload of lumber for £ 100. His cost of production is 4/5 of the price. What is his profit?

Teaching Maths in 1960:

A logger sells a truckload of lumber for £ 100. His cost of production is 4/5 of the price, or £80. What is his profit?

Teaching Maths in 1970:

A logger exchanges a set A of lumber for a set M of money. The cardinality of set M is 100. Each element is worth one dollar. The set C the cost of production, contains 20 fewer elements than set M. What is the cardinality of the set P of profits?

Teaching Maths in 1980:

A logger sells a truckload of lumber for £ 100. His cost of production is £80 and his profit is £20. Your assignment: Underline the number 20.

Teaching Maths in 1990:

By cutting down beautiful forest trees, the logger makes £20. What do you think of this way of making a living? How did the forest birds and squirrels feel as the logger cut down the
trees? (There are no wrong answers.)

Teaching Maths in 2000:

Employer X is at loggerheads with his work force. He gives in to union pressure and awards a pay increase of 5% above inflation for the next five years.

Employer Y is at loggerheads with his work force. He refuses to negotiate and insists that salaries be governed by productivity and market forces.

Is there a third way to tackle this problem? (Yes or No).”

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