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).

# Category: stories

## le travers – april 2006

Published April 9, 2006 by lievenlb

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).

## why mathematicians can’t write

Published March 29, 2006 by lievenlb

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…’

Leave a Comment(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…

## music of the primes

Published March 28, 2006 by lievenlb

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, October 5, 2004

and infuriating

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.

## 3 yrs. later

Published March 20, 2006 by lievenlb

probably, you’ve never seen the dedication in my one quiver to rule them

all paper on the arXiv

unfortunately, i’ve not much to add to this, even 3 years later…

Leave a Comment## arXiv trackback wars

Published March 7, 2006 by lievenlb

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…

## Alain Connes on everything

Published January 6, 2006 by lievenlb

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‚Äô 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‚Äôt try to merge them too fast. For instance in noncommutative

geometry my approach is not the only one, there are other approaches

and it‚Äôs quite important that for these approaches there is no

social pressure to be the same so that they can develop

independently. It‚Äôs 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‚Äôt 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‚Äôt 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 ‚ÄúWitten was seen

reading your book in the library in Princeton‚Äù! So I don‚Äôt 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‚Äôt 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‚Äôt 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.

One Comment## 2005 lists : mathematical novels

Published December 28, 2005 by lievenlb

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)

- In search of Klingsor, by Jorge Volpi
- Popco, by Scarlett Thomas
- Lord Byron’s novel ‘The Evening Land’, by John

Crowley - The Oxford Murders, by Guillermo Martinez
- Nymphomation, by Jeff Noon
- The fractal murders, by Mark Cohen
- Improbable, by Adam Fawer
- Calculating God, by Robert J. Sawyer
- The wild numbers, by Philibert Schogt
- 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…

## Jacobian conjecture remains open

Published December 24, 2005 by lievenlb

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 ‚ÄùThe proof contains some gaps in

section 7‚Äù by the authors without mentioning any objection by

us.

So, the plane Jacobian conjecture remains

open, at least for now..

Leave a CommentAs 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.

## teaching mathematics

Published December 21, 2005 by lievenlb

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).”

Leave a Comment