Another math blog

moved to wordpress

2008-05-25T03:36:00.000-07:00

I'm in the process of moving this blog to wordpress, which has much better LaTex support. The new URL is wdjoyner.wordpress.com.

latex on blogger test

2008-04-19T15:39:00.000-07:00

This is a test following http://wolverinex02.googlepages.com/emoticonsforblogger2.

The latex code

should display some latex code for pi/4. Cool! (Don't forget to use the compose window, not the "Edit Html" window.) Seems to only work for displayed equations.

Here is another test:

sage: x = var("x")
sage: integral(1/(1+x^2),x,0,1)
pi/4
sage: plot(1/(1+x^2),x,0,1)

The plot is below.

The (Hamming) weight enumerator polynomial $A_C$ is defined by

where

denotes the number of codewords of weight $i$.
The support of $C$ is the set

open source firmware for some canon digital cameras

2008-04-04T10:19:00.000-07:00

I just found out that there is an open source firmware for certain Canon cameras http://chdk.wikia.com/wiki/CHDK. Will one for Nikon be created?

J. G. Thompson and J. Tits share 2008 Abels prize

2008-03-28T05:48:00.000-07:00

http://www.reuters.com/article/scienceNews/idUSL2768807220080328

John Griggs Thompson of the United States and Jacques Tits of France were awarded the Abels prize (sharing $1.2 million) on 3-27-2008 for their work in algebra and group theory.

Copyright law as it pertains to mathematics

2008-03-23T16:40:00.000-07:00

This is a brief survey on copyright law, as it pertains to mathematicians. It does not cover other aspects of intellectual property law, such as laws governing patents, trade secrets, and so on (see for example, [K]). The basic reference is the excellent book by Leaffer [L].

I am not a lawyer and this is not meant as legal advice. However, I think everyone would benefit from more information and discussion of copyright law, so please leave comments if you have something to add.

U.S. copyright law applies to writings, or "physical renderings", produced by an author. For this article, we assume the author is a U. S. citizen and the work was produced on U. S. soil. However, a "writing" is not assumed to be human-readable, so, for example, a software program in executable binary form, or "object code", is included [L], section 3.06. The owner of the copyright of a work has the exclusive right for

* reproduce or copy the work,
* prepare derivative works,
* distribute the work,
* perform the work publically,
* display the work publically.

Before explaining these terms, exceptions to these rights, and how these rights relate especially to mathematical works, we discuss works for which copyright law cannot be applied. The law is designed to protect creative written works.

Ideas which are only communicated oraly are generally not subject to copyright, as they have not been "physically rendered." If you tell a friend your unwritten idea of how to solve the Riemann hypothesis, who proceeds to write up the idea and publish it, feel flattered because copyright law won't help you.
An unoriginal work, or a work "mechanically produced", say by a computer program whose use requires no originality, are not copyrightable (more precisely, are not subject to a separate copyright - the program could, for example, output copyrighted elements). For example, the output of an automatic theorem proving program is not copyrightable. On the other hand, the output of
an image processing program which takes an image and applies a de-noising algorithm is a "mechanical" derivation of the original image, so the copyright is the same as that of the original.
Data is not copyrightable. It doesn't matter how much money or man power it took to discover, collect, or obtain it. (However, there are various laws which can be used to protect such intellectual property, such as trade secret laws.) In some cases, a creative arrangement of the data itself is copyrightable, even if the data itself is not.
Works in the public domain (in particular most "official" works by the U. S. government), are not copyrightable. All written works eventually pass into the public domain. Due to the variety of copyright laws which have been passed in the United States over the years, the duration of copyright depends on when the work was written, if it is a joint work (or a "work for hire") or not, and various other factors. However, life plus 50 years is a minimum, according to the Berne convention, so that will apply in most cases.

For the owner of a creative mathematical work, whether it is an article or a piece of software, we explain next what these rights mean.

Reproduction: A reproduction is to fix a copy in a tangible and relatively permanent form, such as a xerox copy or a file on a computer (though a copy stored in your cache is exempted). Aside from non-profit, educational, government, or "fair use", the copyright holder have the sole right to make unlimited copies of your work. For example, if you publish a paper or book, you often sign over your copyright to a publisher. If anyone could make a copy of your article freely, the commercial interest of the publisher would disappear. Similarly, if you wrote a mathematical software program which you wanted to market, you would want to restrict the copies of the program to those who paid for it. A research paper downloaded from the internet and then emailed to a colleague is an example of a reproduction.

However, there is a fair use exception to copyright law regarding copying for personal use if you are a scholar (at a non-profit institute) or the educational use of your students if you are a teacher (at a non-profit institute). These do not apply to commercial think-tanks or to commercial training centers. The guidelines are different for research than for educational use, but the basic idea is to copy no more than is necessary. The guidelines for education are more strict. Generally, 1000 words or 10\% of the material (the minimum of the two) are recommended limits [L], section 10.12.

Derivative works: Only the copyright holder can create a new work which is adapted from the original but which contains copyrightable modifications. For example, if you wrote a mathematical textbook and you retained its copyrights, then only you have the right to create a translation into another language or a second edition. Conversely, if you wrote a mathematical software program which you wanted to give away for free but subject to the open source General Public License (GPL), then you want to restrict the modifications or derivations of your program to those who publically redistribute the modified program under the same open source terms. This is what the carefully crafted legal language of the GPL does for you [F], [W]. (An example of such a project is the SAGE software program [S].)

Distribution: A work is distributed if it is made available to the "public" in some form. For example, a copy in a public library or a file posted on a world-accessible internet site are publically distributed. However, defining the term "public" precisely in this context is a technical legal matter, for which we refer to [L], section 8.13.

Performance and display rights generally refer to works of drama or art, and probably less useful to a mathematician. For these rights, we only mention that a talk on a scholarly paper could be a performance. Legally, such a performance does not constitute a "public distribution" or "reproduction" of the paper itself.

References:
[F] Free Software Foundation, http://www.fsf.org

[K] B. Klemens, Math you can't use,
Brooksings Institute Press, Washington DC, 2006.

[L] M. Leaffer, Understanding copyright law, 4th edition, LexisNexis, 2005.

[S] Sage mathematical software, http://www.sagemath.org

[W] M. Webblink, Understanding Open Source Software,
http://www.nswscl.org.au/journal/51/Mark_H_Webbink.html

East Coast Computer Algebra Day, ECCAD 2008

2008-03-22T07:02:00.000-07:00

ECCAD 2008 homepage

INVITED SPEAKERS

* John F. Nash, Jr.
Department of Mathematics
Princeton University

* Emmanuel N. Barron
Department of Mathematics and Statistics
Loyola University Chicago

* Erich Kaltofen
Department of Mathematics
North Carolina State University

* Y. V. Ramana Reddy
Department of ComputerScience and Electrical Engineering
West Virginia University

* Paul Wang
ICM/Kent
Kent State University

some favorite quotes

2008-03-22T04:47:00.000-07:00

Truth, like gold, is to be obtained not by its growth, but by washing away from it
all that is not gold. Leo Tolstoy

The best thing for being sad is to learn something. That is the
only thing that never fails. You may grow old and trembling in your
anatomies, you may lie awake at night listening to the disorder of
your veins, you may miss your only love, you may see the world about
you devastated by evil lunatics, or know your honor trampled in the
sewers of baser minds. There is only one thing for it then to learn.
Learn why the world wags and what wags it. That is the only thing
which the mind can never exhaust, never alienate, never be tortured
by, never fear or distrust, and never dream of regretting.
T. H. White, in The Once and Future King

Education is what survives when what has been learnt has been forgotten.
B. F. Skinner

The advantage is that mathematics is a field in which one's
blunders tend to show very clearly and can be corrected or
erased with a stroke of the pencil. It is a field which has
often been compared with chess, but differs from the latter
in that it is only one's best moments that count and not
one's worst. A single inattention may lose a chess game,
whereas a single successful approach to a problem, among
many which have been relegated to the wastebasket, will
make a mathematician's reputation.
Norbert Wiener, in Ex-Prodigy: My Childhood and Youth

Wir müussen wissen.
Wir werden wissen.
David Hilbert
[Engraved on his tombstone in Göttingen]

What we hope ever to do with ease we may learn first to do with diligence.
Samuel Johnson

Rigor is to the mathematician what morality is to men.
Andre Weil

Science is a differential equation. Religion is a boundary condition.
Alan Turing

Find out just what any people will quietly
submit to and you have found out the exact measure of injustice
and wrong which will be imposed upon them.
Frederick Douglass

Where the mind is without fear and the head is held high
Where knowledge is free
Where the world has not been broken up into fragments
By narrow domestic walls
Where the words come out
From the depth of truth
Where the tireless striving stretches its arms towards perfection
Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit
Where the mind is led forward by thee
In ever widening thought and action
Into that heaven of freedom, my father
Let my country awake.
Rabindranath Tagore
(from his book Gitanjali)

Everything is vague to a degree you do not realize till you
have tried to make it precise.
Bertrand Russell

For every complicated problem there is a solution that is simple,
direct, understandable, and wrong.
H. L. Mencken

If people do not believe that mathematics is simple,
it is only because they do not realize how complicated life is.
John Louis von Neumann

In mathematics we do not appeal to authority, but rather you are
responsible for what you believe.
Richard Hamming, Americ an Math Monthly, vol 105 no 7.

There are some things which cannot be learned quickly,
and time, which is all we have,
must be paid heavily for their acquiring.
They are the very simplest things,
and because it takes a man's life to know them
the little new that each man gets from life
is very costly and the only heritage he has to leave.
Ernest Hemingway
(From A. E. Hotchner, Papa Hemingway, Random House, NY, 1966)

The scientist does not study nature because it is useful;
he studies it because he delights in it,
and he delights in it because it is beautiful.
If nature were not beautiful,
it would not be worth knowing,
and if nature were not worth knowing,
life would not be worth living.
Henri Poincaré

Believe that none of the effort you put into coming closer to God is ever
wasted -- even if in the end you don't achieve what you are striving for.
Rebbe Nachman of Breslov

Marriage is an alliance entered into by a man who can't
sleep with the window shut and a woman who can't sleep
with the window open.
George Bernard Shaw

If you think education is expensive, try ignorance.
Derek Bok

Whatever you can do, or dream you can do, begin it.
Boldness has genius and power and magic in it.
Johann Goethe
(John Anster's translation of Faust}

Every society honors its live conformists and its dead troublemakers.
Mignon McLaughlin

Praise and blame, gain and loss, pleasure and sorrow come and
go like the wind. To be happy, rest like a giant tree in the
midst of them all.
Buddha

If a dog barks his head off in the forest and no human hears
him, is he still a bad dog?
Anonymous

I believe that a scientist looking at nonscientific problems is
just as dumb as the next guy.
Richard Feynman

To be what we are, and to become what we are capable of becoming,
is the only end in life.
Baruch Spinoza

Watch your thoughts; they become words.
Watch your words; they become actions.
Watch your actions, they become habits.
Watch your habits, they become character.
Watch your character; it becomes your destiny.
Frank Outlaw

Creativity is God's gift to you. What you do with it is your gift to God.
Bob Moawad

Maturity is the ability to do a job whether or not you are supervised,
to carry money without spending it, and to bear an injustice
without wanting to get even.
Ann Landers

If you do not change direction, you may end up where you are heading.
Lao Tzu

I love you when you bow in your mosque, kneel in your temple, pray in
your church. For you and I are sons of one religion, and it is the
spirit.
Kahlil Gibran

The earth is but one country, and mankind its citizens.
Baha'u'llah

new Rubik's cube face turn record

2008-03-21T04:44:00.000-07:00

Tom Rokicki has announced that 25 moves suffice to solve the Rubik's cube. (The previous record was 26, by Gene Cooperman and Dan Kunkle.) His paper is at http://tomas.rokicki.com/rubik25.pdf

Hadamard matrices links

2008-03-07T12:07:00.001-08:00

Here are some interesting links for Hadamard matrices:

* for general info
http://en.wikipedia.org/wiki/Hadamard_matrix

* for tables
http://research.att.com/~njas/hadamard/

* online database
http://www.iasri.res.in/webhadamard/

* some conjectures:
http://www.uow.edu.au/~jennie/hadamard.html

new SAGE email list: sage-edu

2008-02-21T17:52:00.000-08:00

Group specifics:
* Group name: sage-edu
* Group home page: http://groups.google.com/group/sage-edu
* Group email address sage-edu@googlegroups.com
Please join if you are interested in SAGE and education in a high school
or a university.

protest of microsoft offer for yahoo+flickr

2008-02-10T09:51:00.001-08:00

protest of microsoft offer for yahoo+flickr, originally uploaded by David Joyner.

I will quit Flickr if the MS purchase of Yahoo goes through.

SAGE and differential calculus

2008-01-30T04:25:00.000-08:00

I've finished a book on SAGE and differential calculus. The idea was to simply take the old book Granville's Elements of Calculus, which is public domain now, and slightly modernize and "SAGE-ify" it. The source code, with the pdf form (and the pdf scan of the original book of Granville) can be found at
http://www.opensourcemath.org/books/granville-calculus/ or
http://sage.math.washington.edu/home/wdj/teaching/.
It is open-source and about 230+ pages printed. Hope it is useful for some people.
It is not quite in it's final form, so if you find typos, of have comments, please feel free to email me.

first aliquot factor found by SAGE ECM interface

2008-01-02T08:54:00.000-08:00

Paul Zimmermann (http://www.loria.fr/~zimmerma/records/aliquot.html) reports:

The SAGE ECM interface found a first factor of the aliquot sequence starting
from 552:

remains 23648161798622140141259448258749760352819524456141488104537419990481892694930432002158957619604181055633215274583954462907657503167424176909 (140 digits)
found factor by ecm: 58417195751812372006463994075468288063413 with parameters {'poly': 'Dickson(6)', 'sigma': '300411371', 'B1': '3990569', 'B2': '8561602150'}
Other nice factors will surely follow.

An aliquot sequence is simply the iteration of the function n -> sigma(n)-n,
where sigma(n) is the "sum of divisors" function. One open question from
Catalan is whether this sequence always converges to 1 (or to a cycle). The
first to perform extensive computations on aliquot sequences was Lehmer, who
found that all sequences starting from n <= 1000 converge, except perhaps
n=276, 552, 564, 660 and 966. These are the "Lehmer five" sequences. Since
several years, together with other people, I try to extend these Lehmer five
sequences. The main difficulty is that to compute sigma(n), you have to
factor n. For the current large numbers we encounter (150-160 digits) we use
a combination of different algorithms (ECM, QS, NFS). I have now converted
to SAGE the script that (tries to) extend aliquot sequences. The above
factorization is a first success of the new script.

OSS in govt and business and DoD

2007-12-19T07:51:00.000-08:00

I went to an open source conference Dec 11-12 2007, with talks by
Bill Vass, COO of Sun (http://en.wikipedia.org/wiki/Bill_Vass), David A Wheeler (http://www.dwheeler.com), John Weatherby of OSSI (http://oss-institute.org/), Terry Bollinger of MITRE (http://terrybollinger.com/), and representatives of the GSA, the US Army (including Brig Gen N. G. Justice), US Air Force, and several other commercial companies such as Unisys, BearingPoint, Palamida.

Here are some notes in random order:

Must use OS for the increasingly complicated ("exploding")
software/lines of code in communication systems. Systems involve more
data, more "horsepower", and more functionality.
Embedded systems (1998? jet avionics has 1.7M lines
of code, bluray dvd has 8M lines of code) are getting more
and more complex. Proprietary systems
cannot be reused by another contractor, leading to "vendor lock", nor can
they be improved, modified, or debugged. All software requires
maintenance and debugging. OSS shares the cost of maintenance.

Fundamental Principle (Software security): Open design principle is the
statement that any protection mechanism must not depend on attacker
ignorance.
OSS obeys this principle ("security by obscurity isn't").

Terry Bollinger, MITRE:
Use of FOSS in DoD is greatest in intfrastructure support
(network, ...) software development (C, C++, ...), security
(operating systems, cyberattack response, ...), research (math
software, ...). Report at http://www.terrybollinger.com

Anthony Gold (Unisys):
anthonygold.blogspot.com
LZW ( a compression system used by gif) was discovered at
unisys. This is how not to start OS.
OSS is a 20 billion/yr and growing at 20% (Unisys data)
CIO Conundrum:
- IT budgets declining
- most dollars spent on maintainance
- moe accountability
- more demands for new features
- lots of legacy code
- users demand more access
OSS is a great soln

Future of OS adaption, M Tolliver Palamida
OSS- sf.net has > 156K projects.
800K developers (average yrs experience is 11, age is 30)
OSS is very common - even in proprietary systems. Typically
50% of closed source systems is actually open source.
Usually this is unknown to the company writing the software itself.
Why should the taxpayer pay for compression utility over and over?
Software needs to be tracked just like any other supply chain.
Issues - policy, education, transparency, complicance.

Bill Vass, Pres COO Sun
Open systems refer to standards (ask what standards they use and who
maintans those standards)
Open source refers to OSI license (ask whick one)
You want both.
Security through obscurity isn't (this of the Trojan horse - what if the
enemy inside was visible?).
Number 1 reason why IT profs, govt agencies, education insts use OSS?
Security. TCO is number 2.
Percentage of US busineses using OSS: 87%
Every sun product is OS or will be - even hardware. Sun requires *signed*
contributor agreements.
Sun spent 404M dollars on linux (more on OSS products)
OSS is ready for primetime - think gogle, yahoo,
ebay, sun, banks (mysql), ...
Organizations can save millions of dollars using OSS. Use
indemnified providoes like Sun.
Stay away from proprietary extensions. Look carefullly at support costs.
(Think of bottled water as an analogy.)
OSS is *not* about training and it's about change management.

"Scale of problem indicates you must use, OS to obtain security
and functionality." Dewey Houch, CTO, Boeing.
"You cannot retain the intellectual talent to maintain a closed-source
system to solve all problems."

David Wheeler, IDA
Vendor lockin is a security problem!
Open design improves security.
Bruce Schneier: "demand OSS for anything related to security".
Whitfield Diffie: "it's simply unrealistic to depend
on secrecy for security".
Borland - Interbase/Firebird database program was closed source
and had a backdoor (a login and password which would allow any
user access). It was not paking a profit, so released as
open source. Within 5 months, this security problem was
discovered and fixed!
http://www.dwheeler.com/oss_fs_eval.html

Science Dialy: Free Software Brings Affordability, Transparency To Mathematics

2007-12-10T08:38:00.000-08:00

ScienceDaily (2007-12-07) -- Mathematicians are on a mission to replace the costly software used in education and research with a free, open-source version. More than 100 mathematicians around the world are helping to develop the tool.
article

ZDNet article: Sage - not a piece of cake

2007-12-10T08:26:00.000-08:00

Sage - not a piece of cake, but powerful and open by ZDNet's Christopher Dawson -- Developed at the University of Washington, with contributions from mathematicians worldwide, Sage is a relatively new open-source tool designed to supplant proprietary mathematical analysis programs like Maple, Matlab, and Mathematica. All of these programs are mainstays of most mathematicians’ toolkits, but have recently come under scrutiny because of the black-box nature of their calculations [...]

Free Open Source Mathematics Software?!

2007-12-06T15:26:00.001-08:00

The free open source mathematics program Sage (http://sagemath.org) just won first prize in the scientific software division of Les Trophees du Libre, an international competition for free software. Sage, faced initial skepticism from the mathematics and education communities; soon they will face off against the major software companies.

read more | digg story

Letter to the editor of the AMS Notices

2007-08-02T17:53:00.000-07:00

This was written with William Stein:

Mathematical software has greatly contributed to mathematical
research, enabling exciting advances in mathematics and providing
extensive data for conjectures. Perhaps three of the most well-known
applications of computation to mathematical research are resolution of
the four-color conjecture by Appel and Haken in 1976 (though it is
now reproven without computers by N. Robertson, D. P. Sanders,
P. D. Seymour and R. Thomas), Thomas Hales's proof of the
Kepler's conjecture, and the formulation of the Birch and
Swinnerton-Dyer conjecture, which grew out of extensive numerical
computation.

Open source software has had a profound effect on computing during the
last decade. Careful funding of open source mathematical software
can lead to a lower total
cost of ownership in the research and education community, and to more
efficient and trustworthy mathematical software.

``I think we need a symbolic standard to make computer manipulations
easier to document and verify. And with all due respect to the
free market, perhaps we should not be dependent on commercial
software here. An open source project could, perhaps, find better
answers to the obvious problems such as availability, bugs, backward
compatibility, platform independence, standard libraries, etc.
One can learn from the success of \TeX\ and more specialized software
like Macaulay2. I do hope that funding agencies are looking into this.''

-- Andrei Okounkov, 2006 Fields Medalist
(see "Interviews with Three Fields Medalists,''
Notices of the AMS, March 2007, Volume 54 , Number 3 (2007)
405-410).

The term open source is defined in http://www.opensource.org/,
but basically it means anyone (including commercial companies or
the defense department) should be able to inspect open source software,
modify it, and share it with others.

A key difference between mathematical theorems and software, is that
theorems require little maintenance (other than perhaps submitting an
errata list to the publisher for typos), whereas {\em mathematical
software requires substantial and potentially expensive maintenance}
(bug fixes, changes in the underlying interpreter/compiler, updates
when the underlying algorithms are improved, and so on). Mathematical
research usually generates no direct revenue for researchers, and
likewise open source mathematical software does not directly generate
revenue. The financial support of the NSF (and other organizations)
is thus critical to the success of open source mathematical software.

computational sciences video

2007-07-23T06:19:00.000-07:00

There is an excellent lecture on computational sciences by Rainald Lohner (Professor, Computational Sciences, George Mason University) at
the research channel. Highly recommended.

Very red curve

2007-07-18T17:22:00.001-07:00

Very red curve, originally uploaded by David Joyner.

This is one of my favorites.

Short Rubik's cube solving programs

2007-06-26T05:02:00.001-07:00

I just found this site, which seems really interesting:
http://tomas.rokicki.com/cubecontest/winners.html

Zeus chasing a snowflake

2007-06-05T11:35:00.001-07:00

Zeus chasing a snowflake, originally uploaded by David Joyner.

One of my favotite shots.

kerplunk

2007-06-04T05:05:00.001-07:00

kerplunk, originally uploaded by David Joyner.

Taken on Mill Creek during a rain on June 3, 2007.

glass, white and blue

2007-05-26T07:20:00.001-07:00

glass, white and blue, originally uploaded by David Joyner.

This photo has gotten a lot of very kind comments recently.

bridge pylons

2007-05-24T19:42:00.001-07:00

bridge pylons, originally uploaded by David Joyner.

My most popular flickr photo (as of May 24, 2007).

Flickr

2007-05-24T19:32:00.001-07:00

This is a test post from , a fancy photo sharing thing.

Rantings on open source CAS's

2007-05-23T22:39:00.001-07:00

The prevailing view of working mathematicians regarding mathematical software is very practical (first, determine the software which is available and has the desired functionality and then sort that set by ease-of-use). Convenience is king and issues such as proprietariness (if that is a word) is servant. This is natural from a human perspective - there are only so many hours in each day and we only have so much energy to invest in climbing the learning curve of a new system. From a mathematical, or more generally a scientific, perspective, this is not so natural. In this domain, convenience is slave to correctness and verifiability, which rule with an iron fist.

Consequently, it is not surprising that commercial systems built with proprietary code are more popular than free and open source systems. (By the way, MAGMA is technically not commercial - being "not for profit" - but for the purpose of this discussion we shall not distinguish MAGNA from Mathematica or Maple or Matlab, as they all follow a similar funding model.) The cost is based on what the market will bear and that gets leveraged into further development. As they improve, their customer base increases and solidifies.

On the other hand, the current status of many open source computer algebra systems, such as Maxima, is largely based on U.S. government funding (e.g., Dept. of Energy and NSF support) and corporations such as IBM (who developed Scratchpad to illustrate the value of its computers). These days, government finding has dried up and IBM has turned from Scratchpad to programs such as the chess-playing Deep Blue to help sell its latest line of computers.

How does the future look for open source computer algebra systems? Not good, if you think the following hypothetical scenario is reasonable. Programs such as MAGMA will become more and more popular with researchers, especially young ones at NSF-funded top-tier universities with heavy pressure to publish and a software budget to match. Systems such as Maxima will become less and less relavant. Development and maintanace will be supported by community-minded volunteers having full-time
jobs in industry or academia.

Is it healthy for scientific papers, mathematical ones in particular, to be supported by computations which cannot be verified, except by the relatively few employees of the commercial software system they use. Let's think about this for a moment.

By law, the US givernment cannot favor one commercial system over another. Is it ehical for them to favor commercial systems over non-commercial ones? It is right for the NSF or its agents to support proprietary commercial systems over open source systems? It seems to me that this is a sitation where the letter differs significantly from the spirit of the law. In spirit, competition is to be encouraged, with the idea that quality is thereby increased by competitive forces. Open source software fosters competition in the marketplace and at the same time provides a product for lower-income educational institutions. Both of these are in the spirit of the
law. However, the favoring of commercial products by the NSF is not in the spirit of the law. Indeed, in that case, the money simply goes not to the lowest bidder but the best (in the eyes of the NSF agent in charge of awarding the funds) of the commerical products. This is essentially the same as awarding a no-bid contract to the product the NSF thinks is best.

Consider the argument that the NSF shouldn't support open source systems since they (being free) undermine the capitalistic process and do not contribute to the marketplace. This is completely incorrect. Indeed, free software increases the value of the computer and operating system itself. (In fact, this is precisely why corporations such as IBM supported these free systems in the early days. They made the software free since to run it back then, you had to buy their computer.) So, as long as the free program is cross-platform, free software does contribute value to the marketplace as a whole, yet does not favor one company over another.

Finally, let us try to design a CAS based not on human behavior but on objective, logical principles. We want a CAS which is

open source (for verifiability and correctness),
easy to use and free (for greater availablity, thus fostering cooperation
and collaboration, and greater practicality),
scientifically beneficial (obviously).

These are the three basic principles which are demanded by scientific requirements. Should not organizations such as the NSF and ACM support these open source systems rather than other systems?

Jeff Leon's Partition Backtracking code is GPL'd

2007-04-18T13:18:00.000-07:00

I'm at the IMA coding theory, complexity and communication conference this week. (I'll post pictures somewhere later.)

One problem I've been trying to solve is to try to contact Jeffery Leon, a mathematician at UIC who wrote a number of programs using a very difficult combinatorial technique called "partition backtracking". This collection of programs, written in C in the 1980's, will compute automorphisms of designs, linear codes, and matrices. The program Leon wrote does some hard coding theory and combinatorial computations quite fast. The issue is that it does not have an open source license. I think it was written during a time when no one worried about such things. I have tried over the years emailing and calling Leon, but no responses. (BTW, many people have told me that Jeff is a very nice guy but you have to physically talk to him, as opposed to writing.) These days, no one will maintain it unless it has some sort of open source license (such as the GPL or the MIT license or the BSD licence ...). If this is not done, the code will die. Why? Well, bugs have been discovered (some serious, some not) and no one will spend the time to maintain someone else's code. There are many people who are willing to maintain, on volunteer basis, open source software, as part of a community effort though. Also, the code is hard to read, which only compounds the problem.

I happened to ride the airport shuttle to the hotel with Vera Pless, the great (now "retired" from UIC, though she still directs several students) coding theorist who is also visiting the IMA, and told her the problem. When we were dropped off we went our separate ways. Then, the next day we happened to meet at breakfast and she told me to call Steven Smith (the finite group theorist) at UIC and tell him the problem. I sent him and email and he almost immediately responded that he would sit down to talk with Jeff Leon about the situtation. As a result of Vera and Steven's help, Jeff just sent me a very nice email saying, in particular:

I, Jeffrey S. Leon, agree to license all the partition
backtrack code which I have written under the GPL
(www.fsf.org) as of this date, April 17, 2007.

This is great news!

Favorite quotes

2007-04-15T05:52:00.000-07:00

There are some things which cannot
be learned quickly, and time, which is all we have,
must be paid heavily for their acquiring.
They are the very simplest things,
and because it takes a man's life to know them
the little new that each man gets from life
is very costly and the only heritage he has to leave.
- Ernest Hemingway

(From A. E. Hotchner, Papa Hemingway, Random House, NY, 1966)

Finish each day and be done with it.
You have done what you could;
some blunders and absurdities have crept in;
forget them as soon as you can.
Tomorrow is a new day;
you shall begin it serenely and with too high a spirit
to be encumbered with your old nonsense.
- Ralph Waldo Emerson

Whatever you can do, or dream you can do, begin it. Boldness has genius and power and magic in it.
- Johann Goethe
(John Anster's translation of Faust)

This was my uncle David's favorite quote.

Praise and blame, gain and loss, pleasure and sorrow come and go like the wind. To be happy, rest like a giant tree in the midst of them all.
- Buddha

We must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity.
- Marie Curie

The best thing for being sad is to learn something. That is the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honor trampled in the sewers of baser minds. There is only one thing for it then to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting.
- T. H. White, in The Once and Future King

The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.
- Norbert Wiener, in Ex-Prodigy: My Childhood and Youth

Mathematicians who are chess masters

2007-04-10T18:16:00.000-07:00

Here is a list I've compiled (the references below are the same as in the post entitled Mathematics and chess):

Adolf Anderssen (1818-1879). Pre World Championships but is regarded as the strongest player in the world between 1859 and 1866. He received a degree (probably not a PhD) in mathematics from Breslau University and taught mathematics at the Friedrichs gymnasium from 1847 to 1879. He was promoted to Professor in 1865 and was given an honorary doctorate by Breslau (for his accomplishments in chess) in 1865.
Noam Elkies (1966-), a Professor of Mathematics at Harvard University specializing in number theory, is a study composer and problem solver (ex-world champion). Prof. Elkies, at age 26, became the youngest scholar ever to have attained a tenured professorship at Harvard. One of his endgame studies is mentioned, for example, in the book Technique for the tournament player, by GM Yusupov and IM Dvoretsky, Henry Holt, 1995. He wrote 11 very interesting columns on Endgame Exporations (posted by permission).
Some other retrograde chess consructions of his may be found at the Dead Reckoning web site of Andrew Buchanan.
See also Professor Elkies's very interesting Chess and Mathematics Seminar 2003, 2004, Spring [2005-]2006, Fall 2006 pages and the mathematical papers on his chess page.
Machgielis (Max) Euwe (1901-1981), World Chess Champion from 1935-1937, President of FIDE (Fédération Internationale des Echecs) from 1970 to 1978, and arbitrator over the turbulent Fischer - Spassky World Championship match in Reykjavik, Iceland in 1972. I don't know as many details of his mathematical career as I'd like. One source gives: PhD (or actually its Dutch equivalent) in Mathematics from Amsterdam University in 1926. Another gives: Doctorate in philosophy in 1923 and taught as a career. (For more information, see Iversen Lapp's article, where is it mentioned he was also the director of a study center for computers.) Published a paper on the mathematics of chess (Mengentheoretische Betrachtungen uber das Schachspiel", Konin. Akad. Weten., Proc Acad Sciences, Netherlands, vol 32, 1929, 633-642).

Ed Formanek (194?-), International Master. Ph.D. Rice University 1970. Currently on the mathematics faculty at Penn State Univ. Works primarily in matrix theory and representation theory.
Charles Kalme (Nov 15, 1939-March 22, 2002), earned his master title in chess at 15, was US Junior champ in 1954, 1955, US Intercollegiate champ in 1957, and drew in his game against Bobby Fischer in the 1960 US championship. In 1960, he also was selected to be on the First Team All-Ivy Men's Soccer team, as well as the US Student Olympiad chess team. (Incidently, it is reported that this team, which included William Lombardy on board one, did so well against the Soviets in their match that Boris Spassky, board one on the Soviet team, was denied foriegn travel for two years as punishment.) In 1961 graduated 1st in his class at the Moore School of Electrical Engineering, The University of Pennsylvania, in Philadelphia. He also received the Univ of Penn. Cane award for leadership that year. After getting his PhD from NYU (advisor Lipman Bers) in 1967 he to UC Berkeley for 2 years then to USC for 4-5 years. He published 2 papers in mathematics in this period, "A note on the connectivity of components of Kleinian groups", Trans. Amer. Math. Soc. 137 1969 301--307, and "Remarks on a paper by Lipman Bers", Ann. of Math. (2) 91 1970 601--606. He also translated Siegel and Moser, Lectures on celestial mechanics, Springer-Verlag, New York, 1971, from the German original. He was important in the early stages of computer chess programming. In fact, his picture and annotations of a game were featured in the article "An advice-taking chess computer" which appeared in the June 1973 issue of Scientific American. He was an associate editor at Math Reviews from 1975-1977 and then worked in the computer industry. Later in his life he worked on trying to bring computers to elementary schools in his native Latvia. His highest rating was acheived later in his life during a "chess comeback": 2458.
Here is his game against Bobby Fischer referred to above:
```
[Event "?"]
[Site "New York ch-US"]
[Date "1960.??.??"]
[Round "3"]
[White "Fischer, Robert J"]
[Black "Kalme, Charles"]
[Result "1/2-1/2"]
[NIC ""]
[Eco "C92"]
[Opening "Ruy Lopez, Closed, Ragozin-Petrosian (Keres) Variation"]

1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 O-O
8.c3 d6 9.h3 Nd7 10.a4 Nc5 11.Bd5 Bb7 12.axb5 axb5 13.Rxa8 Qxa8
14.d4 Nd7 15.Na3 b4 16.Nc4 exd4 17.cxd4 Nf6 18.Bg5 Qd8 19.Qa4 Qa8
20.Qxa8 Rxa8 21.Bxf6 Bxf6 22.e5 dxe5 23.Ncxe5 Nxe5 24.Bxb7 Nd3
25.Bxa8 Nxe1 26.Be4 b3 27.Nd2 1/2-1/2
```
Emanuel Lasker (1868-1941), World Chess Champion from 1894-1921, PhD (or actually its German equivalent) in Mathematics from Erlangen Univ in 1902. Author of the influential paper [L], where the well-known Lasker-Noether Primary Ideal Decomposition Theorem in Commutative Algebra was proven . (See [K] for a statement in the modern terminology. For more information, search "Lasker, Emanuel" in the chess encyclopedia, as well as the links provided there.)
Lev Loshinski (1913-1976) , F.I.D.E. International Grandmaster of Chess Compositions. Taught mathematics (at Moscow State University?). (PhD unknown but considering the reputation of Moscow State University, he may have one.)
A. Jonathan Mestel, grandmaster in over-the-board play and in chess problem solving, is an applied mathematician specializing in fluid mechanics and is the author of numerous research papers. He is on the mathematics faculty of the Imperial College in London.
Walter D. Morris (196?-), International Master. Currently on the mathematics faculty at George Mason Univ in Virginia.
Nick J. Patterson, International Master (?), D. Phil. (from Cambridge Univ.) in 197? in group theory, under Prof. Thompson. Has published several papers in group theory, combinatorics, and the theory of error-correcting codes. For his chess web page, click here.
John Nunn (1955-), Chess Grandmaster, D. Phil. (from Oxford Univ.) in 1978 at the age of 23 (and the youngest undergraduate at Oxford since Cardinal Wolsey, I've heard). PhD thesis in Algebraic Topology and author of the paper [N] (Search "Nunn" in the chess encyclopedia for more information.)
Martin Kreuzer (1962-), CC Grandmaster, is rated over 2600 in correspondence chess (ICCF, as of Jan 2000). His OTB rating is over 2300 according to the chessbase encyclopedia. His specialty is computational commutative algebra and applications. Here is a recent game of his:
Kreuzer, M - Stickler, A
[Eco "B42"]
1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 a6 5.Bd3 Nc6 6.c3 Nge7 7.0-0 Ng6 8.Be3 Qc7 9.Nxc6 bxc6 10.f4 Be7 11.Qe2 0-0 12.Nd2 d5 13.g3 c5 14.Nf3 Bb7 15.exd5 exd5 16.Rae1 Rfe8 17.f5 Nf8 18.Qf2 Nd7 19.g4 f6 20.g5 fxg5 21.Nxg5 Bf6 22.Bf4 Qc6 23.Re6 Rxe6 24.fxe6 Bxg5 25.Bxg5 d4 26.Qf7+ Kh8 27.Rf3 Qd5 28.exd7 Qxg5+ 29.Rg3 Qe5 30.d8=Q+ Rxd8 31.Qxb7 Rf8 32.Qe4 Qh5 33.Qe2 Qh6 34.cxd4 cxd4 35.Bxa6 Qc1+ 36.Kg2 Qc6+ 37.Rf3 Re8 38.Qf1 Re3 39.Be2 h6 40.Kf2 Re8 41.Bd3 Qd6 42.Kg1 Kg8 43.a3 Qe7 44.b4 Ra8 45.Qc1 Qd7 46.Qf4 1-0
Chess problem composer Hans-Peter Rehm (1942-), a Professor of Mathematics at Karlsruhe Univ. He has written several papers in mathematics, such as "Prime factorization of integral Cayley octaves", Ann. Fac. Sci. Toulouse Math (1993), but most in differential algebra, his specialty. Some of his problems can be found on the internet, for example: problem set (in German). A collection of his problems has been published as: Hans+Peter+Rehm=Schach Ausgewählte Schachkompositionen & Aufsätze (= selected chess problems and articles), Aachen 1994.

Some other possible entries for the above list:

Alexander, Conel Hugh O'Donel (1909-1974), late British chess champion. Alexander may not have been a mathematician but he did mathematical (code and cryptography) work during WWII, as did the famous Soviet chess player David Bronstein (see the book Kahn, Kahn on codes). He was the strongest English player after WWII, until Jonathan Penrose appeared (see below for more on Penrose.) (Search "Alexander" in the chess encyclopedia for more information.)
Magdy Amin Assem (195?-1996) specialized in p-adic representation theory and harmonic analysis on p-adic reductive groups. He published several important papers before a ruptured aneurysm tragically took his life. He was IM strength (rated 2379) in 1996.
Christoph Bandelow teaches mathematics at the Ruhr-University Bochum. He specializes in stochastic processes and has written a number of excellent books on the magic cube (or "Rubik's cube") and related puzzles. Some of his chess problems are (by permission) : problem 1, problem 2, problem 3. (More to come.) Prof Bandelow was also a pioneer in computer problem solving, having written (in 1961) the first German computer program to solve chess problems (this program is described in "Schach und Zahl").
Prof. Vania Mascioni, also IECG Chairperson (IECG is the Internet Email Chess Group), is rated 2326 by IECG (as of 4-99). He is a professor of Mathematics at the University of Texas at Austin (his area is Functional Analysis and Operator Theory).
Kenneth S. Rogoff, Professor of Economics at Harvard University, is a Grandmaster. He has a PhD in Economics but has published in statistical journals.
Kenneth W. Regan, Professor of Computer Science at the State Univ. of New York Buffalo, is currently rated 2453. His research is in computational complexity, a field of computer science which has a significant mathematical component.
Otto Blathy, who is a very famous many mover problemist, held a doctorate in mathematics from Budapest and Vienna universities at his time. (For a reference, see A.Soltis: Chess to Enjoy. pp.30-34.)
Canadian grandmaster Duncan Suttles (b.1945 in San Francisco, moved to Vancouver as a child). Suttles studied for though did not (yet anyway) receive a PhD in mathematics. Suttles also has the grandmaster title in correspondence chess.
Problem composer J. G. Mauldon (deceased, formerly a mathematician at Amherst College) has written several papers in mathematics. One of his retro problems can be found on the internet, for example: problem.
Problem composer John D. Beasley has also written several books on the mathematics of games. He is secretary of the British Chess Variant Society.
Stanislaw Ulam, the famous mathematician and physicist (author of the autobiographical, Adventures of a mathemaician) was a strong chess player. Rating unknown.

There is some misleading information given either in the literature or on some internet web pages.

Karl Fabel (1905-?), F.I.D.E. International Master of Chess Compositions. Not a tournament player but an ingenious problem composer. He received a Doctorate in Chemistry and reportedly worked as a mathematician, civil judge, and patents expert. He was, according to his friend Christoph Bandelow, a chemist not a mathematician. Some Fabel problems. He was also the co-author of the book "Schach und Zahl" on mathematics and chess [EFR] and the problem book Rund um das Schachbrett. Publisher: Walter de Gruyter 1955.
Rueben Fine was not a mathematician (however, his son Ben is an active research mathematician who teaches at Fairfield University in Connecticut). Reuben Fine was a psychologist.
GM James Tarjan (a Los Angeles librarian, I'm told) is the brother of the well-known computer scientist (some of his research has been published in mathematical journals) Robert Tarjan.
Former world chess champion Kasparov is not a mathematician (as far as I know), though he has made contributions to computer science. (There is a well-know mathematician named Kasparov who works in K-theory and C^*-algebras but they are different people.) Kasparov seems to have retired from chess and s pursuing a political career.
Jonathan Penrose (mentioned above - one of the strongest chess players in Britain in the 1950's and 1960's) is the brother of the well-known mathematician and physicist Sir Roger Penrose.

Mathematics and chess

2007-04-10T18:06:00.000-07:00

Chess teaches many things, including strategic thinking. Though one might think at first that this type of thinking is unrelated to mathematics, in fact, chess also teaches a type of "calculation" (see Soltis's book [S] for the exact idea).

A paraphrase from the entry under Mathematics and Chess in [Su]: In 1893, a Professor Binet (of Stanford-Binet IQ test fame) made a study of the connection between mathematics and chess. After questioning a large number of leading players, he discovered that 90% were very good mental calculators. On the other hand, he discovered that although mathematicians are often interested in chess, few become top-class players.... Professor Binet commented that both chess and mathematics have a common direction and the same taste for combinations, abstraction, and precision. One characteristic which was missing from mathematics was the combat, in which two individuals contend for mastery, with all the qualities required of generals in the field of battle.

This page contains information on

which mathematicians (which we define as someone who has earned a PhD or equivalent in Mathematics) play(ed) chess at the International Master level or above (also included are those who have an IM or above in chess problem solving or composing), and
how to get papers on mathematical chess problems.

Papers about mathematical problems in chess:

I only know of a few sources:

Lewis Benjamin Stiller, "Exploiting symmetries on parallel architecture", PhD thesis, CS Dept, Johns Hopkins Univ. 1995 Closely related is his Games of No Chance paper, "Multilinear Algebra and Chess Endgames".
Max Euwe, "Mengentheoretische Betrachtungen uber das Schachspiel", Konin. Akad. Weten. (Proc Acad Sciences, Netherlands), vol 32, 1929, 633-642
Noam Elkies, "On numbers and endgames: Combinatorial game theory in chess endgames", in 1996 "Games of No Chance" = Proceedings of the workshop on combinatorial games held July'94 at MSRI. Available from MSRI Publications -- Volume 29 or Noam Elkies' site.
Mario VELUCCHI's NON-Dominating Queens Problem or math chess problems
Timothy Chow, "A Short Proof of the Rook Reciprocity Theorem", in volume 3, 1996, of the Electronic Journal of Combinatorics.
Herbert S. Wilf, "The Problem of the Kings", and Michael Larsen, "The Problem of Kings", both in volume 2, 1995, of the Electronic Journal of Combinatorics.
Papers on odd king tours by D. Joyner and M. Fourte (appeared in the J. of Rec. Math., 2003) and even king tours by M. Kidwell and C. Bailey (in Mathematics Magazine, vol 58, 1985).
Lesson 3 in the chess lessons by Coach Epshteyn at UMBC.

References

[BFR] Eero Bonsdorff, Dr Karl Fabel, Olavi Riihimaa, Schach und Zahl, unterhaltsame schachmathematik, Walter Rau Verlag, Dusseldorf, 1966
[L] Lasker, E. "Zur theorie der moduln und ideale," Math. Ann. 60(1905)20-116
[K] Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, Boston, 1985
[N] Nunn, J. D. M. "The homotopy types of finite H-spaces," Topology 18 (1979), no. 1, 17--28
[S] A. Soltis, The Inner Game of Chess, David McKay Co. Inc, (Random House), New York, 1994
[St] R. Stanley's Chess Problems webpage
[Su] A. Sunnucks, The Encyclopedia of Chess, 2nd ed, St Martins Press, New York, 1976

Thanks to Christoph Bandelow, Max Burkett, Elaine Griffith, Hannu Lehto, John Kalme, Ewart Shaw, Richard Stanley, Will Traves, Steven Dowd, Z. Kornin, and Noam Elkies for help and corrections on these posts (which started out as a web page).

Rubik's cube news

2007-04-05T20:19:00.000-07:00

Got an email from Gene Cooperman (CS Prof at Northeastern) a few days ago saying that he and some colleagues have shown that 26 moves (in the face-turn metric) suffice to solve Rubik's cube (the previous best upper bound is 27; lower bound is 20 - the superflip position). They used 7 terabytes of distributed disk space (I gotta get me one of those machines) and will be presenting their research at ISSAC-07.