


History of Mathematics / Histoire des mathématiques (Org: Richard O'Lander and/et Ronald Sklar)
 MICHAEL BARR, Department of Mathematics and Statistics, McGill University,
Montreal, Quebec H3A 2K6
The Chu construction: history of an idea
[PDF] 
The Chu construction started out as a way of constricting easy examples
of *autonomous categories. It first became more widely known as a
way of providing easy models of linear logic and then as a way of
simplifying the construction of *autonomous categories. It actually
originates in the construction of ``dual pairs'' in the topological
vector spaces, which goes back ultimately in George Mackey's
dissertation.
 LEN BERGGREN, Simon Fraser University, British Columbia
A tenthcentury mathematician: Abu alJud, his life and work
[PDF] 
Although the standard biographical sources are silent on Abu alJud,
Omar Khayyam tells us he solved an algebra problem, leading to a cubic
equation, that none of his contemporaries had been able to solve. Our
survey of his works, which we report in this talk, suggests that he was
indeed a talented mathematician. But he was also one who occasionally
`rushed into print' he had checked all the details of his argument and
who was embroiled in a nasty controversy with a contemporary on the
solution of a major unsolved problem.
 JONATHAN BORWEIN, CECM, Simon Fraser University, British Columbia
Digitizing the entire mathematical literature: what wild
surmise!
[PDF] 
THE DIGITAL MATHEMATICS LIBRARY.
The `DML' project proposes over the next decade to put on line
(scanned images) the entire printed corpus of Mathematics and to make
it generally available. It is estimated that between five and ten
percent is already available, though hard to find or access! A good
idea of some of the progress already made can be gathered at the
European Math Society's website (
http://elib.uniosnabrueck.de/EMIS/). As was clear from a meeting I
attended at NSF in late July, the project has significant support from
NSF and from its German counterpart. NRCCISTI was also present, and
seems likely to assist in digitizing our own Canadian content.
It is generally agreed that the greatest obstacle to success is neither
financial^{1} nor technical but lies in the incredibly
complicated intellectual property and rights management issues that
will have to be addressed. For example, in some settings one may have
to request permission from the estate of authors deceased as much as 70
years ago, as they certainly never anticipated such a use of their
work.^{2} More surely, while SpringerVerlag is already
`onboard', we shall have to come to some `modus vivendi' with other
large publishers such as Elsvier.
That said, success would represent an epochal event in cultural
history. The material will, with caveats, be assured for posterity, it
will be searchable (eventually the mathematics as well as the text),
and we (mathematicians and others) will discover many things we do not
know that we know.
 JOAN DEBELLO, St. John's University, Jamaica, New York 11439, USA
The history of the Magic Square in mathematics
[PDF] 
The Magic Square has been a wonderful mathematics puzzle for years. It
has shown up in many ancient architectural sites and in many
mathematics writings. This discussion will trace the roots of the
magic square and go through the steps of creating different dimensions
of the magic square. There will also be visuals of where the magic
square appears throughout history.
 FLORIN DIACU, University of Victoria
Spiru Haretu and the stability of the solar system
[PDF] 
We discuss the contributions of Spiru Haretu to the problem of the
solar system's stability and show their importance relative to
the mathematics research of the late 19th century. We also give
a brief survey of the subsequent developments and the consequences
of Haretu's results.
 HARDY GRANT, York University, Toronto, Ontario M3J 1P3
Mathematics in the thought of Nicholas Cusanus
[PDF] 
The famous 15thcentury cardinal appears on at least one list of
``great'' mathematicians; on the other hand his contemporary
Regiomontanus dismissed his efforts in mathematics as ``ridiculous''.
But whatever his technical competence, it is quite certain that
Cusanus's perception of mathematics coloured deeply his influential
views on such issues as the limits of human knowledge and the relation
of man to God. I shall try to sketch from both perspectivesthe
technical and the philosophicalthe place of mathematics in the
worldview of this fascinating figure.
 NIKY KAMRAN, Department of Mathematics and Statistics, University of McGill,
Montreal, Quebec H3A 2K6
The scientific correspondence between Einstein and
CartanLetters on absolute parallelism
[PDF] 
Between 1929 and 1932, Einstein and Elie Cartan carried an intense
scientific correspondence on the geometric and analytic aspects of a
unified field theory of gravitation and electromagnetism which had been
proposed by Einstein in 1929. This correspondence was edited by Robert
Debever, and published by Princeton University Press in 1979 on the
occasion of Einstein's centenary. The framework of this theory is that
of a differentiable manifold endowed with a connection for which all
frames are parallel. Such a connection has necessarily zero curvature,
but it will in general have nonzero torsion. The issues that Einstein
and Cartan discussed in great detail dealt mostly with the local
existence of analytic solutions to the field equations, and their
degree of generality in the sense of CartanKaehler theory. We will
present some of the mathematical and historical highlights of this
fascinating (and sometimes frustrating) correspondence.
 FRANCOIS MAJOR, Universitié de Montréal
Recurrent patterns in the ribosome
[PDF] 
I will introduce the structural graph we have been using for a
representation of ribonucleic acid (RNA) structure since the late
80's. Then, I will formally introduce RNA motifs, that is functional
or structural significant patterns, and present three approaches to
discover them. The first one, from biologists, is subjective and uses
visual examination of RNA structures. The second uses a greedy and
incremental algorithm that is costly and uses a subjective definition
of significance. Finally, the third one was discovered from taking a
natural step in the graph representation, that is by dividing the
structrual graph in a minimal cycle basis. We found redundant cycles
that correspond directly to and others that compose acknowledged
structural and functional motifs. The new approach has also allowed us
to discover new instances of the classical GNRA motif that do not fit
the GNRA sequence definition. We are now building a theory of RNA
cycles that we see as an expression of fundamental thermodynamics rules
at a higher than the atomic level.
 JOHN MCKAY, Concordia University, Montreal, Quebec H3G 1M8
The jfunction and its natural generalization
[PDF] 
I shall follow the development of ideas originating from elliptic
integrals to the jfunction and its natural generalization in recent
years to the class of replicable functions.
 ANGELO MINGARELLI, Faculty of Graduate Studies and Research, Carleton University,
Ottawa, Ontario K1S 5B6
R.G.D. Richardson, Canadian born mathematician
[PDF] 
We give a brief preliminary survey of the life and times of Roland
George Dwight Richardson, Canadian born mathematician of the last
century who, among his many contributions, served as Dean at Brown
University and was ultimately responsible for attracting John
D. Tamarkin there.
 CHRISTIANE ROUSSEAU, Département de mathématiques et de statistique, Université
de Montréal, Montréal, Québec
Divergent series: past, present, future
[PDF] 
Divergent series have been used successfully in mathematics for
centuries and have occupied an important place in mathematics until the
middle of the 19th century. During this period mathematicians could not
explain their success. In the 20th century mathematicians have
justified rigorously the use of divergent series and also explained why
they are so powerful. However divergent series remain a relatively
marginal subject in contemporary mathematics. In this lecture I will
present some history of divergent series related to differential
equations and explain why they are not so marginal in the subject. This
will bring me to the future.
 LUIS SECO, University of Toronto
A historical prespective of mathematics in the financial
industry
[PDF] 
This talk will overview the past history and current situation of the
use of mathematics in the financial industry.
 VIENA STASTNA, University of Calgary, Calgary, Alberta T2N 1N4
B. Bolzano: life and work
[PDF] 
Life amidst politics, religion and mathematics. Deposed by the emperor
Franz I. His contribution in philosophy, theology, logic, and mainly
his example of continous nowhere differentiable function 40 years
before Weierstrass.
 LARRY STOUDER, St. John's University, New York, USA
Network computingpast, present, and future
[PDF] 
In order to envision the future of network computing it is important to
understand its past. How did we get from a world dominated by
largescale monolithic mainframe computers with few, if any,
interconnections to a world where the personal computer and the
Internet reign supreme? Understanding key evolutionary events can
provide insight into the future of network computing and its impact on
our futures.
Looking back in time, the invention and development of the telegraph,
telephone, radio and computer formed the building blocks for
unprecedented integration of capabilities. In its short history, the
Internet has revolutionized the computer and communications world like
nothing before. A scant 10 years ago, the World Wide Web didn't
exist. The idea of doing business over the Internet was ludicrous.
There was no Windows operating system, no Fast Ethernet or Gigabit
Ethernet, no laptops, no PDA's no email, not even shopping at home.
This session reviews some of the significant events in the origins,
history, and evolution of the Internet. In addition, this session
reviews some major trends identified by leading futurists and pundits,
that may shape the industry over the next decade.
 PETER ZVENGROWSKI, Department of Mathematics and Statistics, University of Calgary,
Calgary, Alberta T2N 1N4
Olinde Rodrigues, a mathematician ``in the shadow''
[PDF] 
Olinde Rodrigues lived in the first half of the 19th century, and was
an outstanding mathematician whose achievements are only being fully
recognized today. He was Portugese by birth but French by training and
education. Even his most famous contribution, the Rodrigues formula
for the Legendre polynomials (which appears nowadays in most texts on
differential equations, advanced calculus, etc.), was not
attributed to him until about 50 years after his death. In this talk
we will discuss his mathematical contributions which are in diverse
fields such as analysis, rotation groups (in particular what we now
call SO(3) and Spin(3)), group theory, and combinatorics. We will
also discuss his contributions to an amazingly broad collection of
other disciplines: philosophy (in particular socialism), music,
women's rights, and racial equality. In the latter half of the 19th
century France named a ship in his honour. We will conclude by showing
that recently Rodrigues is finally getting some of the recognition he
deserves, in both mathematics and theoretical physics.
Footnotes:
^{1}Though the cost is likely to be somewhere between
$100 and $200 million US.
^{2}A recent US Supreme Court ruling told the New York Times
that it had to pay freelancers again when it put predigital material
on its website.

