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Subject: Re: Olinde Rodrigues Seminar
Date: Thu, 15 Nov 2001 16:39:04 +0000
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Sergio Plata
OLINDE RODRIGUES AND HIS CIRCLE:
MATHEMATICIANS AND SOCIAL UTOPIAS
A one Day meeting at the
Mathematics Department
Imperial College, London
Sponsored by: The London Mathematical Society and the
Sociiti Mathimatique de France
Saturday, December 1, 2001
9.30-10.00 Registration and coffee
10.00-11.00 Simon L. Altmann (Oxford) and David Siminovitch (Lethbridge):
Olinde Rodrigues and his times
11.00-11.50 Ivor Grattan-Guinness (Middlesex): Mathematics
education in France in Rodrigues s time
11.50-12.40 Paola Ferruta (Bielefeld and EHS, Paris):
Rodrigues's family: the female element
12.45-14.00 Lunch and coffee
14.00-15.00 Eduardo L. Ortiz (Imperial College, London):
Mathematicians and the social utopian
tradition, from Rodrigues to Laisant
15.00-15.50 Ulrich Tamm (Bielefeld):
Olinde Rodrigues and Combinatorics
15.50-16.15 Tea
16.15-17.15 Richard Askey (Wisconsin):
Two neglected results of Rodrigues
17.15-18.00 General discussion; end of the meeting
19.00 22.00 Conference Dinner
CONVENORS: Simon L. ALTMANN (Oxford) and
Eduardo L. ORTIZ, (Imperial College)
VENUE: Mathematics Department, Imperial College,
180 Queen s Gate, London SW7 2BZ
REGISTRATION FEE: #10.00; free for students and concessions. Covers
tea and coffee
CONFERENCE SECRETARY AND INFORMATION:
Sergio PLATA, Imperial College, [log in to unmask]
OLINDE RODRIGUES AND HIS CIRCLE:
MATHEMATICIANS AND SOCIAL UTOPIAS
ABSTRACTS
Olinde Rodrigues and his times
Simon L. Altmann and David Siminovitch
Oxford University and The University of Lethbridge
Olinde Rodrmgues spanned a period in which the freedoms granted to
citizens after the French Revolution had major cultural effects, not
totally quenched by the Restoration; and his life mirrors perfectly
those events. He was the first Jewish mathematician of the century,
as a difference from Jacobi, an academic career became closed to him.
As a mathematician, a banker, a social reformer, and a
Saint-Simonian, he was influential in the various cultural and social
advances of the first half of the century. His life, however, is not
well documented, and this paper fills a number of gaps in our
knowledge about his family and his education. We briefly review all
the mathematical works that he published and give an account of his
life and works as a banker, Saint Simonian, and social reformer.
Two neglected results of Rodrigues
Richard Askey,
University of Wisconsin
In his early work, Rodrigues found what is now called Rodrigues's
formula for Legendre polynomials and a bit more. His paper was
overlooked by mathematicians for almost 50 years. The type of
formula he found was also found by Laplace for Hermite polynomials,
and his result for Legendre polynomials was rediscovered by Ivory and
Jacobi long before Hermite found the earlier paper of Rodrigues.
There is a later paper of Rodrigues on a generating function for the
number of inversions of the permutations of the set {1,2,...,n} which
was also overlooked, this time by over 125 years. Again, the result
found by Rodrigues was rediscovered, but it took almost 75 years for
this to happen. Both of these results are of current interest
because of recent developments. Both the mathematics and the history
will be discussed.
Rodrigues's family: the female element
Paola Ferruta
University of Bielefeld and Icole des Hautes Itudes, Paris
A sketch is given of several women in the Rodrigues's family, based
on documents and correspondence extracted from various European
archives.
Mathematics education in France in Rodrigues s time
Ivor Grattan-Guinness,
Middlesex University
The period 1795-1830 saw a remarkable community of mathematicians of
great quality emerge in France, in a new institutional situation. I
shall indicate the principal institutions and figures involved, and
the main achievements of the community as a whole. The new doctorial
programme of the "Universiti" will be explained, and the The relative
inferiority of the Universiti to the Icole Polytechnique and related
colleges will be stressed
Mathematicians and the social utopian tradition, from Rodrigues to Laisant
Eduardo L. Ortiz
Imperial College, London
Among des intelligences d ilite attracted by Saint Simon and his
followers in Paris one can detect a group of gifted mathematicians.
The mathematical interests of some of them are closely related to
Rodrigues s own. The life and work of one of the younger members of
this group is briefly discussed. The broken progression from
Rodrigues s ideas to Hamilton s quaternions in France is discussed
through the scientific work of Laisant, Although entirely based on
Hamilton in his mathematical work, Laisant fits well into Rodrigues s
geometrical and philosophical tradition. The ensuing debate over
quaternions seems to have retained a flavour of Saint Simon s
radicalism; the impact of this debate on mathematics outside France
is briefly discussed.
Olinde Rodrigues and Combinatorics
Ulrich Tamm
University of Bielefeld
In several small papers in Liouville's Journal, 1838 and 1839, Olinde
Rodrigues provided new insights into combinatorial structures. His
nice recursive derivation on the number of ways to divide a polygon
into triangles was included by Netto in the first textbook on
Combinatorics 70 years later. Another note on the total number of
inversions of permutations on n elements was rediscovered by Leonard
Carlitz and his student Charles Church only in 1969.
Benjamin Olinde Rodrigues
Olinde Rodrigues is a very unusual man: he pursued several parallel
careers, some of them simultaneously, and because of this he appears
in different ways to different people. So, such biographical accounts
as we have are incomplete and often contradictory. He is presented
as a politician (Saint-Simonist), a social reformer, pioneer of
workers rights, proto-feminist, utopian socialist, banker, promoter
of social housing and of the railways - in most cases ignoring that
he was a mathematician some of whose work was so much ahead of his
time that it was not recognized until late in his century.
Rodrigues was born at Bordeaux on 16 October 1794, the son of a
distinguished Jewish family, bankers settled there for several
generations. Despite not having been admitted to the Icole
Polytechnique or the Icole Normale Supirieure, he managed to present
a doctoral thesis in 1815 to the newly founded University of Paris.
This work contains the famous Rodrigues formula for Legendre
Polynomials, one of the few mathematical works for which he is
properly credited.
On the other hand, his paper of 1840 on the rotation group instead,
his major work, and perhaps the most important done in this subject
until the end of the century, was so badly known that none less than
Eli Cartan refers to it as authored by Olinde and Rodrigues, a
mistake carelessly propagated in the literature.
Euler had shown in 1775 that the composition of two rotations is
another rotation, but Rodrigues went much further: given the axis and
angle of rotation of two rotations, he produced a geometrical
construction (normally referred to unjustly as the Euler
construction) that determines those two quantities for the resultant
rotation. But even more, by ingenious use of spherical trigonometry
he was able to find a multiplication rule for rotations in terms of
the cosines of the half angles of rotation and of the components of
the corresponding axes of rotation. This rule is precisely the
composition rule for quaternions, later found by Hamilton in 1843:
but Hamilton did not correctly correlate his quaternions with
rotations, because he insisted in the use of the full angle of
rotation as a parameter in them. This considerably retarded the
proper study of rotations until well into the end of the century. The
full significance of Rodrigues's paper was not properly understood
until the 1980's, when the precise way in which Hamilton's
quaternions had gone astray in attempting to describe rotations, and
how and why Rodrigues had hit the right results and the right
interpretation, began to be discussed. Rodrigues even studied
infinitesimal rotations in the 1840 paper, thus anticipating by
almost half a century results on the theory of continuous groups.
Despite the undoubted significance of Rodrigues both as a
mathematician and as a social reformer, so much was he neglected that
even the date of his death has long been surrounded by confusion,
different authorities quoting 26 December 1850 or 17 December 1851;
incontrovertible evidence has been found for the second date. A
conference is being organized at Imperial College London, on
Saturday, December 1, 2001, to commemorate 150 years of Rodrigues's
death, and as an opportunity to bring together scholars working on
different sides of Rodrigues's life, work, and times.
>From: [log in to unmask] (J. V. Field)
>To: "S. Plata" <[log in to unmask]>
>Subject: Re: Olinde Rodrigues Seminar
>Date: Wed, 14 Nov 2001 19:29:48 +0000
>
>Please note that I always trash unexpected attachments. You should
>paste the information into an email.
>
> Moreover, you sent your email, and attachment, twice.
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