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Re: [HM] Olinde Rodrigues
Posted:
Nov 13, 2001 11:55 AM
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Dear Julio,
This is to let you know that a meeting on the not well know life and work
of the French mathematician Olinde Rodrigues will take place at Imperial
College, London, on December 1, 2001. It commemorates the 150th
anniversary of his death. It is jointly sponsored by the London
Mathematical Society and the Societe Mathematique de France.
Maybe some of your readers may be interested to know about it, and some,
perhaps, attend it.
Best regards,
Eduardo
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
Soci/et/e Math/ematique 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 RodriguesÃÂs 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 QueenÃÂs Gate, London SW7 2BZ
REGISTRATION FEE: \Sterling10.00; free for students and concessions. Covers tea and coffee
CONFERENCE SECRETARY AND INFORMATION:
Sergio PLATA, Imperial College, spi@hp.fciencias.unam.mx
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 Rodrigues 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 /Ecole des Hautes /Etudes, 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 RodriguesÃÂs 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 "Universit/e" will be explained, and the The relative inferiority of the Universit/e to the /Ecole 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'/elite" 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 RodriguesÃÂs 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 /Ecole Polytechnique or the /Ecole Normale Sup/erieure, 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 19
80'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.
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