However, Dubreil-Jacotin first describes the multitude of contributions made by women to mathematics yet scarcely recognised until recent times. Here is the part of the article in which she makes many important general points about women's contributions:- |

Women who have left behind a name in mathematics are very few in number-three or four, perhaps five. Does this say, as a common prejudice would tend to persuade us, that mathematics, so very abstract, is not congenial to the feminine disposition? This would be to ignore the true character of mathematics, to forget, as Henri Poincaré said:-

... the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know. And this is sensitivity.

And should not this very sensitivity, contrary to the prejudice, make mathematics a feminine domain? Moreover, if we consider the other sciences, the great inventions whose applications have staggered the world, we do not find any more women's names associated with these areas. Must it then be said, as Maurice d'Ocagne seems to conclude in his *Etudes sur les Femmes de Science et sur les Mathématiciennes,* that woman is generally destitute of inventive spirit and creative genius? The growth of female education, the overthrow of prejudices, the profound changes in the kind of life and in the role assigned to woman during the last few years will doubtless bring about a revision of her position in science. Then we shall see in what measure she can, as the equal of man, emerge from the role of the excellent pupil or the perfect collaborator, and join those of our scientists whose work has opened new paths and bears the mark of genius.

Yet, it is as early as Greek antiquity that the first woman who can be considered as a mathematician makes her appearance: Hypatia, born at Alexandria in the year 370 of our era. In a school which she opened in her native city, she expounded at one and the same time Plato, Aristotle, the works of Diophantus and the conic sections of Apollonius of Perga. It is also believed that a commentary on the tables of Ptolemy, which has come down to us under Theon's name, is due to her. Hypatia acquired a great reputation as much for her science as for her eloquence and her beauty. She died tragically at the age of 45; she was thrown from her carriage and stoned by a crowd inflamed by monks at the instigation, it appears, of the patriarch St Cyril.

Then, from the 16th century on, while the lords devoted themselves to politics and war, the ladies of high society gave themselves to the joys of the mind, and mathematics, by its very abstraction and beauty, had a preferential place there which did nothing but expand in the two following centuries, when a certain snobbishness seems, however, to have been mingled with the charm found by certain women in algebra and geometry. And it is perhaps this very epoch that saw the fullest appearance of those truly feminine qualities which make some great lady not a scientist, but the best of pupils or the fine and clear-sighted collaborator of some great scientist. There was Viète, the creator of algebra, who had as his best pupil Catherine de Parthenay, Princess of Rohan-Soubise. Then Descartes, who had as his disciple Christine, Queen of Sweden, and Elizabeth of Bohemia, Palatine Princess; and Leibniz with Sophie, Electress of Hanover, and her daughter Sophie Charlotte, Queen of Prussia and mother of the great Frederick. Euler wrote his Lettres a une princesse d'Allemagne to teach science to the Princess Anhalt-Dessau. Newton was studied and understood by Caroline of Brandenburg Anspach, and Emilie de Breteuil, Marquise du Châtelet, noted for her liaison with Voltaire, translated his principles and added certain personal notes to her translation-notes with which it may be Clairaut was not entirely unfamiliar. The latter, moreover, used the long calculations made for him by Mme Lepaute, the charming wife of the celebrated watch- maker of Louis XV, without even mentioning her, "to oblige," says Lalande, "a woman jealous of the attainments of Mme Lepaute and who had pretensions without any kind of knowledge. She succeeded in making a wise but weak scientist, whom she had captivated, commit this injustice."

But let us abandon these brilliant women, more or less amateurs, and the admirable astronomers' assistants such as Mme Yvon Villarceau, Mme Lefrançais de Lalande, and others, in order to come to those who, if they cannot all be set among the greatest names, can at least cut an honourable figure among the great mathematicians. ...

JOC/EFR March 2006

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