Women in Mathematics. Snezana Lawrence MEI conference, July 2008 University of Hertfordshire

Transcription

1 Women in Mathematics Snezana Lawrence MEI conference, July 2008 University of Hertfordshire

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4 The four women mathematicians Emilie du Chatelet ( ) Maria Gaetana Agnesi ( ) Caroline Herschel ( ) Marie-Sophie Germain ( ) And what is so special about women doing mathematics

5 Emilie du Chatelet Gabrielle Emilie Le Tonnelier de Breteuil, marquise du Chatelet Born 17 Dec 1706 in Paris Died 10 Sept 1749 in Lunéville, France

6 Remarkable upbringing as a child she learnt Latin and later Italian and English, studied mathematics and was given lessons in fencing, riding and gymnastics Married at 19 to Marquis Florent-Claude Chatelet Prettly unremarkable marriage apart from the fact that her husband not only didn t mind her having a very public affair with Voltaire, but accepted Voltaire s money to refurbish the mansion at Cirey where Voltaire and Emilie lived last ten years of her life.

7 Voltaire wrote of their life together I found in 1733 a young lady who felt more or less as I did, and who resolved to spend several years in the country to cultivate her mind, far from the tumult of the world. It was the marquise Du Châtelet, the woman who in all France had the greatest disposition for all the sciences.... Seldom has so fine a mind and so much taste been united with so much ardour for learning; but she also loved the world and all the amusements of her age and sex. Nevertheless she left all this to go and bury herself in a dilapidated house on the frontiers of Champagne and Lorraine, where the land was very fertile and very ugly. She beautified the house, to which she added pleasant gardens. I built a gallery, in which I created a very fine collection of scientific instruments. We had a large library.

8 The relationship with the husband I also stopped at Cirey. It is a rare sight. The two of them are there alone, plunged in gaiety. One writes verse in his corner, the other triangles in hers. writing to a friend upon return from visiting Emilie and Voltaire

9 Had three children, a daughter and a son - for whom she later wrote popular treatise on Newton s Principia. After the birth of her third child, a daughter, she died (was 43). At the birth of the child, her husband, Voltaire and her then lover, Jean-Francois de Saint- Lambert were all present. As the daughter was born, she was laid on a quarto book of geometry (reported by Voltaire)

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13 Chatelet on prejudice I feel the full weight of the prejudice which so universally excludes us from the sciences; it is one of the contradictions in life that has always amazed me, seeing that the law allows us to determine the fate of great nations, but that there is no place where we are trained to think... Let the reader ponder why, at no time in the course of so many centuries, a good tragedy, a good poem, a respected tale, a fine painting, a good book on physics has ever been produced by a woman

14 Why these creatures whose understanding appears in every way similar to that of men, seem to be stopped by some irresistible force, but until they do, women will have reason to protest against their education.... I am convinced that many women are either unaware of their talents by reason of the fault in their education or that they bury them on account of prejudice for want of intellectual courage. My own experience confirms this. Chance made me acquainted with men of letters who extended the hand of friendship to me.... I then began to believe that I was a being with a mind...

15 Major work - translation of Newton s Principia (third edition 1731) into French Her remains the standard translation Wrote an extensive commentary in which she gave her own description of the System of the World, and analytical solutions to key disputed aspects of Newton s theory of universal gravitation. Included mathematical summaries that clarified and confirmed Newton s application of his theory to observed phenomena: Alexis- Claude Clairaut s on the shape of the Earth, and Daniel Bernoulli s on the effects of the Sun and Moon on the tides.

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18 She worked on Newton s translation from 1745 to her death in 1749 Final version of the translation appeared only in 1759 Because she was writing for the young and inexperienced researcher, her translation contains explanation for all terms however simple (for example orbit and ellipse) She refers to experiments and annotates her explanations with citations to Newton s writings or others upon which she had drawn

19 What must be one of the first mathematical jokes A Jesuit had told his Superior that he had discovered spots on the Sun; the Superior responded in a grave manner, that is impossible, I have read Aristotle two or three times, and I found nothing like that in his book

20 Well respected by her contemporaries In 1746, in the Journal Universel it was noted that Emilie has been elected to the Bologna Academy, and was described as notre infatigable Marquise Respect shown to her by the three men she was surrounded with at her death also shows unusual position she was in - genius is forgiven the social trespasses

21 Description in contemporary literature on Chatelet Alone, after dinner. Through the long window leading on to her terrace the low hills of eastern France were barely visible in the dusk. She d loved this house, her home, but after a decade spent with Francois, the man she d lived for above all others, their life together had begun to shatter. In his place she d thought she d found a better man, younger and more handsome, but then he too had turned cool to her. She d tried to avoid admitting it at first but his coldness never ended: she was experienced with men, and knew when passion was over

22 Maria Gaetana Agnesi Born 16 May 1718 in Milan Died 9 Jan 1799 Milan

23 Father Pietro, links with the University of Bologna but not a professor as sometimes reported, but silk merchant Pietro had twenty-one children with three wives (not at the same time), Maria eldest. Education from young age, at 9 knew Latin and published a discourse on the higher education of women Cultural salon - Maria presents thesis on various subjects and defends them in disputation Maria Teresa her sister, meanwhile plays the harpsichord (she became a composer) Parallels with Mozart?

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25 When 20 (1738) published Propositiones Philosophicae - a series of essays on philosophy and natural sciences. Contains 191 theses defeneded by Agnesi. Agnesi s views on woman s ability and fitness to study sciences and the arts - Propositiones s main theme. Her thesis that woman are able to develop faculties and practices involved in the scientific enterprise as exemplified by the notion of attention.

26 Mathematics as only science and one in which one can contemplate truths derived with absolute certainty Teaching girls at the church of Santa Caterina and in San Calimero Eventually became Priora della Dottrina Cristiana (school director) Run a hospital for poor and fallen women until her death (increasingly devoted to this and away from mathematics)

27 Her major work adaptation of Newton s work Instituzioni analytiche ad uso della gioventu italiana (analytic institutions for the use of young Italians) published in 1748, written in Italian. Agnesi s translation of Newton Early systematisation of the techniques of calculus Clearly written and as such in use for many years Conceptually soon superseded Aimed at popular public

28 First woman to publish a mathematical book - and not any book - on an esoteric branch of the mathematical sciences Pope Benedict XIV appointed Agnesi professor of mathematics at the University of Bologna in Never taught there.

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31 John Colson ( ) Origin of the Witch of Agnesi

32 The Witch of Agnesi This curve was known to Fermat ( ) and Luigi Guido Grandi ( ), who called it versiera (from Latin vertere - to turn). Agnesi explained it, but the Italian word la versera was taken for l aversiera (meaning female devil, devil s wife, or shedevil in Italian) was used by John Colson who translated Principia into English from the original in 1736 and from Agnesi s Italian version in 1760, translated it witch, and the mistake is lovingly preserved in most texts in English language.

33 The Witch of Agnesi x = 2a tan!, y = 2acos 2! or 8a 3 y = x 2 + 4a 2 several conclusions about it as x! ±", y! 0 Area between the curve and x is the area of the generating circle) 4!a 2 (or 4 x

34 Later Agnesi became symbol of feminine wisdom and as such Symbol of Catholic Enlightenment Heroine of counterrevolution and political restoration A prophet of the national unification of Italy A Catholic modernist A proto-feminist The ideal fascist woman Potential saint of the church (recent invitations to canonize her).

35 Caroline Herschel Born 16 March 1750 Hannover, Germany Died 9 Jan 1848 Hannover, Germany

36 Sister of William Herschel ( ), astronomer, musician, and mathematician In 1766 William becomes organist in Bath Caroline joins him in 1772

37 Both had fond memories of their father... on a clear frosty night into the street, to make me acquainted with several of the beautiful constellations, after we had been gazing at a comet which was then visible

38 Studied mathematics, music and astronomy together. Caroline pursued a somewhat successful singing career: As first treble in the Messiah, Judas Macabaeus, etc., she sang at Bath or Bristol sometimes five nights in the week, but declined an engagement for the Birmingham festival, having resolved to appear only where her brother conducted. (DOB) Interested in applied mathematics. Astronomy a hobby for both of them when in 1781 William discovered Uranus.

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41 Employment with George III ensued, Herschels moving to few places around London before finally to Clay Hall near Windsor. William on a pay from GIII, 200 p.a. In 1786 moved to Observatory House in Slough where on 1 August 1786 Caroline discovered her first comet - called by some first lady s comet Caroline on GIII pay - 50 p.a. Discovered eight comets between 1768 and 1797 when she began cross-referencing and correcting the star catalogue produced by Flamsteed.

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43 Returned to Hanover after William s death in Completed the catalogue of 2500 nebulae and in 1828 Royal Astronomical Society awarded her its gold medal. Became something of a celebrity, visited by Gauss. Together with Mary Somerville she was elected to honorary membership of the Royal Society in First women honorary members.

44 Marie- Sophie Germain Born 1 April 1776 in Paris Died 27 June 1831 in Paris

45 Middle daughter of a silk merchant. Her parents home meeting place for those interested in liberal reforms. Defining moment of interest when she read the account of Archimedes death. Parents didn t approve at first, so studying hiding. Obtained notes from many courses at the Ecole Polytechnique

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47 Submitted a paper to Lagrange at the end of his course on analysis under the pseudonym M LeBlanc. Corresponded with Lagrange and later Gauss (began with the same pseudonym). Worked on Fermat s Last Theorem using modular arithmetic. Came to what has became known as Germain s Theorem.

48 Probably the most frustrating life history - In 1808 The Institute of France set a prize competition with the challenge: Formulate a mathematical theory of elastic surfaces and indicate just how it agrees with empirical evidence. A deadline set for two years. No one submitted apart from Germain Lagrange s opinion was that the mathematical modesl available were not adequate to solve the problem

49 She did not win the reward, but Lagrange who was a judge in the contest corrected the errors in Germain s equation and came up with what he believed was a good description. The contest deadline extended for two years, and Germain again the only entrant. She worked on Lagrange s amendments and was able to show that Lagrange s equation did yield some results but could not give a satisfactory derivation of equation from physical principles.

50 For this work she received an honourable mention. The contest reopened in 1813 and Germain was awarded a gold medal, but did not come to collect it.

51 Germain s primes A theorem and prime numbers bearing her name If number is a prime p, and 2p+1 is also a prime, then p is Germain prime Theorem states that if p and 2p+1 are both primes, then there are no integers x, y, and z for which x p + y p = z p

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53 Conclusions? Perception of whether women can do mathematics How many women have done mathematics? Is there anything to contribute? How do we really treat women/girls through the popular culture? And how do we treat maths?

54 Some of the things we can do Inspire in different ways History of mathematics Learning fantasies Empower (Garden of Knowledge not teacher preacher concept) Involve young people Show the ways of making a contribution

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57 Thank you for listening!