Women in Mathematics

Snezana LawrenceMEI conference, July 2008University of Hertfordshire

http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article4099034.ece

The four womenmathematicians

• Emilie du Chatelet (1706-1749)• Maria Gaetana Agnesi (1718-1799)• Caroline Herschel (1750-1848)• Marie-Sophie Germain (1776-1831)

• And what is so special about womendoing mathematics…

Emilie duChatelet

• Gabrielle Emilie LeTonnelier de Breteuil,marquise du Chatelet

• Born 17 Dec 1706 inParis

• Died 10 Sept 1749 inLunéville, France

• Remarkable upbringing– as a child she learnt Latin and later Italian and

English, studied mathematics and was givenlessons in fencing, riding and gymnastics

• Married at 19 to Marquis Florent-ClaudeChatelet

• Prettly unremarkable marriage apart from thefact that her husband not only didn’t mindher having a very public affair with Voltaire,but accepted Voltaire’s money to refurbishthe mansion at Cirey where Voltaire andEmilie lived last ten years of her life.

• Voltaire wrote of their life togetherI found in 1733 a young lady who felt more or lessas I did, and who resolved to spend several yearsin the country to cultivate her mind, far from thetumult of the world. It was the marquise DuChâtelet, the woman who in all France had thegreatest disposition for all the sciences. ... Seldomhas so fine a mind and so much taste been unitedwith so much ardour for learning; but she alsoloved the world and all the amusements of her ageand sex. Nevertheless she left all this to go andbury herself in a dilapidated house on the frontiersof Champagne and Lorraine, where the land wasvery fertile and very ugly. She beautified thehouse, to which she added pleasant gardens. I builta gallery, in which I created a very fine collectionof scientific instruments. We had a large library.

• The relationship with the husband…

I also stopped at Cirey. It is arare sight. The two of them arethere alone, plunged in gaiety. Onewrites verse in his corner, theother triangles in hers.

writing to a friend upon return fromvisiting Emilie and Voltaire

• Had three children, a daughter and a son - forwhom she later wrote popular treatise onNewton’s Principia. After the birth of herthird child, a daughter, she died (was 43). Atthe birth of the child, her husband, Voltaireand her then lover, Jean-Francois de Saint-Lambert were all present. As the daughterwas born, she was

‘laid on a quarto book of geometry’

(reported by Voltaire)

• Chatelet on prejudiceI feel the full weight of the prejudicewhich so universally excludes us fromthe sciences; it is one of thecontradictions in life that has alwaysamazed me, seeing that the law allowsus to determine the fate of greatnations, but that there is no placewhere we are trained to think ... Letthe reader ponder why, at no time inthe course of so many centuries, a goodtragedy, a good poem, a respected tale,a fine painting, a good book on physicshas ever been produced by a woman…

Why these creatures whose understandingappears in every way similar to that ofmen, seem to be stopped by someirresistible force, but until they do, womenwill have reason to protest against theireducation. ... I am convinced that manywomen are either unaware of their talentsby reason of the fault in their education orthat they bury them on account ofprejudice for want of intellectual courage.My own experience confirms this. Chancemade me acquainted with men of letterswho extended the hand of friendship tome. ... I then began to believe that I was abeing with a mind ...

• Major work - translation of Newton’sPrincipia (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 theWorld, and analytical solutions to keydisputed aspects of Newton’s theory ofuniversal gravitation.

• Included mathematical summaries thatclarified and confirmed Newton’s applicationof his theory to observed phenomena: Alexis-Claude Clairaut’s on the shape of the Earth,and Daniel Bernoulli’s on the effects of theSun and Moon on the tides.

• She worked on Newton’s translation from1745 to her death in 1749

• Final version of the translation appeared onlyin 1759

• Because she was writing for the young andinexperienced researcher, her translationcontains explanation for all terms howeversimple (for example orbit and ellipse)

• She refers to experiments and annotates herexplanations with citations to Newton’swritings or others upon which she had drawn

What must be one of the firstmathematical jokes…

‘A Jesuit had told his Superior that hehad discovered spots on the Sun; theSuperior responded in a grave manner,that is impossible, I have read Aristotletwo or three times, and I found nothinglike that in his book…’

• Well respected by her contemporaries• In 1746, in the Journal Universel it was

noted that Emilie has been elected to theBologna Academy, and was described as‘notre infatigable Marquise’

• Respect shown to her by the three men shewas surrounded with at her death also showsunusual position she was in - genius isforgiven the social trespasses

Description in contemporaryliterature on Chatelet

‘Alone, after dinner. Through the long windowleading on to her terrace the low hills of easternFrance were barely visible in the dusk. She’d lovedthis house, her home, but after a decade spentwith Francois, the man she’d lived for above allothers, their life together had begun to shatter.

In his place she’d thought she’d found a betterman, younger and more handsome, but then hetoo had turned cool to her. She’d tried to avoidadmitting it at first… but his coldness neverended: she was experienced with men, and knewwhen passion was over…’

Maria GaetanaAgnesi

• Born 16 May 1718in Milan

• Died 9 Jan 1799Milan

• Father Pietro, links with the University ofBologna but not a professor as sometimesreported, but silk merchant

• Pietro had twenty-one children with threewives (not at the same time), Maria eldest.

• Education from young age, at 9 knew Latinand published a discourse on the highereducation of women

• Cultural salon - Maria presents thesis onvarious subjects and defends them indisputation

• Maria Teresa her sister, meanwhile plays theharpsichord (she became a composer)

• Parallels with Mozart?

• When 20 (1738) published PropositionesPhilosophicae - a series of essays onphilosophy and natural sciences. Contains 191theses defeneded by Agnesi.

• Agnesi’s views on woman’s ability and fitnessto study sciences and the arts -Propositiones’s main theme.

• Her thesis that woman are able to developfaculties and practices involved in thescientific enterprise as exemplified by thenotion of ‘attention’.

• Mathematics as only science and one in whichone can contemplate truths derived withabsolute certainty

• Teaching girls at the church of SantaCaterina and in San Calimero

• Eventually became Priora della DottrinaCristiana (school director)

• Run a hospital for poor and ‘fallen’ womenuntil her death (increasingly devoted to thisand away from mathematics)

• Her major work adaptation of Newton’s workInstituzioni analytiche ad uso dellagioventu italiana (analytic institutions forthe 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

• First woman to publish a mathematicalbook - and not any book - on anesoteric branch of the mathematicalsciences

• Pope Benedict XIV appointed Agnesiprofessor of mathematics at theUniversity of Bologna in 1750. Nevertaught there.

• John Colson (1680-1760)

Origin of the‘Witch of Agnesi’

The Witch of AgnesiThis curve was known to Fermat (1601-1665)and Luigi Guido Grandi (1671-1742), whocalled it versiera (from Latin vertere - toturn). Agnesi explained it, but the Italianword ‘la versera’ was taken for ‘l’aversiera’(meaning female devil, devil’s wife, or she-devil in Italian) was used by John Colson whotranslated Principia into English from theoriginal in 1736 and from Agnesi’s Italianversion in 1760, translated it ‘witch’, ‘and themistake is lovingly preserved in most texts inEnglish language.

• The Witch of Agnesi

• several conclusions about it• as

• Area between the curve and x is (or 4 xthe area of the generating circle)

x = 2a tan!, y = 2acos2!

or

y =8a

3

x2+ 4a

2

x! ±", y! 0

4!a2

• Later Agnesi became symbol of femininewisdom 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).

Caroline Herschel

• Born 16 March1750 Hannover,Germany

• Died 9 Jan 1848Hannover,Germany

• Sister of William Herschel (1738-1822),astronomer, musician, andmathematician

• In 1766 William becomes organist inBath

• Caroline joins him in 1772

• Both had fond memories of theirfather…... on a clear frosty night into thestreet, to make me acquainted withseveral of the beautifulconstellations, after we had beengazing at a comet which was thenvisible

• Studied mathematics, music and astronomytogether.

• Caroline pursued a somewhat successfulsinging career:

‘As first treble in the Messiah, Judas Macabaeus,etc., she sang at Bath or Bristol sometimes fivenights in the week, but declined an engagement forthe Birmingham festival, having resolved toappear only where her brother conducted.’ (DOB)

• Interested in applied mathematics.• Astronomy a hobby for both of them when in

1781 William discovered Uranus.

• Employment with George III ensued,Herschels moving to few places aroundLondon before finally to Clay Hall nearWindsor.

• William on a pay from GIII, £200 p.a.• In 1786 moved to Observatory House in

Slough where on 1 August 1786 Carolinediscovered her first comet - called by some‘first lady’s comet’.

• 1787 Caroline on GIII pay - £50 p.a.• Discovered eight comets between 1768 and

1797 when she began cross-referencing andcorrecting the star catalogue produced byFlamsteed.

• Returned to Hanover after William’sdeath in 1822.

• Completed the catalogue of 2500nebulae and in 1828 Royal AstronomicalSociety awarded her its gold medal.

• Became something of a celebrity, visitedby Gauss.

• Together with Mary Somerville she waselected to honorary membership of theRoyal Society in 1835. First womenhonorary members.

Marie-Sophie

Germain

• Born 1 April1776 in Paris

• Died 27 June1831 in Paris

• Middle daughter of a silk merchant. Herparents’ home meeting place for thoseinterested in liberal reforms.

• Defining moment of interest when sheread the account of Archimedes’ death.Parents didn’t approve at first, sostudying hiding.

• Obtained notes from many courses atthe Ecole Polytechnique

• Submitted a paper to Lagrange at theend of his course on analysis under thepseudonym M LeBlanc.

• Corresponded with Lagrange and laterGauss (began with the samepseudonym).

• Worked on Fermat’s Last Theoremusing modular arithmetic. Came towhat has became known as Germain’sTheorem.

• 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 withempirical 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 solvethe problem

• She did not win the reward, but Lagrangewho was a judge in the contest corrected theerrors in Germain’s equation and came upwith 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 andwas able to show that Lagrange’s equationdid yield some results but could not give asatisfactory derivation of equation fromphysical principles.

• For this work she received anhonourable mention.

• The contest reopened in 1813 andGermain was awarded a gold medal, butdid not come to collect it.

Germain’s primes

• A theorem and prime numbers bearingher name

• If number is a prime p, and 2p+1 is alsoa prime, then p is Germain prime

• Theorem states that if p and 2p+1 areboth primes, then there are no integersx, y, and z for which xp + yp = zp

Conclusions?

• Perception of whether women can domathematics

• How many women have donemathematics?

• Is there anything to contribute?• How do we really treat women/girls

through the popular culture? And howdo we treat maths?

Some of the things we can do

• Inspire in different ways– History of mathematics– Learning fantasies

• Empower (Garden of Knowledge notteacher preacher concept)

• Involve young people• Show the ways of making a contribution

Thank you for listening!snezana@mathsisgoodforyou.com