Sofia - PowerPoint Presentation

Slide1

Sofia Kovalevskaya1850-1891

A 19

th century pioneer for women in mathematics

June Barrow-GreenThe Open UniversityFlorence Nightingale DayLancaster University17 December 2015Slide2

Hypatia

of Alexandria (c.370-415)

Wrote commentaries on Diophantus’

Arithmetica and Apollonius’ Conics.

Marquise du

Chatelet (1706-1749)French translation of Newton’s Principia (1759).Maria Agnesi (1718-1799) Institutzioni Analitche (1748), first text book to include calculus.Caroline Herschel (1750-1848) Worked on astronomy with her brother William; discoverer of eight comets. Sophie Germain (1776-1831) Grand Prix of the French Academy of Sciences for work on the vibration of elastic surfaces (1816).Mary Somerville (1780-1872) The Mechanism of the Heavens (1831). Ada Lovelace (1815-1852) Translated and wrote extensive notes on Menabrea’s Mémoire on Charles Babbage’s Analytical Engine (1846).Florence Nightingale (1820-1910) Made pioneering studies of mortality statistics.

Women mathematicians born before 1850Slide3

Moscow

b.1850Slide4

Moscow

b

.1850

Palabino1858Slide5

Moscow

b.1850

Palabino

1858Slide6

Russia 1869 University Courses for women are opened, which opens the profession of teacher, law assistant and similar lower academic professions for womenUK 1878 London University first university in UK to award

degrees to women [Oxford (1920), Cambridge (1947)]

University education for women in the 19th centurySlide7

Moscow

b

.1850

Palabino1858

St Petersburg

1868Slide8

St Petersburg 1868

‘Fictitious’ marriage to Vladimir

KovalevskiSlide9

St Petersburg

1868Slide10

St Petersburg

1868

London

1869Slide11

St Petersburg

1868

London

1869Slide12

George Eliot at once turned to [Spencer]. “I’m so glad you have come today” she said, “I can introduce you to the living refutation of your theory – a woman mathematician. Allow me to present my friend,” she continued, turning to me still without mentioning his name, “only I have to warn you that he denies the very existence of a woman mathematician. … Try to make him change his mind!” Sofia Kovalevskaya ‘My recollections of George Eliot’

Kovalevskaya meets Herbert Spencer in London, 1869Slide13

St Petersburg

1868

London

1869

Heidelberg

1869Slide14

St Petersburg

1868

London

1869

Heidelberg

1869Berlin1870Slide15

Berlin 1870-1874Studies with Karl Weierstrass, one of the leading German mathematicians of the day, and acknowledged as a great teacher.Slide16

PhD 1874Awarded PhD summa cum laude in absentia from University of GöttingenPartial Differential Equations

Abelian Integrals

Shape of Saturn’s RingsSlide17

Partial Differential EquationsPDEs contain the partial derivatives of a function of more than one variable.E.g. the wave equation [in modern notation]:

first formulated by Jean-Baptiste le

Rond

d’Alembert in

1747 in connection with his solution of the problem of

the vibrating string. Kovalevskaya’s work included the definitive formulation of what is now known as the Cauchy-Kovalevskaya theorem. Slide18

Abelian Integrals Abelian integrals are named

after the Norwegian mathematician Niels Henrik Abel (1802–1829).Most integrals are impossible to solve using elementary functions. The simplest type of non-elementary integral are

elliptic integrals.E.g.

Kovalevskaya investigated a certain class of Abelian Integrals which reduce to elliptic integralsElliptic integrals originally arose in connection with the problemof finding the arc length of an ellipse.Slide19

Shape of Saturn’s rings 1675 Rings first seen by Domenico Cassini

1787 Pierre-Simon Laplace suggested that the rings are formed of solid ringlets; assumed their cross-section to be elliptical

1856 James Clerk Maxwell showed that solid rings are unstable and would break apartSlide20

Shape of Saturn’s rings Published in 1885Kovalevskaya used Fourier series to represent the

cross-section which gave an oval (rather than an ellipse)This led her, via some impressive juggling which involved elliptic integrals, to a system of infinitely many equations in infinitely many unknowns! Slide21

Shape of Saturn’s rings Published in 1885

Kovalevskaya used Fourier series to represent thecross-section which gave an oval (rather than an ellipse)This led her, via some impressive juggling which involved elliptic integrals, to a system of infinitely many equations in infinitely many unknowns!

In the simplest case she was led to expressions of the form

which she didn’t compute!

Kovalevskaya’s

techniques were found to be useful in other contextsSlide22

Adrien Marie Legendre (1752–1797)

Important work on elliptic integrals3 volume book published 1825–1830 Slide23

Adrien Marie Legendre (1752–1833)

Louis Legendre (1752–1797)French politician

Adrien Marie Legendre in 1820

Caricature discovered in 2005

Important work on elliptic integrals

3 volume book published 1825–1830 Slide24

St Petersburg & Moscow 1874-1881Slide25

1876 Meets Gösta Mittag-Leffler“More than anything else in St. Petersburg what I found most interesting was getting to know Kovalevskaya ... As a woman, she is fascinating. She is beautiful and when she speaks, her face lights up with such an expression of feminine kindness and highest intelligence, that it is simply dazzling. As a scholar she is characterised by her unusual clarity and precision of expression ... I understand fully why

Weierstrass considers her the most gifted of his students.

St PetersburgSlide26

1877 Writes scientific and literary articles1878 Recommences correspondence with Weierstrass Birth of her daughter Fufa1880 Mittag-Leffler starts trying to get her a job

1881 Leaves Vladimir St Petersburg & Moscow 1874-1881Slide27

Berlin

1881Slide28

Berlin

1881

Paris

1881Slide29

Paris 1881-1883Slide30

Paris 1881-1883

1883 Vladimir commits suicide Sofia obtains a position in Stockholm Slide31
Slide32

This lady, a native of Russia, is a celebrated mathematician, who lectured last winter at the University of Stockholm, and who has just been appointed Professor of Mathematics at that University. We believe that this is the first time, since the Middle Ages (in Italy), that a woman has been appointed to an academical

chair at any University in Europe. Sweden is a country where much interest has been felt in the claims of the fair sex to a full opportunity of acquiring and exercising intellectual accomplishments. The position now conceded to Madame Kowalevski is worthy of notice as a sign of the times, and will be observed with gratification by many English friends and advocates of higher education for women.Slide33

Stockholm 1883-1891Slide34

Stockholm 1883-1888

1883 Privat Docent (5 year appointment)1884 Appointed to editorial board of Acta Mathematica

1886 Announcement of question for Prix Bordin of 1888

Fufa comes to Stockholm1887 The Struggle for Happiness (two plays written jointly with Anna-Carlotta Leffler)1888 Submits entry to Prix BordinSlide35

Prix Bordin 1888“Improve, in some important point, the theory of the movement of a rigid body”Slide36

Prix Bordin 18881 June Sofia sends in half-finished memoirLate summer

Sofia sends in revised (but still incomplete) memoir “On the Problem of the Rotation of a Solid Body about a Fixed Point”

“Improve, in some important point, the theory of the movement of a rigid body”Slide37

Prix Bordin 18881 June Sofia sends in half-finished memoirLate summer

Sofia sends in revised (but still incomplete) memoir “On the Problem of the Rotation of a Solid Body about a Fixed Point”

December Sofia learns she has won the competition Prize money raised from 3,000 to 5,000 francs

“Improve, in some important point, the theory of the movement of a rigid body”Sofia impressed the committee by applying the recently developed and highly abstract theory of Abelian functions to solve a problem in physics. Slide38

Paris 1888-1889

24 December 1888 Sofia receives the Prix Bordin

Spring/Summer 1889Travels in EuropeLooks for a position in ParisMittag-Leffler urgently trying to get her a permanent position in StockholmSlide39

Stockholm 1889-18911889 Professor in Stockholm Publication of Prix Bordin memoir Slide40

Stockholm 1889-18911889 Professor in Stockholm Publication of Prix Bordin memoir

1890 Wrote Nihilist Girl (also called Vera Vorontsova) [printed in Switzerland in 1892;

in Russia in 1906, then banned; a Czech translation allowed in Russia

in 1908]Slide41

Stockholm 1889-18911889 Professor in Stockholm Publication of Prix Bordin memoir

1890 Wrote Nihilist Girl (also called Vera Vorontsova) [printed in Switzerland in 1892;

in Russia in 1906, then banned; a Czech translation allowed in Russia

in 1908]1891 Dies of pneumoniaSlide42

Sofia Kovalevskaya 1850–1891Her competence and poise as a member of the faculty in Stockholm established that society can, without falling apart, allow women to become the colleagues of men on university faculties. Although the realisation of all her ambitions for women in mathematics is not yet complete, it continues apace. The impetus she gave to this movement a century ago and the permanent advances in knowledge which her works gave to the world form the enduring foundation of her fame.Roger Cooke

The Mathematics of Sonya Kovalevskay (1984)

“

It is impossible to be a mathematician without being a poet in soul”