WOMEN IN MATHEMATICS
"All abstract speculations, all knowledge which is dry, however useful
it may be, must be abandoned to the laborious and solid mind of man....
For this reason women will never learn geometry."
In these words Immanuel Kant, more than a century ago, gave expression
to an opinion that had obtained since the earliest times respecting the
incapacity of the female mind for abstract science, and notably for
mathematics. Women, it was averred, could readily assimilate what is
concrete, but, like children, they have a natural repugnance for
everything which is abstract. They are competent to discuss details and
to deal with particulars, but become hopelessly lost when they attempt
to generalize or deal with universals.
De Lamennais shares Kant's opinion concerning woman's intellectual
inferiority and does not hesitate to express himself on the subject in
the most unequivocal manner. "I have never," he writes, "met a woman who
was competent to follow a course of reasoning the half of a quarter of
an hour--_un demi quart d'heure_. She has qualities which are wanting in
us, qualities of a particular, inexpressible charm; but, in the matter
of reason, logic, the power to connect ideas, to enchain principles of
knowledge and perceive their relationships, woman, even the most highly
gifted, rarely attains to the height of a man of mediocre capacity."
But it is not only in the past that such views found acceptance. They
prevail even to-day to almost the same extent as during the ages of
long ago. How far they have any foundation in fact can best be
determined by a brief survey of what woman has achieved in the domain of
mathematics.
Athenaeus, a Greek writer who flourished about A.D. 200, tells us in his
_Deipnosophistae_ of several Greek women who excelled in mathematics, as
well as philosophy, but details are wanting as to their attainments in
this branch of knowledge. If, however, we may judge from the number of
women--particularly among the hetaerae--who became eminent in the various
schools of philosophy, especially during the pre-Christian era, we must
conclude that many of them were well versed in geometry and astronomy as
well as in the general science of numbers. Menagius declares that he
found no fewer than sixty-five women philosophers mentioned in the
writings of the ancients[108]; and, judging from what we know of the
character of the studies pursued in certain of the philosophical
schools, especially those of Plato[109] and Pythagoras, and the
enthusiasm which women manifested in every department of knowledge,
there can be no doubt that they achieved the same measure of success in
mathematics as in philosophy and literature.[110]
The first woman mathematician, regarding whose attainments we have any
positive knowledge, is the celebrated Hypatia, a Neo-platonic
philosopher, whose unhappy fate at the hands of an Alexandrian mob in
the early part of the fifth century has given rise to many legends and
romances which have contributed not a little toward obscuring the real
facts of her extraordinary career. She was the daughter of Theon, who
was distinguished as a mathematician and astronomer and as a professor
in the school of Alexandria, which was then probably the greatest seat
of learning in the world. Born about the year 375 A. D., she at an early
age evinced the possession of those talents that were subsequently to
render her so illustrious. So great indeed was her genius and so rapid
was her progress in this branch of knowledge under the tuition of her
father that she soon completely eclipsed her master in his chosen
specialty.
There is reason to believe--although the fact is not definitely
established--that she studied for a while in Athens in the school of
philosophy conducted by Plutarch the Younger and his daughter
Asclepigenia. After her return from Athens, Hypatia was invited by the
magistrates of Alexandria to teach mathematics and philosophy. Here in
brief time her lecture room was filled by eager and enthusiastic
students from all parts of the civilized world. She was also gifted with
a high order of eloquence and with a voice so marvelous that it was
declared to be "divine."
Regarding her much vaunted beauty, nothing certain is known, as
antiquity has bequeathed to us no medal or statue by which we could form
an estimate of her physical grace. But, be this as it may, it is certain
that she commanded the admiration and respect of all for her great
learning, and that she bore the mantle of science and philosophy with so
great modesty and self-confidence that she won all hearts. A letter
addressed to "The Muse," or to "The Philosopher"--[Greek: Te
Philosopho]--was sure to be delivered to her at once. Small wonder,
then, to find a Greek poet inditing to her an epigram containing the
following sentiment:
"When I see thee and hear thy word I thee adore; it is the ethereal
constellation of the Virgin, which I contemplate, for to the heavens thy
whole life is devoted, O august Hypatia, ideal of eloquence and
wisdom's immaculate star."[111]
But it was as a mathematician that Hypatia most excelled. She taught not
only geometry and astronomy, but also the new science of algebra, which
had but a short time before been introduced by Diophantus. And, singular
to relate, no further progress was made in the mathematical sciences, as
taught by Hypatia, until the time of Newton, Leibnitz and
Descartes,--more than twelve centuries later.
Hypatia was the author of three works on mathematics, all of which have
been lost, or destroyed by the ravages of time. One of these was a
commentary on the _Arithmetica_ of Diophantus. The original treatise--or
rather the part which has come down to us--was found about the middle of
the fifteenth century in the Vatican Library, whither it had probably
been brought after Constantinople had fallen into the possession of the
Turks. This valuable work, as annotated by the great French
mathematicians Bachet and Fermat, gives us a good idea of the extent of
Hypatia's attainments as a mathematician.
Another of Hypatia's works was a treatise on the _Conic Sections_ by
Apollonius of Perga--surnamed "The Great Geometer." Next to Archimedes,
he was the most distinguished of the Greek geometricians; and the last
four books of his conics constitute the chief portions of the higher
geometry of the ancients. Moreover, they offer some elegant geometrical
solutions of problems which, with all the resources of our modern
analytical method, are not without difficulty. The greater part of this
precious work has been preserved and has engaged the attention of
several of the most illustrious of modern mathematicians--among them
Borelli, Viviani, Fermat, Barrow and others. The famous English
astronomer, Halley, regarded this production of Apollonius of such
importance that he learned Arabic for the express purpose of translating
it from the version that had been made into this language.
A woman who could achieve distinction by her commentaries on such works
as the _Arithmetica_ of Diophantus, of the _Conic Sections_ of
Apollonius, and occupy an honored place among such mathematicians as
Fermat, Borelli, and Halley, must have had a genius for mathematics, and
we can well believe that the glowing tributes paid by her contemporaries
to her extraordinary powers of intellect were fully deserved. If, with
Pascal, we see in mathematics "the highest exercise of the
intelligence," and agree with him in placing geometers in the first rank
of intellectual princes--_princes de l'esprit_--we must admit that
Hypatia was indeed exceptionally dowered by Him whom Plato calls "The
Great Geometer."
There is still a third work of this ill-fated woman that deserves
notice--namely, her _Astronomical Canon_, which dealt with the movements
of the heavenly bodies. It is the general opinion that this was but a
commentary on the tables of Ptolemy, in which event it is still possible
that it may be found incorporated in the work of her father, Theon, on
the same subject.
In addition to her works on astronomy and mathematics, Hypatia is
credited with several inventions of importance, some of which are still
in daily use. Among these are an apparatus for distilling water, another
for measuring the level of water, and a third an instrument for
determining the specific gravity of liquids--what we should now call an
areometer. Besides these apparatus, she was likewise the inventor of an
astrolabe and a planisphere.
One of her most distinguished pupils was the eminent Neo-platonist
philosopher, Synesius, who became the Bishop of Ptolemais in the
Pentapolis of Libya. His letters constitute our chief source of
information respecting this remarkable woman. Seven of them are
addressed to her, and in four others he makes mention of her. In one of
them he writes: "We have seen and we have heard her who presides at the
sacred mysteries of philosophy." In another he apostrophizes her as "My
benefactress, my teacher,--_magistra_--my sister, my mother."
In science Hypatia was among the women of antiquity what Sappho was in
poetry and what Aspasia was in philosophy and eloquence--the chiefest
glory of her sex. In profundity of knowledge and variety of attainments
she had few peers among her contemporaries, and she is entitled to a
conspicuous place among such luminaries of science as Ptolemy, Euclid,
Apollonius, Diophantus and Hipparchus.[112]
It is a matter of regret to the admirers of this favored daughter of the
Muses that she is absent from Raphael's _School of Athens_; but, had her
achievements been as well known and appreciated in his day as they are
now, we can readily believe that the incomparable artist would have
found a place for her in this masterpiece with the matchless form and
features of his beloved Fornarina.
After the death of Hypatia the science of mathematics remained
stationary for many long centuries. Outside of certain Moors in Spain,
the only mathematicians of note in Europe, until the Renaissance, were
Gerbert, afterward Pope Silvester II, and Leonardo da Pisa. The first
woman to attract special attention for her knowledge of mathematics was
Heloise, the noted pupil of Abelard. According to Franciscus Ambrosius,
who edited the works of Abelard and Heloise in 1616, the famous prioress
of The Paraclete was a prodigy of learning, for besides having a
knowledge of Latin, Greek and Hebrew, which was something extremely rare
in her time, she was also well versed in philosophy, theology and
mathematics, and inferior in these branches only to Abelard himself, who
was probably the most eminent scholar of his age.[113]
Many Italian women, as we have seen in a preceding chapter, were noted
for their proficiency in the various branches of mathematics. Some of
the most distinguished of them flourished during the seventeenth and
eighteenth centuries. Among these were Elena Cornaro Piscopia,
celebrated as a linguist as well as a mathematician; Maria Angela
Ardinghelli, translator of the _Vegetable Statics_ of Stephen Hales;
Cristina Roccati, who taught physics for twenty-seven years in the
Scientific Institute of Rovigo, and Clelia Borromeo, fondly called by
her countrymen _gloria Genuensium_--the glory of the Genoese. In
addition to a special talent for languages, she possessed so great a
capacity for mathematics and mechanics that no problem in these sciences
seemed to be beyond her comprehension.[114] Then there was also Diamante
Medaglia, a mathematician of note, who wrote a special dissertation on
the importance of mathematics in the curriculum of studies for women,
_Alle matematiche, alle matematiche prestino l'opera loro le donne, onde
non cadano in crassi paralogismi_--"To mathematics, to mathematics,"
she cries, "let women devote attention for mental discipline."[115]
The most illustrious, by far, of the women mathematicians of Italy was
Maria Gaetana Agnesi, who was born in Milan in 1718 and died there at
the age of eighty-one. At an early age she exhibited rare intelligence
and soon distinguished herself by her extraordinary talent for
languages. At the age of five she spoke French with ease and
correctness, while only six years later she was able to translate Greek
into Latin at sight and to speak the former as fluently as her own
Italian. At the early age of nine she startled the learned men and women
of her native city by discoursing for an hour in Latin on the rights of
women to the study of science. This discourse--_Oratio_--was not, as
usually stated, her own composition, but a translation from the Italian
of a discourse written by her teacher of Latin. That a child of nine
years should speak in the language of Cicero for a full hour before a
learned assembly and without once losing the thread of her discourse
was, indeed, a wonderful performance, and we are not surprised to learn
that she was regarded by her countrymen as an infant prodigy.[116]
In addition to Italian, French, Latin and Greek, she was acquainted with
German, Spanish and Hebrew. For this reason she was, like Elena Cornaro
Piscopia, the famous "Venetian Minerva," called Oracolo
Settilingue--Oracle of Seven Languages.[117]
But it was in the higher mathematics that Maria Gaetana was to win her
chief title to fame in the world of learning. So successful had she been
in her prosecution of this branch of science that she was, at the early
age of twenty, able to enter upon her monumental work--_Le Instituzioni
Analitiche_--a treatise in two large quarto volumes on the differential
and integral calculus. To this difficult task she devoted ten years of
arduous and uninterrupted labor. And if we may credit her biographer,
she consecrated the nights as well as the days to her herculean
undertaking. For frequently, after working in vain on a difficult
problem during the day, she was known to bound from her bed during the
night while sound asleep and, like a somnambulist, make her way through
a long suite of rooms to her study, where she wrote out the solution of
the problem and then returned to her bed. The following morning, on
returning to her desk, she found, to her great surprise, that while
asleep she had fully solved the problem which had been the subject of
her meditations during the day and of her dreams during the night. Could
the psychiatrist who so loves to deal with obscure mental phenomena find
a more interesting case to engage his attention or one more worthy of
the most careful investigation?
Finally Maria Gaetana's _opus majus_ was completed and given to the
public. It would be impossible to describe the sensation it produced in
the learned world. Everybody talked about it; everybody admired the
profound learning of the author, and acclaimed her: "Il portento del
sesso, unico al Mondo"--the portent of her sex, unique in the world. By
a single effort of her genius she had completely demolished that fabric
of false reasoning which had so long been appealed to as proof positive
of woman's intellectual inferiority, especially in the domain of
abstract science. Maria Gaetana's victory was complete, and her victory
was likewise a victory for her sex. She had demonstrated once for all,
and beyond a quirk or quibble, that women could attain to the highest
eminence in mathematics as well as in literature, that supreme
excellence in any department of knowledge was not a question of sex but
a question of education and opportunity, and that in things of the mind
there was essentially no difference between the male and the female
intellect.
The world saw in Agnesi a worthy accession to that noble band of gifted
women who count among their number a Sappho, a Corinna, an Aspasia, a
Hypatia, a Paula, a Hroswitha, a Dacier, an Isabella Rosales who, in the
sixteenth century, successfully defended the most difficult theological
theses in the presence of Paul III and the entire college of cardinals.
And so delighted were the women--especially those in Italy--with the
signal triumph of their eminent sister that they defied the traducers
of their sex--_muliebris sapientiae infensissimis hostibus_--to continue
any longer their unreasonable campaign against the rights of women which
were based on the intellectual equality of the two sexes.
So highly did the French Academy of Science value Agnesi's achievement
that she would at once have been made a member of this learned body had
it not been against the constitutions to admit a woman to membership. M.
Motigny, one of the committee appointed by the Academy to report on the
work, in his letter to the author, among other things, writes: "Permit
me, Mademoiselle, to unite my personal homage to the plaudits of the
entire Academy. I have the pleasure of making known to my country an
extremely useful work which has long been desired, and which has
hitherto"--both in France and in England--"existed only in outline. I do
not know any work of this kind which is clearer, more methodic or more
comprehensive than your _Analytical Institutions_. There is none in any
language which can guide more surely, lead more quickly, and conduct
further those who wish to advance in the mathematical sciences. I admire
particularly the art with which you bring under uniform methods the
divers conclusions scattered among the works of geometers and reached by
methods entirely different."
As an indication of the exceptional merit of Agnesi's work, even long
after its publication in 1748, it suffices to state that the second
volume of the_ Instituzioni Analitiche_ was translated into French in
1775 by Antelmy and annotated by the Abbe Bossuet, a member of the
French Academy and a collaborator of D'Alembert on the mathematical part
of the famous _Encyclopedie_.
A still greater proof of the estimation in which Agnesi's work was held
by men of science is the fact that it was translated in its entirety
into English by the Rev. John Colton, Lucasian Professor of Mathematics
in the University of Cambridge, and published in 1801, fifty-two years
after it had appeared in Italian. His impression of the methods followed
by the Milanese _savante_ was so favorable that, in the words of a
contemporary writer, it "gave rise to his very spirited resolution of
learning a new language at an advanced period of life, that he might
make himself perfect master of them."[118]
Gratifying, however, as were the tributes of admiration and appreciation
which came to Agnesi from all quarters, from learned societies, from
eminent mathematicians, from sovereigns--the Empress Maria Theresa sent
her a splendid diamond ring and a precious crystal casket bejeweled with
diamonds--that which touched her most deeply was, undoubtedly, the
recognition which she received from the great Maecenas of his age, Pope
Benedict XIV. As Cardinal Lambertini and Archbishop of Bologna, he had
taken a conspicuous part in the honors showered on Laura Bassi when she
received her doctorate, and was specially delighted when she was made
professor of physics in his favored university. Being himself familiar
with the higher mathematics, he recognized at once the exceptional merit
of Maria Gaetana's work and showed his appreciation of it not only by
letters and presents, but also by having her, _motu proprio_, appointed
by the Bolognese senate as professor of higher mathematics in the
University of Bologna.
In advising her of this appointment, he writes her that he had in view
the honor of the University in which he had always taken a special
interest, and that the appointment carried with it no obligation of
thanks on her part but rather on his--_che porta seco ch'ella non deve
ringraziar Noi, ma che Noi dobbiamo ringraziar lei_. The interest that
this wise and broad-minded pontiff exhibited in the advancement of
learned women and the rewards he was ever ready to accord to their
achievements in science and literature--especially in the cases of Laura
Bassi and Maria Gaetana Agnesi--is in keeping with the policy pursued by
his predecessors, and accounts in great measure for that large number of
learned women in Italy who, since the opening of the first universities,
have been the glory of their sex and country.
But ardent as was the desire of the Supreme Pontiff to have Agnesi
occupy the chair of mathematics, and numerous as were the appeals of her
friends and the members of the university faculty to have her accept the
appointment that carried with it such signal honor, she could never be
induced to leave her beloved Milan. For, after completing her
masterpiece, she resolved to retire from the world and devote the rest
of her life to the care of the poor, the sick and the helpless in her
native city. She did not, however, as is so frequently asserted, enter
the convent and become a nun.[119] During many years after her
retirement from the world, she lived in her own home, a part of which
she had converted into a hospital. During the last fifteen years of her
life she had charge of the Pio Albergo Trivulzio--a large institution
founded by Prince Trivulzio for the aged poor who were without home or
assistance.
She had devoted ten years of the flower of her life to the writing of
her _Instituzioni Analitiche_--prepared primarily for the benefit of one
of her brothers who had a taste for mathematics--and, after it was
finished, she entered upon that long career of heroic charity which was
terminated only at her death at the advanced age of eighty-one.
One loves to speculate regarding Maria Gaetana's possible achievements
if she had continued during the rest of her life that science in which,
during a few short years, she had won such distinction. She had made her
own the discoveries of Newton, Leibnitz, Roberval, Fermat, Descartes,
Riccati, Euler, the brothers Bernouilli, and had mastered the entire
science of mathematics then known. Her pinions were trimmed for essaying
loftier flights than any hitherto attempted, and her intellect was
prepared, as one of her scientific friends expressed it, "for fixing the
limits of the infinite." But while the world of science was still
sounding her praises and predicting for her still greater triumphs in
the field of analysis, it learned with surprise and sorrow that she had
bid adieu to those studies in which she had achieved such extraordinary
success, and had consecrated her life to the service of the poor and the
afflicted. She disappeared completely from those literary and scientific
reunions where she had so long been the most conspicuous figure, and was
thenceforth known only as the ministering angel of the suffering and the
abandoned. For half a century hers was a life of the most heroic charity
and self-abnegation. Very readily, therefore, we can understand why a
recent representative of the scientific world should desire to see her
name placed on the calendar of saints.[120]
Had Agnesi devoted her entire life to science instead of abandoning it
just when she was prepared to do her best work, she might to-day be
ranked among such supreme mathematicians as Lagrange, Monge, Laplace and
the Bernouillis, all of whom were her contemporaries. Even as it was,
she has been placed beside Cardan, Leibnitz and Euler for her remarkable
powers of analysis of infinitesimals, while the best proof of the
literary value of her _Instituzioni Analitiche_ is the fact that it has
been selected by the famous society Della Crusca as a _testo di
lingua_--a work considered as a classic of its kind and used in the
preparation of the great authoritative dictionary of the Italian
language.
But by consecrating herself to charity she probably accomplished far
more for humanity and for the well-being of her sex than if she had
elected to continue her work in the higher mathematics. There had been
many learned women in Italy before her time and many since; many who
were distinguished as Hellenists, as Latinists, as polyglots, as
mathematicians--women like the Roccati, the Borghini, the Brassi, the
Ardinghelli, the Barbapiccola, the Caminer Turra, the Tambroni; but
Maria Gaetana Agnesi surpasses them all, not only in knowledge, but as a
potent influence for the diffusion of culture and the spirit of
brotherhood, for the expansion of benevolence and charity, and, above
all, for the elevation of woman. She was also, as her latest and best
biographer beautifully expresses it, "an inspired _condottiera_ who, in
the field of civility, anticipated the conquests of these latter days."
She was, indeed, as her epitaph informs us, _pietate_, _doctrina_,
_beneficentia insignis_, and as such she will live in the memory of our
race as long as men shall admire genius and love virtue.
In the year following the publication of Agnesi's _Instituzioni
Analitiche_ was recorded the premature and tragic death of the
distinguished French mathematician, the Marquise Emilie du Chatelet. She
has been described as a "thinker and scientist, precieuse and pedant,
but not the less a coquette--in short, a woman of contradictions."[121]
To most readers she is better known by reason of her liaison with
Voltaire, of whom she is regarded as a mere satellite, than for her work
in science. But she was far more than a satellite that shone by the
light received from the sage of Ferney. For there can be no doubt that
she was a highly gifted woman who, besides having a thorough knowledge
of several languages, including Latin, possessed a special talent for
mathematics. It was said of her that "she read Virgil, Pope and algebra
as others read novels," and that she was able "to multiply nine figures
by nine others in her head." No less an authority than the illustrious
Ampere declared her to be "a genius in geometry."
Among her teachers in mathematics were Clairaut, Koenig, Maupertuis,
Pere Jaquier and Jean Bernouilli, the immediate predecessors of such
distinguished mathematicians as Monge, Lagrange, d'Alembert and Laplace.
At her Chateau of Cirey, where she and Voltaire spent many years
together, she was visited by learned men from various parts of Europe.
Among these was the Italian scholar, Francisco Algarotti, who was the
author of a work entitled _Newtonism for Women_. And as Mme. du Chatelet
was an ardent admirer of Newton, the author of the _Principia_ soon
became a strong bond of union between her and the brilliant Italian. She
called the savants who frequented her chateau at Cirey the _Emiliens_
and purposed writing memoirs to be entitled _Emiliana_--a design,
however, which she was never able to execute.
The first work of importance from the pen of the Marquise was entitled
_Institutions de Physique_. In it she gave an exposition of the
philosophy of Leibnitz and dissertations on space, time and force. In
the discussion of the last topic she seems to have anticipated some of
the later conclusions of science respecting the nature of energy.
Her most noted achievement, however, was her translation of Newton's
_Principia_, the first translation into French of this epoch-making
work. To translate this masterpiece from its original Latin, it was
necessary that the Marquise, in order to make it intelligible to others,
should have a thorough understanding of it herself. To the translation
she added a commentary, which shows that Mme. du Chatelet had a
mathematical mind of undoubted power. She labored assiduously on this
great undertaking for many years and completed it only shortly before
her death; but it was not published until ten years after her demise.
In his _Elogie Historique_ on the Marquise's translation of the
_Principia_, Voltaire, in his usual flamboyant style, declares "Two
wonders have been performed: one that Newton was able to write this
work, the other that a woman could translate and explain it." In an
effort to express in a single sentence all his admiration for his
talented friend he does not hesitate to state: "Never was woman so
learned as she, and never did anyone less deserve that people should say
of her, 'She is a learned woman.'" Again he refers to her with
characteristic Frenchiness as "a woman who has translated and explained
Newton, in one word a very great man--_en un mot un tres grand
homme_."[122]
But, although the extent of her attainments and her ability as a
mathematician were unquestionable, she fell far short of her great
contemporary, Gaetana Agnesi, both in the depth and breadth of her
scholarship and in her power of infinitesimal analysis. As to her moral
character, she was infinitely inferior to the saintly savante of
Milan. She was by inclination and profession an Epicurean and an
avowed sensualist. In her little treatise, _Reflexions sur le
Bonheur_--Reflections on Happiness--she unblushingly asserts "that we
have nothing to do in this world except procure for ourselves agreeable
sensations." Considering her profligate life, bordering at times on
utter _abandon_, we are not surprised that one of her countrymen has
characterized her as "_Femme sans foi, sans moeurs, sans pudeur_,"--a
woman without faith, without morals, without shame.[123]
Anna Barbara Reinhardt of Winterthur in Switzerland was another woman of
exceptional mathematical talent. She is remarkable for having extended
and improved the solution of a difficult problem that specially engaged
the attention of Maupertuis. According to so competent an authority as
Jean Bernouilli, she was the superior, as a mathematician, of the
Marquise de Chatelet.
Of a more original and profound mathematical mind was Sophie Germain, a
countrywoman of the Marquise du Chatelet. Hers was the glory of being
one of the founders of mathematical physics. A pupil of Lagrange and a
co-worker with Biot, Legendre, Poisson and Lagrange, she has justly been
called by De Prony "the Hypatia of the nineteenth century."
Her success, however, was not achieved without overcoming many and great
difficulties. In the first place, she had to overcome the opposition of
her family, who were decidedly averse to her studying mathematics. "Of
what use," they asked, "was geometry to a girl?" But in trying to
extinguish her ardor for mathematics they but augmented it. Alone and
unaided she read every work on mathematics she could find. The study of
this science had such a fascination for her that it became a passion. It
occupied her mind day and night. Finally her parents, becoming alarmed
about her health and resolved to force her to take the necessary repose,
left her bedroom without fire or light, and even removed from it her
clothing after she had gone to bed. She feigned to be resigned; but when
all were asleep, she arose and, wrapping herself in quilts and blankets,
she devoted herself to her favorite studies, even when the cold was so
intense that the ink was frozen in her ink-horn. Not infrequently she
was found in the morning chilled through, having been so engrossed in
her studies that she was not aware of her condition. Before such a
determined will, so extraordinary for one of her age, the family of the
young Sophie had the wisdom to permit her to dispose of her time and
genius according to her own pleasure. And they did well. Like the great
geometer of Syracuse, Archimedes, who had ever been her inspiration in
the study of mathematics, she would have died rather than abandon a
problem which, for the time being, engaged her attention.
She first attracted the attention of savants by her mathematical theory
of Chladni's figures. By the order of Napoleon, the Academy of Science
had offered a prize for the one who would "Give the mathematical theory
of the vibration of elastic surfaces and compare it with the results of
experiment." Lagrange declared the problem insoluble without a new
system of analysis, which was yet to be invented. The consequence was
that no one attempted its solution except one who, until then, was
almost unknown in the mathematical world; and this one was Sophie
Germain.
Great was the surprise of the savants of Europe when they learned that
the winner of the _grand prix_ of the Academy was a woman. She became at
once the recipient of congratulations from the most noted mathematicians
of the world. This eventually brought her into scientific relations with
such eminent men as Delambre, Fourier, Cauchy, Ampere, Navier,
Gauss[124] and others already mentioned.
It was in 1816, after eight years of work on the problem, that her last
memoir on vibrating surfaces was crowned in a public seance of the
_Institut de France_. After this event Mlle. Germain was treated as an
equal by the great mathematicians of France. She shared their labors and
was invited to attend the sessions of the _Institut_, which was the
highest honor that this famous body had ever conferred on a woman.
The noted mathematician, M. Navier, was so impressed with the
extraordinary powers of analysis evinced by one of Mlle. Germain's
memoirs on vibrating surfaces that he did not hesitate to declare that
"it is a work which few men are able to read and which only one woman
was able to write."
Biot, in the _Journal de Savants_, March, 1817, writes that Mlle.
Germain is probably the one of her sex who has most deeply penetrated
the science of mathematics, not excepting Mme. du Chatelet, _for here
there was no Clairaut_.[125]
Like Maria Gaetana Agnesi, Mlle. Germain was endowed with a profoundly
philosophical mind as well as with a remarkable talent for mathematics.
This is attested by her interesting work entitled _Considerations
Generales sur l'Etat des Sciences et des Lettres aux Differentes Epoques
de Leur Culture_. All things considered, she was probably the most
profoundly intellectual woman that France has yet produced. And yet,
strange as it may seem, when the state official came to make out the
death certificate of this eminent associate and co-worker of the most
illustrious members of the French Academy of Sciences he designated her
as a _rentiere_--_annuitant_--not as a _mathematicienne_. Nor is this
all. When the Eiffel tower was erected, in which the engineers were
obliged to give special attention to the elasticity of the materials
used, there were inscribed on this lofty structure the names of
seventy-two savants. But one will not find in this list the name of that
daughter of genius, whose researches contributed so much toward
establishing the theory of the elasticity of metals,--Sophie Germain.
Was she excluded from this list for the same reason that Agnesi was
ineligible to membership in the French Academy--because she was a
woman? It would seem so. If such, indeed, was the case, more is the
shame for those who were responsible for such ingratitude toward one who
had deserved so well of science, and who by her achievements had won an
enviable place in the hall of fame.[126]
Four years after the birth of Sophie Germain was born in Jedburgh,
Scotland, one whom an English writer has declared was "the most
remarkable scientific woman our country has produced." She was the
daughter of a naval officer, Sir William Fairfax; but is best known as
Mary Somerville. Her life has been well described as an "unobtrusive
record of what can be done by the steady culture of good natural powers
and the pursuit of a high standard of excellence in order to win for a
woman a distinguished place in the sphere naturally reserved for men,
without parting with any of those characteristics of mind, or character,
or demeanor which have ever been taken to form the grace and the glory
of womanhood."[127]
The surroundings of her youth were not conducive to scientific pursuits.
On the contrary, they were entirely unfavorable to her manifest
inclinations in that direction. Having scarcely any of the advantages of
a school education, she was obliged to depend almost entirely on her own
unaided efforts for the knowledge she actually acquired. She, like
Sophie Germain, was essentially a self-made woman; and her success was
achieved only after long labor and suffering and in spite of the
persistent opposition of family and friends.
When she was about fifteen years old, the future Mrs. Somerville
received her first introduction to mathematics; and then, strange to
say, it was through a fashion magazine. At the end of a page of this
magazine, "I read," writes Mrs. Somerville, "what appeared to me to be
simply an arithmetical question; but in turning the page I was surprised
to see strange-looking lines mixed with letters, chiefly X's and Y's,
and asked 'What is that?'" She was told it was a kind of arithmetic,
called algebra.
Her interest was at once aroused; and she resolved forthwith to seek
information regarding the curious lines and letters which had so excited
her curiosity. "Unfortunately," she tells us, "none of our acquaintances
or relatives knew anything of science or natural history; nor, had they
done so, should I have had courage to ask of them a question, for I
should have been laughed at."
Finally she was able to secure a copy of a work on algebra and a Euclid.
Although without a teacher she immediately applied herself to master the
contents of these two works, but she had to do so by stealth in bed
after she had retired for the night. When her father learned of what was
going on, he said to the girl's mother, "Peg, we must put a stop to
this, or we shall have Mary in a straightjacket one of these days." The
mother, who had no more sympathy with her daughter's scientific pursuits
than had the father, and, fully convinced, like the great majority of
her sex, that woman's duties should be confined to the affairs of the
household, strove to divert her daughter's mind from her "unladylike"
pursuits. But her efforts were ineffectual. The young woman, in spite of
all obstacles and opposition, contrived to continue her cherished
studies; and, through her uncle, the Rev. Dr. Somerville, afterward her
father-in-law, she was able to become proficient in both Latin and
Greek. When she was thirty-three years of age she became the happy
possessor of a small library of mathematical works. "I had now," she
writes, "the means, and pursued my studies with increased assiduity;
concealment was no longer necessary, nor was it attempted. I was
considered eccentric and foolish, and my conduct was highly disapproved
of by many, especially by some members of my own family."[128]
In March, 1827, Mrs. Somerville received a letter from Lord Brougham,
who had heard of her remarkable acquirements, begging her to prepare for
English readers a popular exposition of Laplace's great work--_Mecanique
Celeste_. She was overwhelmed with astonishment at this request, for her
modesty made her diffident of her powers; and she felt that her
self-acquired knowledge of science was so far inferior to that of
university men that it would be sheer presumption for her to undertake
the task proposed to her. She was, however, finally persuaded to make
the attempt, with the proviso that her manuscript should be consigned to
the flames unless it fulfilled the expectations of those who urged its
production.
In less than a year her work, to which she gave the name of _The
Mechanism of the Heavens_, was ready for the press. But it was far more
than a translation and epitome, as originally intended by its projector,
Lord Brougham; for, in addition to the views of Laplace, it contained
the independent opinions of the translator respecting the propositions
of the illustrious French savant. No sooner was the work published than
Mrs. Somerville found herself famous. She had, as Sir John Herschel
expressed it, "written for posterity," and her book placed her at once
among the leading scientific writers and thinkers of the day. She was
elected an honorary member of the Royal Astronomical Society at the same
time as Caroline Herschel, they being the first two women thus honored.
Her bust, by Chantry, was placed in the great hall of the Royal Society,
and she was made a member of many other scientific societies in Europe
and America. In recognition of her services to science she was granted
by the government a pension of L200 a year--a sum which was shortly
afterward increased to L300. In addition to all this, Mrs. Somerville
had the satisfaction of learning that her work was so highly esteemed by
Dr. Whewell, the great master of Trinity, that it was, chiefly on his
recommendation, introduced as a textbook in the University of Cambridge
and prescribed as "an essential work to those students who aspire to the
highest places in the examinations." What Mme. du Chatelet had done for
Newton, Mrs. Somerville did for Laplace.
Among other books from the pen of this highly gifted woman is her
_Connection of the Physical Sciences_ and a work entitled _Physical
Geography_, which, together with the _Mechanism of the Heavens_, was the
object of the "profound admiration" of Humboldt. Then there is a number
of very abstruse monographs on mathematical subjects, one of which is a
treatise of two hundred and forty-six pages _On Curves and Surfaces of
Higher Orders_, which, she tells us, she "wrote _con amore_ to fill up
her morning hours while spending the winter in Southern Italy."
Her last work was a treatise _On Molecular and Microscopic Science_
embodying the most recondite investigations on the subject. This book,
begun after she had passed her eightieth birthday, occupied her for many
years and was not ready for publication until she was close upon her
ninetieth year. Her last occupations, continued until the day of her
death at the advanced age of ninety-two, were the reading of a book on
_Quaternions_ and the review and completion of a volume _On the Theory
of Differences_.
Like her illustrious friend, the great Humboldt, Mary Somerville was
possessed of extraordinary physical vigor, and, like him, she retained
her mental powers unimpaired until the last. And like her great rival in
mathematics, Maria Gaetana Agnesi, she was always "beautifully womanly."
Her scientific and literary occupations did not cause her to neglect
the duties of her household or to disregard "the graceful and artistic
accomplishments of an elegant woman of the world." Her daughter Martha
writes of her: "It would be almost incredible were I to describe how
much my mother contrived to do in the course of the day. When my sister
and I were small children, although busily engaged in writing for the
press, she used to teach us for three hours in the morning, besides
managing her house carefully, reading the newspapers--for she was always
a keen and, I must add, a liberal politician--and the most important new
books on all subjects, grave and gay. In addition to this, she freely
visited and received her friends.... Gay and cheerful company was a
pleasant relaxation after a hard day's work."[129]
The life of Mary Somerville, like that of Gaetana Agnesi, proves that
the pursuit of science is not, as so often asserted, incompatible with
domestic and social duties. It also disposes of the fallacy, so
generally entertained, that intellectual labor is detrimental to the
health of women and antagonistic to longevity. The truth is that it is
yet to be demonstrated that intellectual work, even of the severest
kind, is, _per se_, more deleterious to women than to those of the
stronger sex.
Scarcely less remarkable as a mathematician was Mrs. Somerville's
distinguished contemporary, Janet Taylor, who was known as the "Mrs.
Somerville of the Marine World." She was the author of numerous works on
navigation and nautical astronomy which in their day were highly prized
by seafaring men. In recognition of her valuable services to the marine
world she was placed on the civil list of the British government.
As an eminent mathematician as well as a "representative of the highest
intellectual accomplishments to which women have attained," Sonya
Kovalevsky will ever occupy an honored place among the votaries of
science. In many respects this richly endowed daughter of Holy Russia
was _par excellence_ the woman of genius of the latter half of the
nineteenth century.
She was born in Moscow in 1850, but although her career was brief it was
one of meteoric splendor. At an early age she exhibited an unusual
talent for mathematics and an unquenchable thirst for knowledge. Not
being able to obtain in her own country the educational advantages she
desired, she resolved at the age of eighteen to go to Germany with a
view of pursuing her studies there under more favorable auspices.
She first matriculated in the University of Heidelberg, where she spent
two years in studying mathematics under the most eminent professors of
that famous old institution. Thence she went to Berlin. She could not
enter the University there, as its doors were closed to female students;
but she was fortunate enough to prevail on the illustrious Professor
Weierstrass, regarded by many as the father of mathematical analysis, to
give her private lessons. He soon discovered to his astonishment that
this child-woman had "the gift of intuitive genius to a degree he had
seldom found among even his older and more developed students." Under
this eminent mathematician Sonya spent about three years, at the end of
which period she was able to present to the University of Goettingen
three theses which she had written under the direction of her professor.
The merit of her work and the testimonials which she was able to present
from Weierstrass, Kirchhoff and others were of such supreme excellence
that she was exempted from an oral examination and was enabled, by a
very special privilege, to receive her doctorate without appearing in
person.
Not long after receiving her doctor's degree--one of the first to be
granted to a woman by a German university--she was offered the chair of
higher mathematics in the University of Stockholm. She was the first
woman in Europe, outside of Italy, to be thus honored. But her
appointment had to be made in the face of great opposition. No other
university, it was urged by the conservatives, had yet offered a
professor's chair to a woman. Strindberg, one of the leaders of modern
Swedish literature, wrote an article in which he proved, "as decidedly
as that two and two make four, what a monstrosity is a woman who is a
professor of mathematics, and how unnecessary, injurious and out of
place she is."[130]
The fame that came to Sonya through her achievements in the German and
Swedish universities was immensely enhanced when, on Christmas eve,
1888, "at a solemn session of the French Academy of Sciences, she
received in person the _Prix Bordin_--the greatest scientific honor
which any woman had ever gained; one of the greatest honors, indeed, to
which any one can aspire."
She became at once the heroine of the hour and was thenceforth "a
European celebrity with a place in history." She was feted by men of
science whithersoever she went and hailed by the women of the world as
the glory of her sex and as the most brilliant type of intellectual
womanhood.
Mme. Kovalevsky's printed mathematical works embrace only a few memoirs
including those which she presented for her doctorate and for the _Prix
Bordin_. But brief as they are, all of these memoirs are regarded by
mathematicians as being of special value. This is particularly true of
the memoirs, which secured for her the _Prix Bordin_; for it contains
the solution of a problem that long had baffled the genius of the
greatest mathematicians.
The prize had been opened to the competition of the mathematicians of
the world, and the astonishment of the committee of the French Academy
was beyond expression when it was found that the successful contestant
was a woman.[131]
Everyone admired her varied and profound knowledge, but, above all, her
amazing powers of analysis. A German mathematician, Kronecker, did not
hesitate to declare that "the history of mathematics will speak of her
as one of the rarest investigators."[132]
Shortly before her premature death, she had planned a great work on
mathematics. All who are interested in the intellectual capacities and
achievements of woman must regret that she was unable to complete what
would undoubtedly have been the noblest monument of woman's scientific
genius. She was then in the prime of life and perfectly equipped for the
work she had in mind. Considering the extraordinary receptive and
productive power of this richly dowered woman, there can be little
doubt, had she lived a few years longer, that she would have produced a
work that would have caused her to be ranked among the greatest
mathematicians of the nineteenth century.
It is pleasant to record that this woman of masculine mind, masculine
energy and masculine genius, far from being mannish or unwomanly, was,
on the contrary, a woman of a truly feminine heart; and that, although a
giantess in intellectual attainments, she was in grace and charm and
delicacy of sentiment one of the noblest types of beautiful womanhood.
She could with the greatest ease turn from a lecture on _Abel's
Functions_ or a research on Saturn's rings to the writing of verse in
French or of a novel in Russian or to collaborating with her friend, the
Duchess of Cajanello, on a drama in Swedish, or to making a lace collar
for her little daughter, Fouzi, to whom she was most tenderly
attached.[133]
Little more than a quarter of a century has elapsed since Strindberg,
expressing the sentiment of the great majority of the men of his time,
declared that a woman professor of mathematics is a monstrosity. But
during this short period what a change has been effected in the attitude
of the world toward women who devote themselves to the study and the
teaching of science! Women mathematicians are found to-day in all
civilized countries, and no sane person now considers it any more
"unwomanly" or more "monstrous" for them to study or teach mathematics
than for them to teach music or needlework. Yet more. They are now
frequent contributors to mathematical magazines and to the official
bulletins of learned societies, and not infrequently they are on the
editorial staffs of publications devoted exclusively to mathematics.
They are also found as computers in some of the largest astronomical
observatories, where the speed and accuracy of their work have evoked
the most favorable comment.
Of women in America, who have distinguished themselves by their work in
the higher mathematics, it suffices to mention the name of Miss
Charlotte Angas Scott, recently deceased, who was for years professor of
mathematics in the College of Bryn Mawr. Her writings on various
problems of the higher mathematics show that she faithfully followed in
the footsteps of her illustrious predecessors,--Hypatia, Agnesi, du
Chatelet, Germain, Somerville and Kovalevsky.
FOOTNOTES:
[108] "Ipse mulieres Philosophas in libris Veterum sexaginta quinque
reperi," _Historia Mulierum Philosopharum_, p. 3, Amstelodami, 1692.
[109] Plato had inscribed above the entrance of his school, [Greek:
Oudeis ageometretos eisito]. Let no one enter here who is not a
geometer.
[110] Menagius in referring to this matter, op. cit., p. 37, writes as
follows: "Meritrices Graecas plerasque humanioribus literis et
mathematicis disciplinis operam dedisse notat Athenaeus."
[111] The sentiment of the Greek epigram is well expressed in the
following Latin verses:
"Quando intueor te, adoro, et sermones,
Virginis domum sideream intuens.
E coelis enim tua sunt opera,
Hypatia casta, sermonum venustas,
Impollutum astrum sapientis doctrinae."
[112] Among modern works on Hypatia may be mentioned _Hypatia, die
Philosophin von Alexandria_, by St. Wolt, Vienna, 1879; _Hypatia von
Alexandria_, by W. A. Meyer, Heidelberg, 1886; _Ipazia Alessandrina_, by
D. Guido Bigoni, Venize, 1887, and _De Hypatia_, by B. Ligier, Dijon,
1879.
[113] Ambrosius in his preface to the works of Abelard and Heloise
refers to the latter as "Clarum sui sexus sidus et ornamentum," and
declares "necnon mathesin, philosophiam et theologiam a viro suo edocta,
illo solo minor fuit."
[114] Mazzuchelli says of her in his _Museo_, "Sembra non avervi nella
Natura cosa la piu intralciata ed oscura nelle storie, ne finalemente la
piu astrusa nelle matematiche e nelle mecchaniche, che a lei conta non
sia e palese, e che sfugga la capacita del suo spirito." _Dizionario
Biografico_, Vol. I, p. 122, by Ambrogio Levati, Milano, 1821.
[115] _Delle Donne Illustri Italiane del XIII al XIX Secolo_, p. 268,
Roma.
[116] The full title of this celebrated discourse is _Oratio qua
ostenditur Artium liberalium studia a Faemineo sexu neutiquam abhorere,
habita a Maria de Agnesis Rhetoricae Operam Dante, Anno aetatis suae nono
nondum exacto, die 18, Augusti, 1727_. It is found at the end of a work
entitled _Discorsi Academici di varj autori Viventi intorno agli Stuj
delle Donne in Padova_, 1729. This subject, it may be remarked,
frequently engaged the attention of Maria Gaetana as she advanced in
years, for we find it among the questions discussed in her
_Propositiones Philosophicae_, pp. 2 and 3, Mediolani, 1738.
[117] M. Charles de Brosses, in his _Lettres Familieres ecrites de
l'Italie en 1739 et 1740_, speaks of Agnesi in terms that recall the
marvelous stories which are related of Admirable Crichton and Pico della
Mirandola. "She appeared to me," he tells us, "something more
stupendous--_una cosa piu stupenda_--than the Duomo of Milan." Having
been invited to a _conversazione_ for the purpose of meeting this
wonderful woman, the learned Frenchman found her to be a "young lady of
about eighteen or twenty." She was surrounded by "about thirty people
... many of them from different parts of Europe." The discussion turned
on various questions of mathematics and natural philosophy.
"She spoke," writes de Brosses, "wonderfully well on these subjects,
though she could not have been prepared beforehand any more than we
were. She is much attached to the philosophy of Newton; and, it is
marvelous to see a person of her age so conversant with such abstruse
subjects. Yet, however much I was surprised at the extent and depth of
her knowledge, I was still more amazed to hear her speak Latin ... with
such purity, ease and accuracy, that I do not recollect any book in
modern Latin written in so classical a style as that in which she
pronounced these discourses.... The conversation afterwards became
general, everyone speaking in the language of his own country, and she
answering in the same language; for, her knowledge of languages is
prodigious."
[118] At the conclusion of an elaborate review of Colton's translation
of Agnesi's _Instituzioni Analitiche_ in the _Edinburgh Review_ for
January, 1804, the writer expresses himself as follows: "We cannot take
leave of a work that does so much honor to female genius, without
earnestly recommending the perusal of it to those who believe that great
talents are bestowed by nature exclusively on man, and who allege that
women, even in their highest attainments, are to be compared only to
_grown children_, and have, in no instance, given proofs of original and
inventive powers, of a capacity for patient research, or for profound
investigation. Let those who hold these opinions endeavor to follow the
author of the _Analytical Institutions_ through the long series of
demonstrations, which she has contrived with so much skill and explained
with such elegance and perspicuity. If they are able to do so, and to
compare her work with others of the same kind, they will probably
retract their former opinions, and acknowledge that, in one instance at
least, intellectual powers of the highest order have been lodged in the
brain of a woman.
"At si gelidus obstiterit circum praecordia sanguis; and if they are
unable to attend this illustrious female in her scientific excursions,
of course, they will not see the reasons for admiring her genius that
others do; but they may at least learn to think modestly of their own."
[119] It is surprising how many legends have obtained respecting the
life of Agnesi after the publication of her _Instituzioni Analitiche_.
Thus, the writer of the article in the _Edinburgh Review_, above quoted,
declares that "she retired to a convent of _blue nuns_,"--a statement
that has frequently been repeated in many of our most noted
encyclopedias.
In a _Prospetto Biografico delle Donne Italiane_, written by G. C.
Facchini and published in Venice in 1824, it is stated that Maria
Gaetana was selected by the Pope to occupy "the chair of mathematics
which had been left vacant by the death of her father," while Cavazza in
his work _"Le Scuole dell," Antico Studio Bolognese_, pp. 289-290,
published in Milan in 1896, assures us that Gaetana Agnesi taught
analytical geometry in the University of Bologna for full forty-eight
years. The facts are that neither the father nor the daughter ever
taught even a single hour either in this or in any other university. Cf.
_Maria Gaetana Agnesi_, p. 273 et seq., by Luisa Anzoletti, Milano,
1900. This is far the best life of Milan's illustrious daughter that has
yet appeared. The reader may also consult with profit the _Elogio
Storico_ di Maria Gaetana Agnesi, by Antonio Frisi, Milano, 1799, and
_Gli Scrittori d'Italia_, of G. Mazzuchelli, Tom. I, Par. I, p. 198 et
seq., Brescia, 1795.
[120] M. Rebiere, in _his Les Femmes dans la Science_, p. 13, Paris,
1897, writes, "Ne pourrait-on aller plus loin et canonizer notre Agnesi?
J'estime, moi profane, que ce serait une sainte qui en vaudrait bien
d'autres."
[121] _An Eighteenth Century Marquise, a Study of Emilie du Chatelet_,
p. 5, by F. Hamel, New York, 1911.
[122] Preface to Mme. du Chatelet's translation of the _Principia_ of
Newton, Paris, 1740.
[123] Voltaire's last tribute, "The Divine Emilie," or, as Frederick II
was wont to call her, "Venus-Newton," concluded with the following
verses:
"L'Univers a perdu la sublime Emilie;
Elle aimait les plaisirs, les arts, la verite;
Les dieux, en lui donnant leur ame et genie,
N'avaient garde pour eux que l'immortalite."
The universe has lost the sublime Emilie; she loved pleasure, the arts,
truth; the gods, in giving her their soul and genius, retained for
themselves only immortality.
For further information of this extraordinary woman, see _Lettres de la
Mme. du Chatelet, Reunies pour la premiere fois_, par Eugene Asse,
Paris, 1882.
[124] At the beginning of her correspondence with Gauss, Legendre and
Lagrange Mlle. Germain concealed her sex under a pseudonym, "in order,"
as she declared, "to escape the ridicule attached to a woman devoted to
science"--_craignant le ridicule attache au titre de femme savante_.
She, too, suffered from the widespread effects of Moliere's _Les Femmes
Savantes_, as had many a gifted woman before her time and as have many
others of a much later date.
[125] This celebrated mathematician, as is well-known, was a
collaborator with Mme. du Chatelet in her translation of Newton's
_Principia_.
[126] For further information respecting this remarkable woman the
reader is referred to _Oeuvres Philosophiques de Sophie Germain Suivies
de Pensees et de Lettres Inedites et Precedees d'une Etude sur sa Vie et
ses Oeuvres_, par. H. Stupy, Paris, 1896. One may also consult
Todhunter's _History of the Theory of Elasticity and of the Strength of
Materials_, Vol. I, pp. 147-160, Cambridge, 1886, in which is given a
careful resume of Mlle. Germain's mathematical memoirs on elastic
surfaces.
[127] _Saturday Review_, January 10, 1874.
[128] _Personal Recollections, From Early Life to Old Age, of Mary
Somerville_, p. 80, Boston, 1874.
[129] _Personal Recollections_, ut sup., p. 5.
[130] _Sonya Kovalevsky, Her Recollections of Childhood, With a
Biography_, by Anna Carlotta Leffler, p. 219, New York, 1895.
[131] "The prize was doubled to five thousand francs, on account of the
'quite extraordinary service rendered to mathematical physics by this
work,' which the Academy of Sciences pronounced 'a remarkable work.' The
competing dissertations were signed with mottoes, not with names, and
the jury of the Academy made the award in utter ignorance that the
winner was a woman. Her dissertation was printed, by order of the
Academy, in the _Memoires des Savants Etrangers_. In the following year
Mme. Kovalevsky received a prize of fifteen hundred kroner from the
Stockholm Academy for two works connected with the foregoing."
[132] Men of science will realize the capacity of this gifted Russian
woman as a mathematician when they learn that she gave in the University
of Stockholm courses of lectures on such subjects as the following:
Theory of derived partial equations; theory of potential functions;
applications of the theory of elliptic functions; theory of Abelian
functions, according to Weierstrass; curves defined by differential
equations, according to Poincare; application of analysis to the theory
of whole numbers. How many men are there who give more advanced
mathematical courses than these?
[133] To a friend, who expressed surprise at her fluttering to and fro
between mathematics and literature, she made a reply which deserves a
place here, as it gives a better idea than anything else of the
wonderful versatility of this gifted daughter of Russia. "I understand,"
she writes, "your surprise at my being able to busy myself
simultaneously with literature and mathematics. Many who have never had
an opportunity of knowing any more about mathematics confound it with
arithmetic, and consider it an arid science. In reality, however, it is
a science which requires a great amount of imagination, and one of the
leading mathematicians of our century states the case quite correctly
when he says that it is impossible to be a mathematician without being a
poet in soul. Only, of course, in order to comprehend the accuracy of
this definition, one must renounce the ancient prejudice that a poet
must invent something which does not exist, that imagination and
invention are identical. It seems to me that the poet has only to
perceive that which others do not perceive, to look deeper than others
look. And the mathematician must do the same thing. As for myself, all
my life I have been unable to decide for which I had the greater
inclination, mathematics or literature. As soon as my brain grows
wearied of purely abstract speculations it immediately begins to incline
to observations on life, to narrative, and _vice versa_, everything in
life begins to appear insignificant and uninteresting, and only the
eternal, immutable laws of science attract me. It is very possible that
I should have accomplished more in either of these lines, if I had
devoted myself exclusively to it; nevertheless, I cannot give up either
of them completely."
From Ellen Key's _Biography of the Duchess of Cajanello_, quoted in Anna
Leffler's biography of Sonya Kovalevsky, ut sup, pp. 317-318.