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de 1' Academic franchise , in Melanges scientifiques et litteraires III,
Paris 1858, 143 156. C.-A. Valson, La vie et les travaux du
Baron Cauchy (Tome I: Partie historique. Tome II: Partie scienti-
fique), Paris 1868. Valson, Communication relative a la nouvelle
edition des reuvres completes d'Aug. Cauchy, in Congres scientifique
international des Catholiques tenu a Paris du 8 au 13 avril 1888 II,
Paris 1888, 514 520. Jos. Bertrand, A.-L. Cauchy, Discours
prononce a la seance annuelle de 1' Academic des sciences 1898 (re-
printed in Cosmos, Revue des sciences et de leurs applications, Paris
12 fevr. 1898, 211 217. Kneller in Stimmen aus Maria-Laach
LXIV, Freiburg 1903, 138148 285298.



AUGUSTIN LOUIS CAUCHY. 51

even Euler and Gauss, had worked in vain. Election
to the Academy, and the highest educational posts in
France were the reward of these first works. His sub-
sequent achievements were no less remarkable ; they
are, indeed, beyond praise. Joseph Bertrand, a learned
colleague of Cauchy's, but by no means a sharer of
his convictions, in his discourse on Cauchy in the
Academy in 1897 expressly declares his inability to
render him the praise which is his due.

"For a long time now", he says, "it has been beyond
the power of any eulogy to heighten the splendour of his
reputation, a reputation which can never die. We come
too late to say anything but what all the world knows, and
yet our predecessors who spoke immediately after his death
were too early. The reputation of Cauchy grew wider as
years went on; his most enthusiastic admirers of half-
a-century ago could not have foreseen or foretold it. He had
explored new regions : the heights to which he had climbed
all the world knew, but no one could then have rightly
appreciated the spaciousness, the consistency, the inexhaus-
tible fertility of his researches." *

Cauchy's biographer, A. Valson, joint editor of the
collection of his works published at the expense of
the Academy, disscussing the place which Cauchy oc-
cupies in his Science, writes:

"I confine myself to the statement that many scientific
authorities consider Cauchy the first mathematician of our
century : no one at any rate disputes his claim to be ranked
among the greatest masters. His methods and conclusions
form the point of departure of most contemporary mathe-



1 Le role de Cauchy grandit chaque jour ; les admirateurs les
plus enthousiastes, il y a 50 ans, ne pouvaient ni le predire ni le
prevoir. II explorait des regions nouvelles, on savait a quelle hauteur;
nul n'en pouvait deviner 1'etendue , la consistance et 1'inepuisable
fecondite. Bertrand ante 211.

4*



52 II. MATHEMATICS.

maticians. Herein, above all, lies the characteristic quality
of his life's work." *

According to O. Terquem also, the distinguishing
feature of Cauchy is the creative verve of his genius;
he laid new paths open whereever he went 2 . Our ad-
miration of his extraordinary endowments is increased
by the fact that his works are not limited to a single
province of Mathematics, but deal with almost every
part of this science. His genius for work was so amazing
that at nearly every weekly meeting of the Academy
he had something new to offer, and the reprint of his
collected works will, according to Valson's calculation,
run to 11,531 quarto pages.

At his entrance into his professorate, Cauchy had
taken an oath of loyalty to the king. This oath had
very serious consequences for him. When the July
Revolution broke out, he considered it a breach of his
bounden duty to take the oath of allegiance to Louis-
Philippe also : on his refusal to do so he lost all his
professional posts, and all the efforts of his friends to
procure him a fresh public appointment were in vain
until the Revolution of 1848. This annulled the political
oath, and when the oath of personal loyalty was re-
introduced, Cauchy was released from it by Napoleon III.
In the first anguish of 1830, Cauchy had left France.
Soon after, on the invitation of Charles X., he went to



1 Congres scientifique international des catholiques tenu a Paris
1888 II, Paris 1888, 514.

2 Mathematician dans le sens le plus large , 1'esprit de Cauchy
n'etait pas cantonne dans un coin de la science. Partout il fon-
dait, partout il creait, partout il etait au premier rang. Quoted by
M. Marie, Hist, des sciences mathematiques et physiques XII, Paris
1888, 166.



AUGUSTIN LOUIS CAUCHY. 53

Prague as tutor to the Count de Chambord, and did
not return to France till 1838.

This rapid sketch of Cauchy's life is sufficient to
show that he was not only a man of genius, but also
a man of character. And this greatness of character
rested wholly and absolutely on Christian conviction
and practical piety. He not merely discharged faith-
fully all the duties of a Catholic, but was ever fore-
most among those who are ready at the call of events
to defend or propagate religion or to set on foot
works of charity. He was a zealous member of the
Conference of St. Vincent de Paul, and did all that
he could do to relieve the needs of others. "Nearly
every day", said the Mayor of Sceaux (where Cauchy
had a country house), over his grave, "he paid me a
visit. He had a poor invalid, or a foundling to recom-
mend, a young person looking for a situation, or a
soldier who was the sole support of his family and
begged to be allowed to return to it." 1 Many pious
and philanthropic societies were established by his efforts,
as, for example, a Society to secure the universal ob-
servance of the Sunday's rest, and the still existing
Society for the maintenance of schools in the East.
Of other charitable enterprises he was a leading sup-
porter as e. g. the Society of St. Francis Regis for
the legitimation of irregular unions. When in 1846 Ire-
land was visited by a terrible famine, Cauchy succeeded
in inducing the Pope to issue a Rescript on behalf of
that country. In Sceaux he secured the settlement of
a community of nuns, and founded a union for the
protection of youth. On his deathbed he gave a touching



1 Valson, Vie de Cauchy I 273.



54 II. MATHEMATICS.

manifestation of his deep piety. When the priest in-
formed him that he was about to bring the Consecrated
Host to him, he gave instructions that all the most
beautiful flowers in the garden should be strewn along
the stairs which were to be honoured by the passage
of Our Lord. The thought which most troubled his
last hours was the future of a community of the Christian
Brothers which he had introduced into Sceaux.

He was very intimate with many Jesuit priests,
especially with the celebrated pulpit orator P. Ravignan.
When shortly before the February Revolution a violent
assault was made on the Schools of the Order in France,
Cauchy published two pamphlets in defence of them.
In one of these we find the following explicit Con-
fession of Faith which may well find a place here.

"I am a Christian, that is to say, I believe in the divinity
of Jesus Christ as did Tycho Brahe, Copernicus, Descartes,
Newton, Fermat, Leibniz, Pascal, Grimaldi, Euler, Guldin,
Boscovich, Gerdil; as did all the great astronomers, physi-
cists, and geometricians of past ages: nay more I am like
the greater part of these a Catholic: and were I asked for
the reasons of my faith I would willingly give them. I
would show that my convictions have their source not in
mere prejudice but in reason and a -resolute enquiry. I am
a sincere Catholic as were Corneille, Racine, La Bruyere,
Bossuet, Bourdaloue, Fenelon, as were and still are so many of
the most distinguished men of our time, so many of those who
have done most for the honour of our science, philosophy, and
literature, and have conferred such brilliant lustre on our
Academies. I share the deep convictions openly manifested
in word, deed, and writings by so many savants of the
first rank, by a Ruffini, a Haiiy, a Laennec, an Ampere,
a Pelletier, a Freycinet, a Coriolis l and if I avoid naming



1 Two of those whom he here mentions , distinguished them-
selves in Mathematics ; a brief account of them will not be out of



AUGUST1N LOUIS CAUCHY. 55

any of those living, for fear of paining their modesty, I
may at least be allowed to say that I loved to recognise
all the noble generosity of the Christian faith in my il-
lustrious friends the creator of Cyrstallography (Haiiy), the
introducers of quinine and the stethoscope (Pelletier and
Laennec), the famous voyager on board the 'Urania', and
the immortal founders of the theory of Dynamic Electricity !
(Freycinet and Ampere).

These discourses were delivered by Cauchy at the
Institut Catholique of Paris for the establishment of
which he was in part responsible and were directed
to the protection of the young students from the danger
of unbelief. Many similar passages might be quoted



place here. Paolo Ruffini, born 1765 at Valentino in the Papal
States, died 1822 at Modena, made such rapid progress in the exact
sciences , that when only 23 years of age , he was elected Pro-
fessor in the University of Modena in the room of his former master.
He lost this position during the French invasion, because he would
not take the oath of allegiance to the new government. He wrote
some valuable works on the theory of Equations. He was also a
doctor, and in 1817 during an epidemic, won a great deal of grati-
tude and praise by his courage and self-sacrifice. Among the works
in which he shows his religious disposition is a pamphlet against
the Encyclopedists: Dell' immortalita dell' anima , Modena 1 806.
Cf. Heinrich Burkhardt, Die Anfange der Gruppentheorie und
Paolo Ruffini, in the Zeitschrift fur Mathematik und Physik XXXVII
(Supplement), Leipzig 1892, 119 159. Gaspard Gustave de
Coriolis (born in Paris 1792, died there in 1843) was from 1838
Master of Studies at the Polytechnique in Paris. Coriolis "vermochte
der Wissenschaft nicht alle die Dienste zu leisten, die man bei seinen
schonen geistigen Anlagen hatte erhoffen du'rfen ; seine unglaublich
zarte Gesundheit zwang ihn , vor allem jeden Tag das stets neue
Problem zu losen , wie er sein Leben weiter erhalten konne. . . .
Coriolis ist mit General Poucelet einer der ersten Forderer der Reform,
welche sich im Unterricht in der rationellen Mechanik vollzogen hat"
(M. Marie, Hist, des sciences math, et phys. XII 191 192).
1 Quoted by Valson, Vie de Cauchy I 173.



56 II. MATHEMATICS.

from them : but we shall avail ourselves here of the
memorial discourse pronounced by Cauchy over a col-
league.

Not long before his own death, Cauchy stood over
the grave of the President of the Academy of Sciences,
J. P. Maria Binet, who had died on May 12 th 1856.
In his funeral oration, "a discourse perfectly adequate
and worthy of the occasion" he spoke "less of Binet's,
great services to Science, than of the depth of his re-
ligious convictions" 1 .

"Binet", said Cauchy, "was a mathematician of the first
order and the finest intellect, but he was something more. With
the most richly endowed minds of past centuries and also of
the present century, with Descartes, Fermat, Haiiy, Ampere,
Laennec he ascended gladly from the knowledge of scientific
truths to the eternal source of all truth. Contemplation of the
sublime laws, which direct the course of the stars, and pre-
serve order and harmony in the universe, supplied him
constantly with new motives to celebrate the Architect of
all these marvels with praise and prayer. The living faith
of our comrade, his ardent love of God to Whom he render-
ed honour by his talents and his virtues, his comprehen-
sive knowledge and his inexhaustible charity, ought to in-
spire us with the consoling conviction that to-day Binet is
happier and wiser than any of us, that he has gone hence
to find light at the source of all light, and to fathom
those, secret depths which we also shall one day fathom, if
we hold stoutly to the road which his feet travelled. You
will forgive me , gentlemen , if plunged in these sublime
thoughts, I cut short my utterance of them. True grief is
not a lover of words. ... At the sight of the cross planted
on this grave in token of our hope, my tongue is silent.
May we all lift ourselves in thought to the other side of
that tremendous gulf which separates our earthly sciences
so straitened and limited, as they are, even to the noblest



1 Grunerts Archiv XXVII 483.



VICTOR ALEXANDER PUISEUX. 57

intellects - - from the lofty truths of that divine wisdom
which shall be imparted to all in Heaven." *

"The life of Angustin Cauchy", wrote the celebrated
J. B. Biot 2 , "offers a perfect model of Christian virtue,
as well as of supreme intellectual activity. He was one of
the most eminent mathematicians that France has produced,
and his nobility of character was not less remarkable than
his genius for mathematics.'* '

Cauchy's successor at the Sorbonne was his pupil
Victor Alexander Puiseux (1820 ^1883) who held
the position till 1882 3 . He also was a savant of the first
order; according to some he was the best of all
Cauchy's pupils. Bertrand says of Puiseux's masterpiece
that "after 30 years it is not a single day out of date",
and according to Hermite it marks an epoch in ma-
thematical analysis. How highly Pasteur thought of
Puiseux is best indicated by an anecdote related by
Bertrand in his biography of the distinguished astro-
nomer Tisserand. "About 35 years ago, I was com-
missioned, on what occasion I do not remember, to
inspect the Third Year's Division of the Ecole Normale,
in which Tisserand occupied first place. Pasteur, then
director of scientific studies, asked me: 'What do you
think of Tisserand?' 'He is a brilliant student', I re-
plied, 'the best of them all.' My language appeared
to him much too cold. 'Tisserand', he exclaimed, 'why
he is a little Puiseux.' Such praise from such a man



1 Ib. 2 J. B. Biot in Melanges III 143.

3 Cf. Ph. Gilbert in Revue des questions scientifiques XV,
Bruxelles-Paris 1884, I 37; J. Bertrand, Eloge de M. Victor
Puiseux lu dans la seance publique annuelle de 1' Academic des Sciences
du 5 Mai 1884; printed in the Bulletin des sciences math, et astro-
nomiques, 2 nd Series VIII, Annee 1884, Paris 1884, 227 234; F. Tis-
serand, Notice sur V. A. Puiseux, ib. 234 245.



$8 II. MATHEMATICS.

was very high indeed, but it will be understood by
every one who knew Tisserand."

What was most admired in Puiseux as a teacher was
the rare lucidity with which he handled the most in-
tricate problems of the mechanism of the heavens. In
the Bureau des Longitudes (1868 1872), and in the
Astronomical Observatory (1855 1859), ne displayed
wonderful activity. He left it to his colleagues to select
each of them whatever department of the work he
specially wished to investigate, and what remained,
the most arduous portions, he took upon himself. He
worked out, for instance, beginning in 1869, the in-
terminable calculations necessary for satisfactory ob-
servations of the Transits of Venus in 1874 and 1882,
and revised the works of Laplace, verifying every cal-
culation contained in them. He refused for a long
time to become a candidate for the Academy, for his
heart was little set on external dignities. But when in
1871 his name was proposed, his three competitors
voluntarily retired, and from the fifty-five electors Puiseux
received fifty-five votes. The election stands, we believe,
without parallel in the whole century: there was not a
single adverse vote, not a single abstention. Bertrand
declared in this connection: "The election of Puiseux
was due to his merit, the unanimity to his character." 1

This high praise was repeated by Bertrand when in the
Session of the Academy for the following year he pro-
nounced a discourse on the achievements and character



1 Seul parmi nous, seul peut-etre entre tous les Academiciens de
ce siecle, Puiseux a ete elu a 1'unanimite. . . . L'election de Puiseux
etait due a son merite, 1'unanimite a son caractere (Bertrand in
the Academy of Science on Puiseux' death ; Comptes rendus XCVII,
Paris 1883, 656.



VICTOR ALEXANDER PUISEUX. 59

of Puiseux. He begins with a remark of Fontenelle,
who, as permanent secretary of the Academy, had been
called upon to deliver memorial addresses on so many
distinguished savants. He had already, said the latter
in 1822, bestowed on so many dead colleagues the
praise that their lives were as simple as their minds
were sublime, that one might come to attribute this
merit less to individual scientists than to the nature of
their science itself. "Times have changed", remarks
Bertrand, "The indifference towards wealth, the calm ex-
pectation of renown, the ancient Socratic contempt for
everything for which the crowd so eagerly struggles,
hurries, intrigues . . . are to-day neither the dowry of
our science, nor the distinguishing stamp of our scien-
tists. They are met only in exceptional cases: and
such an exception was Victor Puiseux." 1

"One of his most characteristic qualities", writes
Gilbert 2 , "was a complete absence of all spirit of
intrigue, personal ambition, craving for pomp and digni-
ty. His indifference to external distinctions amounted
almost to antipathy. The modesty which led him, in
all enterprises, to assume that part which offered the
most work and the least notoriety, was perfectly sincere
and without any trace of affectation. . . . The calm,
simple, and regular tenor of his life impressed every
one who knew him. He had no other joys than in-
tellectual labour, contemplation of the beauty of nature,
and family affection." In 1870 he was on a holiday
tour in the South when the War broke out : he returned
immediately to Paris to suffer siege there, and to take
part in the defence of the capital. A year before his



1 Ib. 227. 2 Revue des quest, scient. XV 32.



60 II. MATHEMATICS.

death he begged to be relieved of his professorate; "it
was time to make way for younger men". It needed
the unanimous and officially declared request of his
colleagues to induce him to retain the title.

That his greatness of character had its source and
stay in deep religious conviction Bertrand himself tells
us at the close of his discourse, in a rhetorical fashion,
and, as it were, against his will. Gilbert is clearer in
his testimony.

"Victor Puiseux", he writes 1 , "was a man of profoundly
Christian convictions, loyal all his life to the duties required
of him by the religion which he imbibed in youth and
developed with his mature intellect. During his tenure of
office in the ficole Normale he had ample opportunity to
make manifest his belief, to anneal it in the fire of contro-
versy, and to impart it in precious friendships. It was the
time when the famous conferences of Lacordaire were ring-
ing through France. They penetrated into the ficole also;
teachers and students no longer confined themselves to
science but engaged vigorously in philosophical and reli-
gious discussions. Puiseux took an active part in the contro-
versy, and put at the services of his religion the prestige
which his scientific distinction and his amenity of disposition
had won him. But to play the part of leader consorted ill
with his modesty. He preferred to efface himself behind
Pierre Olivaint 2 , then a student in the School of Litera-
ture. Their association was not limited to this contro-
versy. . . . They joined in devoting a part of their holidays
to works of charity, and founded a Conference of St. Vincent
de Paul which is still in existence." 3



1 Ib. XV 3436.

2 Afterwards a Jesuit: fell a victim to the Commune 1871.

3 Cf. Tisserand, Notice 235. On ne s'occupait pas que de
science a 1'Ecole ; les discussions philosophiques et religieuses y etaient
fort vives : M. Puiseux y prenait une part active et mettait au service
de ses convictions religieuses 1'ascendant naturel que son intelligence



BERNARD RIEMANN. 6 I

"Inexhaustible bounty, active charity constituted, as it
were, the soul of his life. He was a loyal and zealous
servant of St. Vincent, and only when struck down by fatal
illness did he cease to climb the stairs of the poor. He
was the stay and support of a multitude of good works
which were unknown, even to his family, until his death.
Side by side with the members of the Institute and of the
Scientific Faculty, there walked at his funeral the outcast and
disinherited children of life, come there to lament their bene-
factor."

With Cauchy and Weierstrass must be associated,
as author of the Mathematical Theory of Functions,
Bernard Riemann, Professor at Gottingen. Born on
Sept. 17 th 1826, at Breselenz in Hanover, where his
father was a Protestant clergyman, he had not com-
pleted his fortieth year when he died of phthisis (July 2O th
1866) at Selasca on Lake Maggiore. Riemann's meta-
physical ideas, derived in part from Th. Fechner, are
often bold even to singularity, and by times are merely
fantastic, but they detract in no way from his religious
fervour. His death, as related in the biographical sketch
prefixed to his collected works, gives sufficient token
of this. "His wife was saying to him the Our Father,
he was no longer able to speak: but at the words
Forgive us our trespasses, he raised his eyes aloft:
she felt his hands grow cold within her own: and after
two or three gasps his noble heart had ceased to beat.



d'elite ... lui avaient assure tout d'abord. . . . Toutefois, dans son
domaine special, M. Puiseux aimait a s'effacer devant Pierre Olivaint,
alors eleve de la section des lettres, entre depuis dans la Compagnie
de Jesus et tombe, en 1871, victime de la Commune. . . . For the
religious aspect of the school and the group of Catholic students.
Cf. Ch. Clair, Pierre Olivaint, pretre de la Compagnie de Jesus, Paris
1878, 2T.



62 II. MATHEMATICS.

The pious habits which he had learned in his childhood
remained with him all his life, and he served God
loyally, if not always after the orthodox forms. Daily
self-examination in the presence of God he regarded,
to use his own expression, as one of the elements of
religion." 1

On Jan. 14 th 1901 there died at Paris " the last of the
great mathematicians of the second half of the nineteenth
century", a grey-haired veteran of seventy-eight, whose
eminence in the history of science was proclaimed in
the highest terms of praise by the highest authorities.
The first of these eulogists was Fouque, President of
the Academy of Sciences of Paris.

"Hermite", he writes, "doyen of our Geometrical section,
and member of the Academy since 1856, was one of our
special glories. All who sit here as geometricians think it
their chief honour to have been pupils of his, all are pene-
trated with gratitude for the generous aid which he has
constantly given them. Wherever science is cultivated, the
name of Hermite is spoken with veneration." 2

To the praise of his scientific genius there was added
recognition of his lovable character.

"With Hermite", wrote La Nature, "there disappears one
of the unsullied glories of French science. Hermite not
only stood among the masters ,of mathematics of the last



1 Bernhard R i e m a n n s Gesammelte mathematische Werke und
wissenschaftlicher Nachlass. Herausgeg. unter Mitwirkung von Richard
Dedekind von Heinr. Weber. Zweite Aufl., bearbeitet von Heinr.
Weber, Leipzig 1892, 557.

2 Comptes rendus hebdomadaires des seances de 1'Academie des
sciences CXXXII, Paris 1901, 49. We quote the following passages
and Notices from the Essay in the Revue des questions scientifiques
XLIX, Louvain 1901, 353 396. Cf. Naturwissenschaftliche Rund-
schau XV, Braunschweig 1901, 333 348.



HERMITE. 63

century; his private life, also, was a model. No one ever
pushed unselfish devotion to science farther than he did.

"He leaves to history an imperishable name, and to all
those who had the happiness to know him, the memory of
a man as great of heart as of intellect. A convinced spiri-
tualist he believed that the soul would one day be crowned
with a complete revelation of those mathematical harmonies
of which only the reflex is accessible to human nature." 1

Not very long before, on Dec. 24 th 1892, France had
celebrated with the greatest splendour Hermite's se-
ventieth birthday. The Minister of Education presided
at the Jubilee Assembly, the most eminent French ma-
thematicians were present, and nearly every learned
society offered an address. The King of Sweden de-
corated Hermite with an order, hitherto conferred on
no one in France except the President of the Republic
and Pasteur. And all these honours were well deserved,
for, as Poincare said in his discourses, Hermite had for



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