fifty years laboured incessantly in all the most difficult
departments of mathematics and had enriched mathe-
matical analysis, Algebra, and the Theory of Numbers
with "inestimable conquests" 2 . When only twenty years
1 Avec M. Hermite disparait une des gloires les plus pures qui
aient jamais illustre la science frangaise. M. Hermite ne fut pas
seulement un des plus grands mathematiciens du dernier siecle, sa vie
fut un exemple, personne n'a pousse plus loin 1'amour desinteresse
de la science etc. (Painleve in La Nature XXXIX, 2 fevr. 1901,
144 146). II laisse pour 1'histoire un nom imperissable et pour
tous ceux qui ont eu le bonheur de 1'approcher le souvenir d'un
homme aussi grand par le coeur que par 1'intelligence. Spiritualiste
convaincu, il pensait que Tame aurait un jour la revelation complete
de ces harmonies mathematiques dont le reflet seul est accessible
a 1'intelligence humaine (Revue des sciences pures et appliquees XII,
15 fevr. 1901, 109 110).
2 Cf. Les fetes jubilaires des MM. Hermite et Pasteur, in Revue
des quest, scient. XXXIII, Louvain 1893, 2 35 2 47-
64 II. MATHEMATICS.
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of age he had addressed to Jacob! an essay of a very
few pages which placed him at one bound on a level
with the first mathematicians in Europe. After the death
of Cauchy, Gauss, Jacobi and Dirichlet, he was uni-
versally regarded as the leader of his science. At the
mathematical Congresses at Zurich in 1897, anc * at Paris
in 1900, he was elected, with acclamation, Honorary
Of his discoveries we may mention one, which will be
understood even by those who have no technical know-
ledge of mathematics. It was Hermite who in 1873 de-
monstrated for the first time that the quantity e is trans-
cendent i. e. it cannot be the root of an algebraic equation
with integral co-efficients. Hermite's line of proof was in
1 88 1 extended by Lindemann to the quantity -, and by
means of it an interesting fact was established. Inas-
much as - cannot be the root of a quadratic equation
it follows that it cannot be determined with rule and com-
pass, in other words, that the "squaring of the circle" is
impossible. That i: does not admit of determination with
other instruments does not of course follow ; in point of
fact it can be determined with the help of the integraph,
invented in 1880 by the Russian Abakanowicz l . An old
problem was thus at last solved: it had taken two thousand
years, and the expenditure of a vast deal of pains and pene-
tration to discover that the attempt so often renewed was
a priori impossible. Professor F. Klein may justly say that
this discovery, suggested and made possible by Hermite,
marks an epoch in the history of mathematical science 2 .
Painleve's reference to Hermite's "spiritualism" will
be more clearly understood if it is stated that the great
mathematician was simply a member of the Catholic
1 Cf. J. G. Hag en S. J. , Synopsis der hoheren Mathematik III
Berlin 1900, 84.
2 The Evanston Colloquium 1893, 5 2 -
BALDASSARE BONCOMPAGNI LUDOVISI. 65
Church. In his younger days his religious views had
undergone certain variations. But "thanks to the charity
of the Sisters of Mercy who nursed him through a
severe illness, thanks also without doubt to the influence
of Cauchy" he returned to the Faith, and, "from the
day in 1856 on which he found his road to Damascus,
the fervour of his religion never diminished 1 ".
"From 1877 on", writes the Catholic Review from
which we borrow these notes, "he took a lively interest
in our review, and constantly congratulated our late-
lamented general secretary and his collaborators on their
articles, which he found so solid and so appropriate to
the intellectual needs of the day". . . . Fifteen years
later he expressed himself to the same effect, and added
that he had the happiness to share the Faith professed
by the writers of the Review 2 . To the Congress of
Catholic Scientists, held at Brussels in 1894, he contri-
buted a paper 3 .
"Hermite", says the celebrated mathematician Emile
Borel, "was deeply attached to the Catholic religion;
it was the stay and the centre of his life. . . . His
opinions and his works were in perfect harmony with
Catholic ideas, and this is certainly no ordinary merit." 4
Highly important contributions to the History of
Mathematics were made by the Roman prince Bal-
dassare Boncompagni Ludovisi (f March 13 th 1894).
1 Revue des quest, scient. XLIX (1901) 364. 2 Ib.
3 Congres Scientifique International des Catholiques VII 5 n.
He also sent contributions to the Papal Academy de" nuovi Lincei III
155 164, and to the Annales of the Societe Scientifique of Brussels I
(1875-1876) II (1877-1878).
4 Laisant et Buhl, Annuaire des Mathematiciens 1901 1902,
Paris 1902, xxr.
Kneller, Christianity. cj
66 II. MATHEMATICS.
"He was", writes a well-qualified judge 1 , "a man of
the most extensive learning. His favourite subject of
study and research was the History of Mathematics.
Guido Bonati, Gerard of Cremona, Plato of Tivoli were,
one may confidently assert, first brought to general
knowledge by the essays devoted to them in the series
of publications for which he was responsible."
It was Boncompagni, too, who by his work on Leo-
nard of Pisa, "the teacher of the three centuries that
came after him", and by the publication of his writings
"evoked and made possible the first true appreciation
of that genius".
"A Review well known to specialists under the name
of the Bulletino BoncompagnF contains many works of
the editor. He often bore the cost of the publication
of the works of other savants. "Enormous were the
sums spent by the prince in this fashion, enormous
were the sums swallowed up by his library which con-
tained 600 MSS. and 18,000 printed works. A prin-
cely fortune, and a mind in the best sense of the word
princely were needed to make such things possible. And
these were not his only benefactions. Whenever Bon-
compagni learned of a promising student, whose deve
lopment was hampered by poverty, he proferred as-
sistance in the most courteous and tactful manner. How
many transcripts of MSS. has he not commissioned
here, there, and everywhere, either in order to put them
1 M. Cantor in the historical and literary department of the
Zeitschrift ftir Mathematik und Physik XXXIX, Leipzig 1894, 201
to 203. ''Alle Arbeiten des Herrn Buoncompagni sind fur jeden, der
dem Studium der Geschichte unserer Wissenschaft seine Zeit und seine
Krafte widmen will, ganz unentbehrlich" (Grunerts Archiv 1856,
Lit. Bericht Nr 105).
CHARLES DUPIN. 67
unselfishly at the disposal of young students, or merely
to give the transcribers a chance of earning something !
And how many bewail in him the death of a benefactor!"
He bore, amongst other charges, the expense of printing
the papers of the Papal Academy.
Only a sudden death prevented Boncompagni from
bequeathing his precious MSS. and books to the Vatican
Library. This alone is enough to show that the Prince
was "a man of both science and faith", who proved
by example that "between scientist and Christian there
is no opposition" *.
To the names mentioned we might add many others.
Charles Dupin (1784 1873) e. g. was during the
first half of the nineteenth century one of the most
eminent and best known scientists in France. Before
he had reached his twentieth year he had already
established several important mathematical theorems,
and both as engineer and as Professor of mathematics
and mechanics he made valuable contributions to every
province of thought that he cultivated 2 . In time, in-
deed, his talent for statistical and economic research
drew him away from Pure Mathematics. He made
a profound study of the political and industrial re-
sources of England and France, and displayed in the
Chamber a commendable zeal for the improvement of
the education and the industrial methods of the country.
1 Cosmos, Paris, 30 avril 1898, 553; cf. 26 mai 1894, 223. Con-
cerning the edifying death of the Prince and his friendship for the
Society of Jesus v. Civ. catt. , Ser. 15, X, Roma 1894, 3^1, and
12 ser. I (1883) 84. For his connection with the Papal Academy,
Etudes XLV, Paris 1888, 134.
2 Jos. Bertrand, Eloges academiques 221. Biographie gene-
rale par Hoefer s. v.
68 II. MATHEMATICS.
When he died full of years in 1873, it was recorded
of him that "his convictions were always sincerely
Christian and Catholic" 1 .
Mention should also be made e. g. of Louis Poinsot
(t l %$9) 2 , Gergonne (f i858) 3 , Michael Chasles
(f i88o) 4 , W. M. Drobisch (f 1896)8 and Philippe
Gilbert (f 1892), Professor at Louvain and author
of widely-used test-books on Higher Mathematics and
Analytical Mechanics, as well of numerous scientific
essays 6 . Amongst those recently deceased we may
instance Eugene Vicaire (f Jan. i8 th 1901) 7 , an en-
gineer who occupied the highest positions in his pro-
fession in France, and laboured with such success in
the province of pure science that he held the pro-
fessorate of Astro-Mechanics in the College de France
from 1883 to 1885, and published works of the first
importance on Astronomy, Solar Physics, and Pure
Mathematics. He was a practical Catholic 8 , and had
the happiness of giving two of his nine children to the
1 Ses convictions furent toujours sincerement chretiennes et calho-
liques. Les Mondes XXX, Paris 1873, J 35-
2 Natur und Offenbarung VI, Munster 1860, 96.
3 Ib. V (1859) 288.
4 Cf. Ph. Gilbert in the Revue des quest, scient. IX (1881)
S 1 7 59- I n concluding this Obituary Notice, he says: "Dieu a
fait a Chasles la grace d'une fin vraiment chretienne. Dans toute la
plenitude de sa volonte et de son intelligence, le grand mathematicien
a regii les consolations que 1'eglise catholiques reserve a ceux qui
meurent dans son sein; puis il s'est endormi confiant et tranquille."
5 Allg. deutsche Biographic XLVIII, 82.
6 Cf. Revue generale LV, Bruxelles, mars 1892, i iv.
7 Revue des quest, scient. XLIX (1901) 420 431.
8 Fermement attache a la foi catholique, il ne s'est jamais ecarte
des directions spirituelles qu'elle lui avait tracees (ib. 423).
DROBISCH. GILBERT. VJCAIRE. GRASSMANN. LAPLACE. 69
Hermann Grassmann (f 1877), Gymnasium professor
at Stettin, is described by Cantor and Leskien as "one
of the most remarkable mathematicians of our times".
At first indeed his works went practically unnoticed.
His "Theory of Extension" put forward in 1844 ideas
on the nature of Geometry which became current many
years later, but it might as well not have been printed.
Two discoveries made by him in Physics met with
no acceptance until they were made anew by Clausius
and Helmholtz. Crushed by this ill-success he turned
to the study of Sanscrit, and although he entered this
province so late he nevertheless made in it important
conquests. This notable man was a loyal Protestant;
he was much interested in Foreign Missions, and left
behind him a work which bears the title "On the Decay
of Belief" 1 .
But the names enumerated above are sufficient for our
purpose. Instead, therefore, of extending the list we shall
devote a page or two to a renowned scientist whose autho-
rity is very frequently invoked to show the irreligious
character not only of mathematicians, but of mathematics
and exact research in general.
No one denies the invaluable contributions made by
Pierre Simon Laplace (f 1827) to the theory of the motion
of the heavenly bodies, as also to many other branches of
Physics and Mathematics. He was commonly called the
French Newton, and was brought into comparison with the
great Englishman in nearly every one of the discourses
pronounced over his grave.
Nowadays it is a commonplace of scepticism to invoke the
authority of Laplace; and an anecdote which is told of him is
supposed to afford proof of his unbelief. When he presented
1 Allgemeine deutsche Biographic IX 595 598. Allgemeine Zeitung,
Augsburg 1877, Nr. 291, Beil. p. 4371.
70 II. MATHEMATICS.
one of his works to Napoleon the latter is reported to have
said: "Newton in his work speaks of God. I have gone
through yours, but find no mention of God." To which
Laplace is said to have replied: "Citizen First Consul, I
found no need for that hypothesis." So runs the anecdote,
and from it many writers eagerly draw the conclusion:
Laplace then has declared that the existence of God is a
mere hypothesis. And so, according to the greatest astro-
nomer of modern times, the existence of the world affords
no proof of the existence of God.
This anecdote had begun to circulate during Laplace's
life-time. When he learned shortly before his death, that
it was to appear in a sketch of his life in an Encyclopedia
of Biography he commissioned Arago to demand that it
should be excised by the editor. This fact was learned
from Arago's own mouth by H. Faye * : it shows that in
any event it was against Laplace's will that he was repre-
sented as an atheist. As for the story itself, its truth is
established by no sufficient evidence, and it is a priori im-
probable that the accommodating Laplace would have spoken
in such a fashion to the all-powerful ruler of France. For
Napoleon was well known to be no friend of atheism, and
to have administered a sharp reproof to the astronomer
Lalande because of his profession of it 2 .
But even supposing that Laplace did use the words, it
does not at all follow that he wished to characterise the
existence of God as an unsupported hypothesis. In the
1 Sur 1'origine du Monde 3 , Paris 1896, 131. Cf. p. 130 132,
where the alleged saying of Laplace is dealt with. Cf. J. dejoannis
in Etudes LXXI, Paris 1897, 541 f.
2 Moreover we may remark in passing that Lalande did not sin-
cerely believe in Atheism. Abbe Emery, who had opportunities of
speaking to him, said to a priest, a friend of his: "M. de Lalande
n'est pas plus athee que vous et moi." To Emery he had expressed
the wish to receive the last sacraments from his hand. The ful-
filment of this wish was prevented by Lalande's friends. Vie de
M. Emery II, Paris 1862, 39. E. Meric, Hist, de M. Emery II,
Paris 1885, 210.
PIERRE SIMON LAPLACE. Jl
anecdote, he contrasts his theory with that of Newton : " it
is necessary then only to bear in mind the points on which
he was at variance with the great Englishman in order to
grasp the sense of the epigram. Newton had at the sight of
so many planets and worlds, circling perpetually round with
reciprocal influence and disturbance, given way to the fear
that these countless, intricate movements must result at last
in inextricable confusion, and that the intervention of God
from time to time was needed to obviate this confusion.
But one of the greatest achievements of Laplace was pre-
cisely his proof that such intervention is unnecessary. He
showed by mathematical considerations, afterwards completed
and extended by Leverrier, that such confusion can never
occur. How intricate soever the paths of .the planets, how-
ever numerous and continual the reciprocal disturbances, all
these disturbances must in the course of time re-adjust
themselves. If Laplace, then, did in fact reply to the First
Consul in the manner alleged, in all probability he had
before his mind merely the advance which he had made in
the Theory of Planetary Motion, as compared with Newton.
The hypothesis which he dismissed as unnecessary would
be, in this interpretation, not the existence of God but that
intervention of God in the economy of the planetary system
which Newton ' regarded as indispensable l . We find in
Laplace's work another criticism of Newton, expressed in
another fashion. The disposition of the planets and satellites
according to number, size, and relative distance could not
in Newton's opinion be derived from mechanical causes, but
1 Cf. v. Madlers Reden und Abhandlungen iiber Gegenstande
der Himmelskunde, Berlin 1870, 334: Laplace's answer "ist voll-
koinmen richtig; denn auch wir bedurften und bediirfen der Hypo-
these von einem einhelfenden, nachbessernden, korrigierenden Gotte
nicht und werden ihrer nie bediirfen. Das Universum ist ein Uhr-
werk, aber kein solches, wo man den Verfertiger zu Hilfe ruft, weil
es nicht mehr recht gehen will. Unser Gott thront iiber Zeit und
Ewigkeit, und bei ihm ist kein Wechsel, und je tiefer wir in seinen
Werken forschen , desto mehr werden wir in dieser Ansicht be-
72 II. MATHEMATICS.
must be regarded as the direct work of Divine Omnipotence.
But Laplace has, by means of his celebrated theory of the
development of the solar system from the rotating fiery
nebula, exhibited it as highly probable that the disposition
of the planets and satellites can be explained by natural
causes, and in this regard he might also have allowed him-
self to criticise Newton. This does not necessarily mean
that he denied the existence of God. In fact the whole
duty of science is to explain the phenomena of nature by
created, secondary causes *. The acceptance of the system
of Laplace is in no way derogatory to the Wisdom and
Omnipotence of the Creator. It is in no wise easier to
create the egg and the acorn out of which the chicken
and the oak are .in due course to develop , than to create
immediately on the spot the chicken or the oak. And
in precisely the same way it is a no lesser manifestation
of Divine Omnipotence to create the nebula, and to en-
dow it with the capacity of developing into the planetary
system than it would be to call the latter at once into
That Laplace is in point of fact to be understood in this
sense is shown by a passage in his "Exposition du systeme
du monde" 2 . He there quotes the passage in which Newton
ascribes the orderly arrangement of the planetary system to
1 "Gott ist nicht das nachste und unmittelbare Prinzip der Natur-
erscheinungen. Er ist auch nicht direkt Gegenstand der Naturwissen-
schaften . . . und es ist, von der frivolen Deutung abgesehen , ganz
berechtigt, wenn Laplace sagt : ich habe Himmel und Erde durch-
forscht und keinen Gott gefunden, wie es berechtigt ist, wenn Vogt
erklart , es sei ihm die Seele und Lebenskraft noch nie unter der
Lupe begegnet" (P. L. Haffner, Das Ignoramus und Ignorabimus
der neueren Naturforschung, in Sammlung zeitgemasser Broschiiren,
Frankfurt-Luzern 1887, 222). Likewise J. Reinke, Die Welt als
Tat 3 , Berlin 1903, 476: "In Laplaces Werke brauchte Gott so wenig
vorzukommen wie im Exerzierreglement. Hatte ich ein Handbuch
der Physiologic zu schreiben, so wiirde das Wort Gott darin gleich-
2 Livre 5, chap. 6, 6 e ed., Bruxelles 1827, 522.
PIERRE SIMON LAPLACE. 73
the immediate, creative act of God, and, to explain its immunity
from confusion, has recourse to the recurrent intervention
of the same creative power. In criticism of this theory
Laplace says: "But may not this disposition of the planets
be itself an effect of the laws of Motion: and may not the
Supreme Intelligence to whose intervention Newton had
recourse, have made this orderly disposition dependent on
a phenomenon of a more general character?" The neces-
sity of a supplementary intervention of God in His own
Creation he repels with the words: "Leibniz, in his contro-
versy with Newton on the discovery of the infinitesimal
calculus, criticised sharply the theory of a Divine intervention
as a corrective of the disturbances of the solar system.
'To suppose anything of the kind', he said, 'is to exhibit
very narrow ideas of the wisdom and power of God.
Newton replied with a criticism just as sharp of the Pre-
Established Harmony of Leibniz which he characterised as
a perpetual miracle. Posterity has not accepted these vain
hypotheses, but it has rendered the most ample justice
to the mathematical achievements of these two men of
It is not difficult to discern in these passages the idea
which lies at the root of the anecdote in question. But it
will be observed that this idea has in it no leaven of
Atheism. Laplace speaks in both places of "empty hypo-
theses". But what is it that he designates by these words?
Obviously not the existence of God, but the Theory of
Pre-Established Harmony, and the assumption that an inter-
vention of God is necessary from time to time in order
to supply the imperfections of the natural order.
On the other hand it is admitted that Laplace cannot be
held up as a model of loyalty to religion. In his writings,
e. g. in the Essai philosophique sur la probability there are
to be found many turns of thought which show the influence
of the philosophy of the eighteenth century. But there are
two facts which cannot be disputed. In the first place the
great mathematician was never in his own estimate a materialist.
In proof of this we have the evidence of one who stood
on the most intimate terms with Laplace, J. B. Dumas the
74 HI. ASTRONOMY.
chemist 1 . And if during his life he made only too many
concessions to the dominant spirit of the time, this is only
another example of that pliancy of character which even
Laplace's greatest admirers constantly deplored. When he
came to die and had nothing further to hope for from the
world, he sent for a priest and devoted himself to settling
his account with heaven 2 .
A religious of the Catholic Church stands by a two-
fold right at the head of the Astronomy of the 19 th
Century, in virtue both of a brilliant discovery and of
the enterprise which led up to it.
1 Discours et Eloges Academiques II 255 : Laplace "fournit aux ma-
terialistes leurs plus specieux arguments, sans partager leurs con-
2 Nr. 66, March 7 th 1827, of La Quotidienne contains the follow-
ng: "Paris, 6 mars. M. le marquis de Laplace, pair de France, membre
de 1'Institut, auteur de la Mecanique Celeste et de plusieurs autres
ouvrages qui Font fait placer parmi les plus grands geometres de ces
derniers temps, est mort hier dans son hotel Rue du Bac, entre les
bras de ses deux pasteurs, M. le cure des Missions Etrangeres et
M. le cure d'Arceuil, qu'il avait fait appeler pour en recevoir les
derniers secours de la religion. Nous aurons a publier une notice
sur la vie de ce savant celebre ; mais nous devons des ce moment
faire remarquer ce que sa mort a presente d'edifiant a sa famille, a
ses amis et a ses admirateurs. C'est un contraste que nous aimons
a opposer au recit de morts scandaleuses qui font la joie des ennemis
de la religion. Ses obseques auront lieu demain mercredi, 7, en 1'eglise
des Missions Etrangeres. . . . The same information is found in the
paper, L'ami de la Religion et du Roi LI, Paris 1827, 107 126
(cf. J. de Joannis in Etudes LXXI 655). M. Marie (Hist, des
sciences math, et phys. X, Paris 1887, 70) calls the wavering Laplace
"reactionnaire et ultra-royaliste", assumes him to "afficher des sen-
timents religieux outres qu'il ne partageait pas" and ascribes to him
"Palinodes", which however would not have been able to retard the
progress for which his Cosmogony had cleared the way.
GIUSEPPE PIAZZI. 75
"The first day of the century", says the celebrated astro-
nomer Frederick William Bess el 1 , "was marked by a
brilliant discovery: Piazzi of Palermo on the first day of
January 1801 found a new planet, 'Ceres'. His discovery was
a by-product of a great and admirable undertaking, the de-
termination, namely, by a long series of observations, of the
positions of some 7000 fixed stars." Bessel proceeds to
explain the significance for astronomical science of this
determination of the latitude and longitude of so many
stars with the greatest possible accuracy, and recounts the
laborious efforts of Tycho Brahe and his successors to
arrive at the same result. "Piazzi", he continues, "had
striven strenuously to secure the erection of an observatory
at Palermo, and to equip it with splendid instruments, the
work of the never-to-be-forgotten Ramsden; and when he
had succeeded in this he stepped at once to the head of
astronomical science. He published in 1803 after incal-
culable labour a catalogue of the positions of some 7 ooo stars,
and so resolute was his determination to secure the most
accurate results attainable with his instruments that he repeat-
ed all his observations, and in 1814 was able to publish a
second and much improved edition of his catalogue. Here
was in truth a worthy beginning of the century. The appe-
tite for thorough observation was roused from the slumber
in which it had lain since the death of Bradley."
At first sight the figures mentioned by Bessel may
not seem very formidable. Some may not consider it
a colossal undertaking to direct a telescope on one