Brill’s Companion to the
Reception of Pythagoras and
Pythagoreanism in the Middle Ages
and the Renaissance
Edited by
Irene Caiazzo
Constantinos Macris
Aurélien Robert
LEIDEN | BOSTON
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Contents
Acknowledgements ix
List of Illustrations and Tables x
Notes on the Contributors xi
Introduction: Pythagoras, from Late Antiquity to Early Modernity:
A Multicultural Approach 1
Irene Caiazzo, Constantinos Macris and Aurélien Robert
part 1
Pythagorean Number Theory and the Quadrivium
1 Pythagoras and the Quadrivium from Late Antiquity to the
Middle Ages 47
Cecilia Panti
2 Music and the Pythagorean Tradition from Late Antiquity to the
Early Middle Ages 82
Andrew Hicks
3 Nicomachean Number Theory in Arabic and Persian
Scholarly Literature 111
Sonja Brentjes
4 The Tribulations of the Introduction to Arithmetic from Greek to Hebrew
Via Syriac and Arabic: Nicomachus of Gerasa, Ḥabib Ibn Bahrīz,
al-Kindī, and Qalonymos ben Qalonymos 141
Gad Freudenthal
5 Medieval Jewish Pythagoreanism: Remarks on Maimonides and on
Sefer Melakhim 171
Tzvi Langermann
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vi Contents
part 2
Pythagorean Way(s) of Life, East and West
6 Popular Pythagoreanism in the Arabic Tradition: Between Biography
and Gnomology 193
Anna Izdebska
7 Pythagoras’ Ethics and the Pythagorean Way of Life in the
Middle Ages 229
Aurélien Robert
Part 3
Theology, Metaphysics and the Soul
8 Pythagoras’ Philosophy of Unity as a Precursor of Islamic Monotheism:
Pseudo-Ammonius and Related Sources 277
Daniel De Smet
9 The “Brethren of Purity” and the Pythagorean Tradition 296
Carmela Ba���oni
10 “Pythagoras’ Mistake”: The Transmigration of Souls in the Latin
Middle Ages and Beyond 322
Irene Caiazzo
11 Pythagoras Latinus: Aquinas’ Interpretation of Pythagoreanism in His
Aristotelian Commentaries 350
Marta Borgo and Iacopo Costa
12 Latin Christian Neopythagorean Theology: A Speculative Summa 373
David Albertson
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Contents vii
Part 4
New Trends in Early Modern Pythagoreanism
13 Pythagoras and Pythagoreanism in the Renaissance:
Philosophical and Religious Itineraries from Pico to Brucker 417
Denis J.-J. Robichaud
14 Pythagorean Number Mysticism in the Renaissance: An Overview 457
Jean-Pierre Brach
Index of Names 489
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chapter 14
Pythagorean Number Mysticism in the
Renaissance. An Overview
Jean-Pierre Brach
Frequently considered, in earlier periods of Western culture, as a symbol or,
at the very least, as an almost legendary individual,1 Pythagoras is never-
theless perceived during the Renaissance as retaining more of an historical
consistency, and the reality of his existence remains generally unquestioned,
if somewhat imprecise. Among other exponents of the supposed prisca
theologia,2 he stands as a typical example of a single individual retaining
the characteristics of a prophet, holy man, seeker of wisdom, political adviser,
scientist, musician and philosopher alike, all qualities which play a central role
in the culturally widened humanistic de��nitions of a “Pythagorean” philoso-
phy. One must of course keep in mind that philosophy is here considered as
being essentially of a revelatory nature, and much akin to a divine illumina-
tion, an empowerment which some of the Early Modern Humanists frequently
bestowed on antique thinkers and religious ��gures,3 endowing them with a
prophetic status almost equal to that hitherto reserved by Christianity for the
Jewish Scriptures.
As recently outlined by Christiane L. Joost-Gaugier, the in��uence of (neo)
Pythagoreanism in the Renaissance is both manifold and widespread.4 It
covers most areas in the realms of science and the arts,5 but is nevertheless
1 Something he already was, for the most part, in Plato’s or Aristotle’s time; Riedweg 2008, 42�f.;
Macris 2018, 810–818 (with bibliography).
2 Gentile 2012.
3 They were probably also in��uenced by the “divine” character commonly attributed to
Pythagoras by his Hellenistic bio/hagiographers. Macris 2003 and 2006.
4 Allen 2014; Joost-Gaugier 2009 (this study is, however, to be consulted with extreme caution).
5 Perillié 2005. In this respect one must also recall the important role played by mathemat-
ics (in general) in the encyclopedic reorganization of knowledge launched by some of the
��rst Humanists, as exempli��ed – among others – by G. Valla’s (1447–1500) De expetendis et
fugiendis rebus (Venice 1501), which includes a section on arithmology: see Tucci 2008 (I am
indebted to M. Ghione for this reference).
© Koninklijke Brill NV, Leiden, 2022 | doi:10.1163/9789004499461_016
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458 Brach
more speci��cally associated with theories about the transmigration of the soul
and the theo-cosmological meaning of numbers.6
“Pythagorean numbers” is one of the favorite and most frequent Early
Modern designations of what is often termed nowadays “number mysticism,”7
“arithmology,”8 sometimes “arithmosophy.” Widespread in the Middle Ages,
in the wake of Augustine and many other Church Fathers,9 the interest in
the qualitative side of mathematics is at a relatively low ebb during the scho-
lastic period, due to the then dominance of Aristotelian doctrines in Latin the-
ology, since these deny number any sort of natural e���cacy, besides being a
mere reckoning tool.10
Given this situation, the Renaissance or Early Modern period (15th–17th
centuries) inherits for the most part the practice of number symbolism as a
hermeneutical tool, mainly concerned with the interpretation of Scripture and
aiming at shedding light on the network of spiritual analogies and correspond-
ences assumed to be linking both Testaments.11
However, the persistent in��uence of Boethius (ca 480–524), who conferred
its de��nitive philosophical luster in the Latin West to the doctrine of the theo-
logical transpositions of number,12 and that of Nicholas of Cusa (1401–1464),
who established mathematics as constituting the most appropriate basis and
symbols for the knowledge of the divine sphere,13 must not be forgotten or
understated, the more so since they are both heavily dependent on Neoplatonic
(and Neopythagorean) sources.14
6 Riedweg 2008, 128–133, stressing the role played by Platonic reinterpretations in the inter-
est displayed by later periods in “Pythagorean” philosophy.
7 The barbaric term “numerology” designates contemporary pseudo-divinatory techniques
linking numbers to names, the study of which lies outside our topic. For an e�fective criti-
cism of this trend, see Bell 1933.
8 Delatte 1915, 139–140; Zhmud 2013, 2016, 2019 and 2020.
9 Kalvesmaki 2013; Brach 2013.
10 Aristotle, Metaphysics M.6, 1080b 16, for example. Porro 2018.
11 Brach 2015.
12 Masi 1983. As is well known, Boethius’ De institutione arithmetica is in fact an adaptation
of (and philosophical commentary upon) a Neopythagorean textbook (end of 2nd cen-
tury CE) by Nicomachus of Gerasa (see Nicomachus 1926).
13 Rusconi 2011.
14 Counet 2000.
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Pythagorean Number Mysticism in the Renaissance 459
1 Coming into One’s Pythagorean Inheritance
Heavily indebted to his reading of Plato and of Neoplatonic philosophers,
whose works he famously translated into Latin,15 Marsilio Ficino’s (1433–
1499) Pythagoreanism is as much about religion as it is about philosophy.
In presenting it in this guise, Ficino is being faithful to his image of the
Samian as a priscus theologus, as well as – very likely – to his own desire of pro-
jecting himself as the last-in-line heir to such ancient doctrines and, accord-
ingly, as their rightful exponent in contemporary Florentine learned circles.16
The main avenues of this so-called Pythagorean doctrine are numbers on the
one hand, “psychology” on the other hand. Psychology revolves here around
the questions of the transmigration of the soul, of its immortality and of its
puri��cation prior to its ascension towards the divine, bearing consequently on
practical religion and ethics as well.17
Number is supposedly at the root of a science of universal realities, includ-
ing immaterial ones, and acts as both a cosmogonic and an ontologically pro-
ductive principle.18 Accordingly, Ficino writes:
There are two ways, especially, to understand the truth of divine things,
namely, mathematics and the purity of the soul.19
On the whole, Ficino’s interest in number symbolism hasn’t yet been made
the object of the overall study it certainly deserves,20 perhaps on account of
the fact that the relevant references on the topic, far from being systematically
arranged, are mostly scattered through his lengthy and numerous treatises and
commentaries.
It is worth noting from the outset that, paradoxically, neither Ficino21 nor
any of the very ��rst authors who have contributed to the rehabilitation of
15 Iamblichus ��gures prominently among these philosophers, as the author of one of
Pythagoras’ biographies alluded to above and of several other treatises on Pythagoreanism
and mathematics; Iamblichus 2006; O’Meara 1989 and 2014; Bechtle and O’Meara 2000;
Macris 2009.
16 Celenza 1999, 705–706; Vasoli 2005.
17 Important to the moral and mystical preparation or puri��cation of the soul are the
famous symbola, familiar to the Christian tradition since Antiquity and much read in the
Renaissance; see Celenza 1999, 693; 2001a, 4–34 and 2002; Robinson 2013.
18 Celenza 1999, 702–705.
19 Quoted by Celenza 1999, 694, n. 88.
20 A partial exception to this is the book by Allen 1994.
21 Ficino has also shown a penchant towards geometrical symbolism: Allen 1999; Toussaint
2000.
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460 Brach
number symbolism within early Renaissance culture wrote a treatise specif-
ically dedicated to this topic. There are several reasons for this, the main one
being probably that numbers and their qualitative aspects, both ontological and
cognitive, were perceived as integral parts of a more general cosmo-theological
worldview, based on correspondences, correlative thinking and philosophical
syncretism.
As we shall see, a systematic treatment of the subject of number mysti-
cism belongs to a relatively later phase of the evolution of Western “esoteric”
literature.
2 “That Which Is Old and New”: Number, Magic and Kabbalah
As early as 1486, in his famous, so-called Oration on the Dignity of Man,22 Pico
della Mirandola (1463–1494) claimed to have somehow rediscovered number
symbolism as a “new way of philosophizing by numbers,” and announced his
intention to restore it as a speculative current à part entière, on a par with
Neoplatonism, magic and kabbalah. Consequently, arithmology ceases to be
mainly a hermeneutical tool for the interpretation of passages from the Bible,
to become – to a certain extent – an almost autonomous “art of numbers”
capable of addressing (and answering) problems of cosmology, morals, meta-
physics or theology.23 In his Conclusiones (or 900 Theses; 1486) and Apology
(1487), Pico introduces the concept of “formal number,” implicating that math-
ematical entities – in typical Neoplatonic fashion – possess a speci��c ontolog-
ical status, corresponding to a particular (rational) cognitive mode. Pertaining
to an intermediary level of reality, situated above the material plane, the
“formal numbers” are endowed with the faculty of bestowing “a power and an
e���cacy” on natural things which belong to the – less “formal,” therefore less
“actual” – physical degree of existence. In this manner, Pico relies much less
on hackneyed numerical analogies than on the close interaction of the cogni-
tive and ontological properties of arithmetic. Number is thus assimilated to a
“formal,” secondary cause, active on the material world.24
The idea according to which the more “formal” is endowed with a higher,
more powerful degree of being than the material, is of course Pico’s version of
a classic Neoplatonic tenet which holds that immaterial entities are actually
22 Copenhaver 2016.
23 See his 85 “mathematical conclusions” in Farmer 1998, 466–485 (especially the fourth
one, pp. 466–467).
24 Brach 2016b, 412�f.
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Pythagorean Number Mysticism in the Renaissance 461
situated higher up the ontological scale and are thus, paradoxically, correlated
to a denser level of existence – and of intellectual capture – than that ordinar-
ily occupied or entailed by physical realities.
Among other things, numbers are therefore perceived as capable of func-
tioning on di�ferent planes, thus permitting their actual use in di�ferent disci-
plines such as natural philosophy, magic or kabbalah.
Since these disciplines, among a series of others, are presented by Pico (in
his Conclusiones, essentially) as displayed according to an ascending hierar-
chical order, albeit closely articulated to one another,25 it follows that material
(or purely quantitative) number – as a cognitive tool in natural philosophy –
must take a back seat to its formal (or Pythagorean) counterpart26 and further,
when dealing with Jewish theosophical literature, to its even higher kabbalistic
analogue, the ten se��rot.27 In the same way, kabbalah – as a supra-discursive
practice – stands above magic and natural philosophy, and leads towards the
union with the Active Intellect by transforming man into an angel – a theory
which is at the root of the later, widespread assimilation of kabbalah with
angelic magic, popularized by the likes of Jean Thenaud (ca 1480–1542) and
Heinrich-Cornelius Agrippa (1486–1535).28
Even though he does not make use of the expression “formal number”
as such, Johann Reuchlin (1455–1522) is familiar with Pico’s (and Ficino’s)
theories.29 He nevertheless takes the problem from a di�ferent angle, by ��rst
stating the identity of Pythagoreanism and of the kabbalah, and furthermore
calling the former a derivation from the latter.30 Although an apocryphal
antiquity was frequently ascribed to Jewish kabbalah by its ��rst Christian
interpreters, Reuchlin’s historical twist is probably also intended to de��ect
an eventual charge of judaizing, coupled to a tendency to present kabbalistic
materials as a “symbolic philosophy,” akin therefore to the method supposedly
lying at the core of Pythagorean teachings.31 As Pico before him, Reuchlin
25 Farmer 1998, 495 (“Magical Conclusion n° 4”) and 499 (“Magical Conclusion n° 15”); Pico
della Mirandola 1572, V, 170; Fornaciari 2010.
26 Farmer 1998, 465 (“Mathematical Conclusion n° 5”) and 469 (“Mathematical Conclusion
n° 6”). Pico later abandoned this Pythagorean outlook, as shown by Valcke 1985.
27 Wirszubski 1989 holds the opinion that “formal number” is for Pico merely synonymous
with se��ra, the respective occurrences of both expressions simply varying with the con-
text, according to him; contra, see Buzzetta 2019, 94–104.
28 In book III of his De occulta philosophia libri tres (Heinrich-Cornelius Agrippa 1992 [ed.
V. Perrone Compagni], 402�f.); Brach 2016a. On J. Thenaud, Fabre and Polizzi 2020.
29 Zika 1998, 171–176 (and passim); Leinkauf 1999.
30 These assertions are found in the introduction to his famous 1517 De arte cabalistica
(Johann Reuchlin 1993); Zika 1998, 144–154.
31 Celenza 2001; Idel 2014; Schmidt-Biggemann 2016.
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462 Brach
was conscious of the fact that Hebrew letters possessed numerical values, thus
turning words and, above all, divine or angelic names into proper numbers.32
An example of this is the importance assigned to the quaternary, considered
in its expression either by the “divine tetractys”33 of the Pythagoreans or by
the Tetragrammaton, the most sacred Biblical name of God, composed of four
letters.34 In a similar way, the ten se��rot were also described by him as both
divine aspects or attributes and intelligible numbers whose essence is derived
from that of the divine intellect. Here again, numbers are presented as inter-
mediary terms between natural and divine realities, simultaneously separate
(like divine things) and inseparable (like natural objects) from matter and,
thus, enabling the human intellect to transition smoothly from one plane to
the other. From the conjunction of the primordial Unity and the in��nite Dyad
(or Binary), numbers “��ow” according to a process of emanation and consti-
tute, with their subsequent production of the tetractys and of the Decad, a
progression which, through dots, lines, plane ��gures, solid ��gures and physical,
three-dimensional bodies, ��nally gives birth to the whole cosmos, down to its
basic natural constituents.
3 The French Connection: Pythagoras, from Natural Magic to
Christian Mysticism
Initially in��uenced – like Reuchlin – by the Florentine authors35 and obvi-
ously borne by the growth of the printing industry, a “French school” of
arithmology followed suit and popularized the topic of both numerical and
geometrical symbolism within learned circles, from the early 16th century
onwards.
This led to the elaboration of various inquiries into mathematical analogies,
as well as to a corresponding number of sub-genres within the relevant litera-
ture, represented by books which in some cases have later become famous. In
32 In this manner, numbers are also associated with the speci��c kind of Christian theurgy
previously adressed by Reuchlin in his 1494 De Verbo miri��co (On the Wonder-Working
Word); Roling 1999.
33 Riedweg 2008, 80–89; the tetractys originally designates a sacred oath formula including
the ��rst four numbers; the word as such means “fourthness.”
34 Johann Reuchlin 1993, passim.
35 J. Lefèvre d’Etaples traveled to Italy for the ��rst time during the Winter of 1491–1492 and
met, among others, Ficino and Pico. Like Pico, he distanced himself rapidly enough from
Ficino’s involvement with magic and from the use of kabbalah, to turn towards Christian
mysticism, under the combined in��uences of N. of Cusa and [Ps.-]Denys the Areopagite;
see J.-M. Mandosio in Lefèvre d’Etaples 2018, VII–LVII.
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Pythagorean Number Mysticism in the Renaissance 463
this regard, one must be aware that the qualitative aspects of number are con-
sidered, by our set of writers, as essential to the study of its arithmetical prop-
erties, in proper “Pythagorean” (and Neoplatonic) fashion. This underlines that
the philosophical or religious meanings ascribed to numerical entities were
actually believed to be the result of certain formal characteristics, which rep-
resent the transposition of their respective quantitative values on subtler or
immaterial planes of reality, thereby illustrating the indissoluble link between
the two faces of number: contemplative and scienti��c.
It is an essentially speculative approach to mathematics that was initiated
by Jacques Lefèvre d’Etaples (?1460–1536). Lefèvre himself dedicated Book II
of his early and hitherto unpublished De magia naturali (written in 1494) to the
practical role supposedly played by numbers in natural magic.36 As under-
lined by J.-M. Mandosio, his magic is essentially of an astral kind,37 and num-
bers are at the root of celestial in��uences on the terrestrial world.
Assimilated by Lefèvre to “ideas,” numbers constitute the source of the
living “chains” linking the di�ferent levels of existence and manifesting the
network of correspondences between sublunar and celestial worlds (and
creatures). Here again, numerical entities exhibit both an ontological and a
cognitive aspect, since they allow us an intellectual grasp of (and supposed
magical mastery over) the interplay of in��uences which maintain the life of
the whole universe, while at the same time being (qua “ideas”) the true ratio-
nale behind those in��uences and their transmission, from beyond the heav-
enly spheres. To this downward progression corresponds analogically (and
in typical Neoplatonic fashion) an upward one, the ascensio mentis along the
scala numerorum, eventually identi��ed with the celestial spheres and angelic
hierarchies, a testimonial, for the author, to the a���nities between “ideas” and
angels, that is, between Lefèvre’s “Pythagorean philosophy” and Christian
theology.38 With the implication, moreover, of numbers as they appear in the
constitution of divine names,39 Pythagoreanism and theology are henceforth
con��ated, along with magic, in a peculiar form of Christian kabbalah underlin-
ing the power of divine names (and, therefore, of numbers) in the production
of wonders and miracles – natural and otherwise –, ultimately culminating in
the paramount name of Jesus, in accordance with Reuchlin’s (and Cusa’s) early
views on the “wonder-working Name.”40
36 Mandosio 2013, 37–79.
37 Ibid., 43; Lefèvre d’Etaples 2018, LIX–XCIX.
38 Mandosio 2013, 72–76.
39 Again, through the numerical values of Hebrew letters, as with Pico or Reuchlin.
40 See n. 32 above; Wilkinson 2015, 313�f.
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464 Brach
Lefèvre’s parallel interest in ordinary mathematics, culminating in the pub-
lication of several textbooks (1496) and in an edition of both Boethius’ De
arithmetica (1503)41 and Euclid’s Elements (1517), exerted a major in��uence on
several French members of his erudite circle who, between 1510/11 and 1521, in
Paris, published a few treatises on number symbolism.
Charles de Bovelles (1479–1567) o�fers a highly philosophical exposition
of the ontology of number and of the correlated elevatio mentis towards the
supreme Unity, supported by geometrical considerations which frequently
owe much to Cardinal Nicholas of Cusa’s (1401–1464) Docta ignorantia (On
Learned Ignorance, 1440).42 Besides that of Cusa, other recognizable in��u-
ences on Bovelles’ metaphysics are those of R. Lull, G. Pico and M. Ficino.43
A true pioneer in the study of geometry,44 his interest and pro��ciency in
this discipline were famous among his contemporaries. Many of his scienti��c
treatises actually exhibit a strong tendency to dwell on the practical applica-
tions of geometry, as well as on the formal analogies between mathematical
��gures or bodies and natural objects, in true Pythagorean fashion.
Bovelles’ combined penchant for the mechanistic aspects of science was
part of a general didactic purpose, and of a plan to reform the contemporary
cursus of studies in the ��eld. Both endeavours can possibly be conceived of as
parallel or complementary to Lefèvre’s own e�forts at the Cardinal Lemoine
College in Paris (where Bovelles was his pupil, from 1495, and later also taught),
as well as to his slightly later involvement in the (religious, this time) forma-
tion of laymen and of the clergy, alongside the bishop and reformer Guillaume
Briçonnet (1470–1534) and his “Groupe de Meaux” (1521–1525).
In contradiction, however, with N. of Cusa’s or L. Pacioli’s (see infra) views
in this respect, number symbolism, in Bovelles’ work, is linked to the philo-
sophical precedence ascribed to arithmetic over geometry. A Platonic com-
monplace, this superiority of number is linked to its greater “abstraction” and
supposed capacity to lift up the mind from physical realities to the intellectual
ones.45 Being “immaterial,” numerical entities appear to Bovelles better suited
41 See n. 12 above. This interest does not keep him, Bovelles or Clichtove from pointing –
from the earliest years of the 16th century – to the opportunities o�fered by mathematical
studies for the puri��cation of the soul and its contemplative ascent, as shown by several
texts published in Rice Jr 1972, passim; Oosterho�f 2018.
42 See Nicholas of Cusa 2013.
43 Victor 1978, 45–46 who also points to his lesser involvement with religious reform, com-
pared to that of his other three colleagues.
44 He was actually the ��rst to publish a manual of geometry in French (Paris: H. Estienne,
1511).
45 As the author puts it: “Numbers are more elevated than magnitudes and more concealed,
since they are posited in the soul, whereas magnitudes are more accessible and belong to
corporeal reality” (Charles de Bovelles 1512, fol. 69v°; my translation).
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Pythagorean Number Mysticism in the Renaissance 465
than geometry to support the anagogical movement of the spirit towards the
divine.46 In this sense, geometry47 can serve as a preliminary introduction to
both the science of arithmetic as such, and to its mystical interpretation. This
last aspect is discussed in the Book of the Twelve Numbers,48 dedicated to the
mystical analogies of the ��rst twelve integers, considered separately and in
their natural order. Relatively important aspects of its contents are the inter-
relation maintained between the quantitative and qualitative characteristics
of certain numbers (a point already stressed above), as well as the continua-
tion of epistolary discussions on the topic of number mysticism held in ear-
lier years between Bovelles and others, such as Germain de Ganay (14?–1520),49
letters which were published in the volume alongside the text itself. Scripture
and Christian theological considerations are remarkably absent (apart from
the theme of the Heavenly Jerusalem a propos the number 12) from the Liber
de duodecim numeris, which insists on the scalar properties which, through
their correspondences and analogies on the various planes of being, con-
stitute numbers as ontological intermediaries in the intellectual ascension
towards Unity.
Accompanying certain chapters, several charts and diagrams attempt, by
ordering and classifying them, to synthesize the manifold numerical analo-
gies associated with a given number (such as 4 and 6). These charts may
have exerted an in��uence on those presented, somewhat later, in Book II of
Agrippa’s Occult Philosophy,50 in chapters which are essentially concerned
with arithmology and its companionship with magic.
46 Such a movement is, for the author, the principal function of human reason, as developed
in the De Sapiente (1510; Charles de Bovelles 1982). See Gonzàlez-Garcia (forthcoming).
47 Bovelles actually dedicates the last book of his Physicorum elementorum libri decem to
the symbolical correspondences of geometrical bodies. For him, however, knowledge of
the Platonic polyhedra, in particular, tends towards a joint apprehension of both sensible
and intelligible substances and can even lead to the contemplation of the mystery of the
Trinity. Here, he may possibly be in��uenced by L. Pacioli (although he apparently never
mentions him, unlike Lefèvre, who did so in the preface to his 1514 edition of N. of Cusa’s
works), as recognized by Sanders 1990, 110–112; 171–173, who also hypothesized (103, n. 37)
an in��uence on Bovelles of Proclus’ Commentary on the First Book of Euclid’s Elements
(Proclus 1970).
48 Charles de Bovelles 1510, which is part of a collection of tracts on di�ferent mathematical
topics.
49 Vasoli 2001. To G. de Ganay were dedicated Lefèvre’s De magia naturali and Clichtove’s
Opusculum (see infra). Letters on the relation between arithmology and the “three prin-
ciples of natural magic” (dating back 1503–1505, to Ganay and several others) are also
featured in Abbot Johann Trithemius’ (1462–1516) published correspondence; Brann 1999,
117–133.
50 The use of charts is already present in Lefèvre’s De magia naturali (Jacques Lefèvre
d’Étaples 2018, 58–62) as well as in other philosophical books by Bovelles (De Nihilo, 1511;
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466 Brach
Another friend of both Lefèvre and Bovelles, and their colleague at the
Cardinal Lemoine College (where the study of the Liberal Arts was very much
in favour), is Josse Clichtove (1472–1543), an important Humanist, ecclesias-
tical reformer and Catholic theologian. His only arithmological publication
is his Small Treatise on the Mystical Meaning of Numbers (contained) in the
Bible (1513).51 If Bovelles sometimes made use of certain medieval sources,52
Clichtove – anticipating in this regard the rather conservative theological
stance he was later to adopt – took number symbolism all the way back to its
medieval understanding, as a tool for the interpretation of numerical passages
in Scripture. The main goal of this learned booklet is thus exegetical in nature,
aiming as it does to illuminate the reading and meditation of the Bible by the
mystical resources o�fered by number symbolism. Unlike in Bovelles’ case,
scriptural and Christian references are central to the author’s purpose, as he
solely references texts emanating from the Church fathers, medieval theolo-
gians or ecclesiastical writers in general.53 Yet, as a result of this attitude, and
in a manner akin to that of Bovelles’ Liber de duodecim numeris, esoteric specu-
lations about the “occult” disciplines (such as magic, kabbalah, Hermeticism,
etc) are remarkably absent from Clichtove’s concise dissertation, which exam-
ines numbers according to their natural order of succession but pushes it (in
conformity with the contents of Scripture) much further than the duodenary
to which Bovelles actually limits himself.
Another (and last) author, a member of the “Groupe de Meaux,” who was
familiar with Lefèvre’s circle and who bene��ted also, at the end of his life, from
the protection of Marguerite d’Angoulême (1492–1549),54 is bishop Gérard
Roussel (1500 ?–1555 ?), who published in 1521 a learned arithmological com-
mentary on Boethius’ De arithmetica (using Lefèvre’s earlier edition of the
Latin text).55 Roussel’s mystica numerorum applicatio is a chapter-by-chapter
commentary, frequently longer than the original text, exploring all manners of
Charles de Bovelles 1983) and – extensively – in Gérard Roussel’s commentary on Boethius
(see infra). It seems to be a pedagogical device typical of treatises involving mathematics
and emanated from this French circle; Oosterho�f (forthcoming).
51 Josse Clichtove 1513. This text actually happens to be the ��rst purely arithmological tract
to have been printed separately – the one by Bovelles being part of a larger collection of
texts, as already stated above: Massaut 1968.
52 Céard 1982.
53 Even though he does mention Pythagoras and Aristotle in his “Preface” to Germain de
Ganay.
54 Her spiritual director, between 1521 and 1524, was none other than Guillaume Briçonnet
himself; see Martineau, Vaissière and Heller 1975–1979.
55 Printed by S. de Colines: Paris 1521. A copy of this work, annotated by the French Christian
kabbalist Guillaume Postel (1510–1581), is now in the collections of the Bibliotheca
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Pythagorean Number Mysticism in the Renaissance 467
analogical transpositions of numbers and displaying a vast amount of erudi-
tion in school mathematics and music, philosophy, theology and arithmology.
Here again, and by necessity, the link between qualitative and quantitative
number comes to the fore, as do the didactic preoccupations, manifested by a
great number of diagrams and charts inserted in the text. In writing his com-
mentary, Roussel has somehow authored a second De arithmetica, of a number
symbolical kind this time, a textbook celebrating the manifold deployment of
basic numerical properties (examined by Boethius) in the realms of Biblical
exegesis, philosophy, musical science or theology, with the help of a vast array
of references ranging from Antiquity to his own time, from scienti��c writers
(such as Euclid or Jordanus) to Christian thinkers.
In true Pythagorean fashion, geometrical considerations are developed on
the basis of the study of ��gured numbers. Besides that of his sources, Roussel’s
doctrinal eclecticism – religious and philosophical – is likely a corollary of his
preoccupation with instruction in general, and the spiritual edi��cation in his
readers – a preoccupation which comes as no surprise from yet another mem-
ber of the evangelical “Groupe de Meaux.” Number, quantitative measurement,
proportion and their mutual relations serve here as rational unifying factors
under the tutelage of Scripture and of Christian tenets, in a new, humanis-
tic version of the Augustinian theological paradigm consisting of Holy Writ,
Reason and Tradition.
4 Allocating Beauty: Proportion, Art, Architecture
Equally removed from preoccupations with “esotericism,” magic and/or the
kabbalah, Luca Pacioli’s (ca 1447–1517) De divina proportione56 is neverthe-
less a curious book made famous by its woodcuts (designed after Leonardo
da Vinci’s (1452–1519) drawings) illustrating all sorts of geometrical bodies.
Juxtaposing theoretical and more technically oriented parts, with an essen-
tially pedagogical aim,57 the work’s main argument is about the importance of
mathematics in general for the understanding of nature, and concerns
Philosophica Hermetica in Amsterdam; Secret 1977, 115–132 (“II. Annotations de G. Postel
à une Arithmetica de Boèce, commentée par Gérard Roussel”).
56 Luca Pacioli 1509 (composed in Milan ca 1496–98).
57 Despite its Latin title, the whole work is actually written in Italian, which obviously con-
tributed to its success. A translator of Euclid in Latin (1509) and, possibly, in Italian as
well, Pacioli privately taught mathematics and accountancy throughout Italy for most of
his career; Bucciarelli and Zorzetto 2018.
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468 Brach
speci��cally the so-called “Golden Mean” (or “Golden Section”)58 and its appli-
cation to architecture and the arts. Culled from both Euclid’s Elements and
Plato’s Timaeus (55a �f.), with passing references to Pythagoras, the mathemat-
ical and symbolic properties of this geometrical division in mean and extreme
ratio, as well as those of the ��ve regular polyhedra, express the perfection of
��ve fundamental divine attributes59 and how such a perfection actually mir-
rors itself, according to Pacioli, in the fabric of the universe: the shape of “the
All” (or “quintessence”) is – according to Plato – the dodecahedron (a solid
with twelve pentagonal faces), for the construction of which Euclid makes use
of the “divine proportion,” thus indicating the analogy between this ratio and
the supernal force at work behind the creation. Seen from this perspective,
geometry is more intrinsically concerned – compared with number itself –
with material and corporeal measures, quantities and dimensions, insofar as
these re��ect, in the author’s view, the divine perfections and the manner in
which they intervene in the pattern of creation.
The second part of the work – an architectural treatise – examines the pro-
portions of the human body, as compared to those found by Vitruvius in clas-
sical architecture.60
5 Pythagorean Syntheses
Wholly diverse in nature and scope from the preceding works, although very
much “Pythagorean” (as well as kabbalistic) in spirit, is the bulky De harmo-
nia mundi published in Venice by the Franciscan monk, Christian kabbalist
and theologian Francesco Zorzi (1466–1540).61 This encyclopedic and in��u-
ential tome, replete with the most eclectic philosophical erudition, is con-
cerned with the fabric and constitution of the universe, understood in terms of
musical harmony, based in turn on mathematical analogies and proportions.62
Divided into three main “canticles” (further subdivided in eight “tones” each63)
respectively correlated to God (Creation), Christ (Redemption) and Man
(Reintegration), and also to the classic threefold division of nature (angelic,
58 A particular case of the geometric proportional mean (of the type ac = b2). Neveux 1995.
59 Unicity, trinity, transcendence, immutability and creative wisdom.
60 Giusti and Maccagni 1994.
61 Francesco Zorzi 2010.
62 Chaignet 1874, t. 2, 330�f.
63 In imitation of the musical octave.
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Pythagorean Number Mysticism in the Renaissance 469
heavenly and terrestrial),64 the De harmonia mundi o�fers a vast synthetical
exposé of the mysteries of creation and of their symbolical relation to the divine
Unity. Under the in��uence of Pico, Ficino and Reuchlin (among so many other
sources), Zorzi attempts to explain, via the symbolism of the Pythagorean
tetractys (and denary),65 allied to that of the ten se��rot or divine aspects mir-
roring each other within the universe, the relations between Unity and multi-
plicity, in marked Neoplatonic fashion. Central to his approach is the concept
of the reducibility of creation to a symbolical language, ultimately identi��ed
with numbers. Manifesting themselves in the constitution of names/words,
musical rhythm and proportions, numbers illustrate the harmony which sup-
posedly describes and encrypts the ontological kinship between Unity and its
hidden expressions, which make up the multiple universe. Centered on Man,
understood as created in God’s image and, therefore, as a perfect synthesis of
the macrocosm, the third “canticle” evokes the eschatological harmony fore-
shadowed in man’s structure. The relations of the human soul to the body are
expressed in terms of musical proportions (borrowed mainly from a famous
passage in Plato’s Timaeus 35a �f.), as is the entire hierarchy of beings in the
universe, which is actually based on the number 27 (another feature from the
Timaeus). 27 represents the “perfect cube” of 3, considered here as the principal
number of reference and the root of the entire harmony of creation,66 whose
ultimate, perfect development is precisely symbolized by 27. The De harmonia
mundi, therefore, presents itself as an architectural model of reality, a model
whose origin and ��nal achievement coincide in God and are anticipated in
Man and in his mystical reintegration. Such themes are described according to
an immense network of numerical proportions and analogies, which suppos-
edly account for the actual layout of creation as well as for the scheme of its
future reintegration, conditioned by Man’s spiritual evolution and expressed
in recurring musical harmonies, in a pars pro toto scalar ontological ascension.
It is worth noting that, on at least one occasion, Zorzi even had the oppor-
tunity of applying his musical, kabbalistic and arithmological principles to
concrete architectural planning and realizations. This took place during his
64 Such a division is also meant to recall the tripartite structure of Dante’s poem, on which
Zorzi left a commentary; Francesco Giorgio Veneto 1991.
65 Although Zorzi’s focus here is mostly on number 9 and its multiples, he nevertheless
explicitly mentions both the Pythagoreans and Plato a propos the denary. On these two
di�ferent understandings of the Decad, Deretić and Knežević 2020. (I owe this reference,
as well as several others regarding Antiquity, to the kind generosity of my colleague
Constantinos Macris.)
66 The creation itself is organized by Zorzi according to a scale of 9 (32), number of the
angelic orders according to [Ps.-] Denys the Areopagite.
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470 Brach
intervention in the reconstruction works undertaken at the church of the
Franciscan convent of San Francesco della Vigna in Venice, for which he wrote
a memoir (1535) dealing with the proportional analogies between the human
body and the proposed monument that he felt (in agreement with the prin-
cipal builder, Jacopo Sansovino) should be respected in the erection of the
new building.67
An avid reader – and sometimes almost self-declared plagiarist – of Pico,
Ficino, Reuchlin, Zorzi and their likes, and a friend and visitor of Trithemius,68
the already mentioned H.-C. Agrippa is the author of a well-known and very
in��uential treatise on magic, entitled De occulta philosophia.69 In this work
he devotes no less than ��fteen chapters70 to the numbers from 1 to 12 and
beyond. Each of these chapters usually ��lls up between 1 and 3 pages of the
book (the longest being devoted to the septenary), and is followed by a chart
simultaneously summarizing and expanding the text by presenting the mani-
fold correspondences and analogies governed by the relevant number, dis-
played according to a six-fold division.71 Most especially concerned in this part
of the book with the role played by mathematics in the three di�ferent types
of magic he famously correlates with the natural, celestial and “intellectual”
(i.e., angelic) worlds, Agrippa devotes as many brief introductory chapters to
the nature and importance of number as such. Against the backdrop of a sig-
ni��cant array of classical, medieval and contemporary authorities, he posits a
Christian Neoplatonic understanding of number as the archetype of created
things in the divine intellect, possessing a real kinship with the “ideas” and
responsible for the cohesion of the whole universe, both on the functional and
ontological levels. Distributed and active on all planes of existence, number is
thus the origin of the secrets and mysteries of creation, in the natural, celes-
tial and “divine” (angelic) realms.72 Needless to say, Agrippa is here exclusively
concerned with what he calls “formal and rational” mathematics, as opposed
to their “material” counterpart. In a way which is very much inspired by Pico,
he insists on the formalis ratio present in “natural” number, which is the
67 Foscari and Tafuri 1983.
68 The abbot was the actual dedicatee of the ��rst version of Agrippa’s Occult Philosophy,
which has been preserved in manuscript.
69 See n. 28 above. I am quoting from this critical edition of the text.
70 Heinrich-Cornelius Agrippa 1992, 249–299.
71 The division in question is composed of elements belonging successively to the divine or
“archetypal” world, to the three-fold partition of the cosmos, to the “microcosmos” (Man)
and to the infernal world. The chapter devoted to the number 12 has 2 charts, respectively
concerned with kabbalistic and “Orphic” doctrines – an obvious echo of Pico’s syncre-
tism; Lehrich 2003.
72 Heinrich-Cornelius Agrippa 1992, book II, chap. 2, pp. 252–253.
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Pythagorean Number Mysticism in the Renaissance 471
rationale behind the mysteries of God and of Nature compounded in “abstract”
mathematical entities. One must be capable of e�fecting the conjunction and
consonance of those numbers with the divine ones, in order to understand and
operate the wonders that can be brought about via the magical use of mathe-
matics. Still following Pico’s wake, Agrippa holds that numbers pertaining to
the ��rst decad actually refer to divine realities and that those belonging to the
tens, hundreds and thousands indicate the celestial, terrestrial and eschatolog-
ical planes respectively. He then proceeds to correlate the three mathematical
means73 to the relations between the parts of the soul, of the body and of the
whole living being.74
Although he was also a versatile, yet leading scientist of the Elisabethan
Renaissance, and consequently much more personnally interested in the var-
ied practical applications of mathematics than Agrippa ever was, it is another
magician,75 John Dee (1527–1608), who took it upon himself to write an
important preface to the ��rst English translation of Euclid’s Elements, pub-
lished in 1570.76 In this seminal text, Dee articulated a spirited defence of
the usefulness of applied mathematics in general (of which he was himself
a skilled practioner77) to an encomium of “formal number” as the superior
level of mathematical entities and of their understanding.78 Dee shares with
Pacioli (albeit in the course of a single text instead of several successive trea-
tises, and despite considerable di�ferences in tone and intent), a willingness
to write in the vernacular and to attempt bridging a theological discourse on
divine and cosmic harmony with certain elements belonging to scienti��c and
practical knowledge.
Ultimately deriving from the supreme Monad, number as such is present
as a pattern in the mind of the Creator, in angelic and human intellects, as
well as in the natural realm. Representing the essence of reality, mathematics
are thus endowed with a magical power, as they encompass all levels of cre-
ation and mediate – once again – between the divine and material spheres.
Since they operate on all these planes, they are essential in implementing
an ambitious synthesis of science, magic, kabbalah, and natural philosophy.
Notwithstanding, Dee was also part of a long line of humanist thinkers who
were not satis��ed with scholarly sources and an exclusively bookish approach
73 In other words, the so-called arithmetical, geometrical and harmonic proportional means
(cf. n. 58).
74 Heinrich-Cornelius Agrippa 1992, book II, ch. 3, pp. 254–255.
75 Harkness 1999; Clucas 2006.
76 London: J. Daye, 1570; reprint John Dee 1975.
77 And of which he distinguished no less than 19 di�ferent branches or arts methodicall.
78 Mandosio 2012.
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472 Brach
to knowledge but who also maintained, like Pacioli or Bovelles, an interest
in underlining or even developing the technical applications of algebra and
geometry. In so doing, they intended to put contemporary mathematical dis-
coveries at the immediate disposal of craftsmen and artisans alike, in order
to provide them with the scienti��c background necessary to shed theoretical
light on empirical procedures.79
6 One of a Kind: One Number Says It All
Having secured for itself, by the last quarter of the 16th century, an epistemo-
logical legitimacy in both the scienti��c and philosophical ��elds, Pythagorean
number mysticism, before it produced some encyclopedic treatments, devel-
oped a peculiar kind of essay: the study of a given symbolic or religious theme
through the lenses of a monography on a single number of the Decad. Already
attested in Antiquity,80 this speci��c sub-genre of arithmological literature
focuses most frequently on the Septenary, although some of the treatises deal
with other numbers, mainly the Ternary.81
Among the most meaningful examples of such endeavours is Alessandro
Farra’s Settenario dell’humana ridutione (Septenary of the Human Conversion).82
A jurist and civil administrator, and a young member83 of the newly-founded
literary Academy of the A���dati in the city of Pavia, Farra composed his most
conspicuous opus according to a seven-fold division. Under the strong (and
avowed) in��uence of Pico and Ficino, his Settenario is a spiritual and philo-
sophical discourse mixing up Pythagorean and kabbalistic themes about the
seven steps of the mystical itinerary of the soul. Number symbolism is particu-
larly in��uential in the seventh and ��nal section of the book, the one devoted
to the ��loso��a simbolica ovvero le imprese (the “symbolic philosophy or the
images”),84 which represents the ��nal stage of the ridutione (conversion) men-
tioned in the title, in other words the acquisition of wisdom. Such wisdom
resides, for Farra, in the contemplation of the intelligible principles regulating
the cosmic proportions, accessed through numerical and geometrical symbols
79 Brach 2015, 115–117.
80 Especially, but not exclusively, for the Septenary. Cf. L. Zhmud’s works (cited above, n. 8).
81 A list of these (to which may be added Croci’s Breve discorso della perfezione del numero
ternario [see Antonio Croci 1623]) can be found in Brach 1994, 76, 84, 90, 92, 94.
82 Alessandro Farra 1571/1594.
83 Born some time during the 1540’s, Farra was elected in 1562. The Academy typically spe-
cialized in works of rhetorics and eloquence.
84 For a more detailed analysis, see Brach 1994, 73–75; Maggi 1998, 23–45.
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Pythagorean Number Mysticism in the Renaissance 473
manifesting the network of correspondences at work behind the harmony
of creation.
Shortly afterwards, Fabio Paolini (ca 1550–1604) also published his Hebdo-
mades sive Septem de Septenario libri (Hebdomads, or Seven Books on the
Septenary),85 which constitute a learned commentary on a single verse of
Virgil’s Aeneid.86 A trained Humanist and physician, and a teacher of both the
Greek and Latin languages and literature in several local institutions, Paolini is
also a founding member of the second Venetian Academy, that of the Uranici
(1587–1593). Certainly his most famous work, the Hebdomades represent an
encyclopedic treatment of rhetorics and poetry, combined with speculative
philosophy, astrology and symbolism, under the joint in��uences of Ficino,
Pico, and his friend, the famous musician Giose�fo Zarlino (1517–1590).87 The
mere existence of treatises like Farra’s or Paolini’s (as well as of many others,
dedicated to a single number) actually testi��es to the widespread interest for
the art of memory within the learned circles and Academies of Northern Italy.
In such a context, the art of memory is combined with number symbolism,
Ficinian astral magic, Christian kabbalah and musical theories as practical
means to enhance the perception of both cosmic and esthetic harmony. Paolini
develops a syncretic theory, which closely associates Orpheus and Pythagoras,
who symbolically stand for the poetic/emotional and mathematical aspects of
music, respectively. At the top of the septenary scale of knowledge, the myster-
ies of “natural magic” and “theology” (chap. 6 and 7) are conjoined with those
of Pythagorean (or “ideal”) numbers (chap. 5) in order to activate and vivify
the three types of music originally distinguished by Boethius,88 which are
combined in turn with poetic discourse to actually produce the most perfect
kind of harmony, supposedly capable of achieving all wonders, spiritual and
otherwise,89 and of which Orpheus is the symbol.
Quite similar speculations about the cosmological use of numbers, associ-
ating rhetoric, literature, poetical declamation and music, but somewhat less
preoccupied with purely magical background or goals, are found in the works
of the 17th-century author Teodato Osio (1605–1673). This little known writer
published a spate of books in Milan, between 1637 and 1668, about the applica-
tion of mathematics and music to the rhythm of Latin and Italian poetry and
85 Fabio Paolini 1589.
86 Aen. VI, 646: Obloquitur numeris septem discrimina vocum ([Orpheus] “accompanies their
voices with the seven-note scale”).
87 Vasoli 1998, 193–210, part. 204–207; McDonald 2012, 222–248.
88 Musica humana, intrumentalis, mundana (vocal, instrumental and “cosmic” music).
89 Radaelli 1999.
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474 Brach
prose,90 along with another work on architecture and land surveying.91 Osio
develops some classic musical considerations about “Pythagorean” (mainly
Platonic) musical theory, whose intervals and proportions he applies to the
prosody and tonal accents of the languages referred to above. Assimilating the
continuous and discrete modes of quantity to the “Same” and “Other” of Plato’s
cosmogony in the Timaeus, he basically compares the components and funda-
mental structure of language – spoken as well as written – to the genesis of the
geometric bodies, insisting on the cosmological role of proportion and num-
bers and bringing together the doctrine of world harmony and that of language
constitution (syllables, tones, letters, word composition and etymology).92 In
his later productions, Osio insists less on language than on philosophical con-
siderations about discrete and continuous quantity as tools of divine creation
and fundamental elements of the universe, associated with the three main
proportional means (see above) and to the terms of the famous quotation of
the Book of Wisdom,93 drawing analogies between the divine operations and
those of human craftsmen. Dealing occasionally with magic and divination
(using a method combining astrology, mathematics and music), such a cosmo-
logical discourse constitutes a very curious and understudied instance of
Platonic speculations about nature and mathematical harmony in Northern
Italy around the middle of the 17th century.
7 Pythagorean Number as a Philosophical Abstraction
The quite complex and much-studied natural philosophy and cosmology of
Giordano Bruno (1548–1600) harbour a very personal conception of num-
ber and of “mathematical magic” which – despite the well-known in��uence
of Agrippa on the De monade, numero et ��gura94 – has in fact little to do
with Pythagorean number mysticism as understood in the present article.95
The Neoplatonic scheme of the scala entis and the correlative distribution of
mathematical entities along its ontological hierarchy, let alone their “magical”
power over physical realities, have no place in Bruno’s thought. Although the
De monade appears outwardly as a compendium of the signi��cations attached
to each number of the primary Decad, presented in their natural order, the
90 Teodato Osio 1637, 1653 and 1668.
91 Id. 1639.
92 Brach 1994, 90–92; Wuidar 2008, passim; Gaspari 2011 (who mentions several extant
unpublished manuscripts on number symbolism and Pythagorean lore).
93 Book of Wisdom, XI, 21 (“You [sc. God] ordered all things in measure, number and weight”).
94 Printed with two other important Latin philosophical poems in Giordano Bruno 1591.
95 Bonnet 2002; Giovannozzi 2012.
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Pythagorean Number Mysticism in the Renaissance 475
accent is in reality on the relations between physics and mathematics, and the
focus of the book on the notions of order, form, ��gure and quality. As the inter-
nal components of reality, numbers and geometrical ��gures are essentially
distinguished by their qualitative structural di�ferences, bestowed upon them
by the multiplicity of forms. Their main role is to order natural realities, receiv-
ing from them the qualitative determinations of which mere abstract quan-
tity is devoid in itself. Abstract quantity as such belongs to the logical plane,
intrinsically superior to the imagination but unable, nevertheless, to activate
it. However, since all forms are dependent on the unique universal substance,
mathematical abstraction, accounting for their common characters, allows us
to grasp the relations of these multiple forms to the unity of their substratum,
and thus to apprehend the underlying substantial constitution of being. The
science of numbers leads us therefore towards the understanding of the unity
of being and, conversely, geometry sheds light on the process by which plural-
ity, intrinsically immanent to this unity, is actually deployed in the outward
existence of forms and ��gures. By these considerations,96 Bruno shows the
ancillary character of both arithmetic and geometry towards natural philoso-
phy and metaphysics, as well as their common abstract character, intermedi-
ary between the essence of reality and its material expansion.97
In his magical writings (drafted between 1588 and 159298), whose contents
are rooted in the natural philosophy elaborated in the earlier Italian dialogues
(such as De la causa, principio e uno, Cena delle ceneri, and others), Bruno actu-
ally criticizes Agrippa’s conception of the e�fective relation between language
and being. Natural magic, for Bruno, is really inseparable from the physical
properties of things and beings, and not subject to occult virtues.
8 Pythagoreanism as the Key to Universal Knowledge
An encyclopedic dimension is conferred to Pythagorean number symbolism
by the publication of Pietro Bongo’s (?-1601) enormously erudite Numerorum
Mysteria.99 Written by a member of an ancient and noble family from Bergamo,
96 Naturally somewhat oversimpli��ed here; for a detailed study of the general status of
mathematical disciplines in G. Bruno’s works, Bönker-Vallon 1995.
97 Such a hierarchy is only valid on the cognitive plane, and is not to be understood as imply-
ing an ontological counterpart. The scalar nature of being is entirely deconstructed in
Bruno’s works, from the so-called “Italian Dialogues” onwards.
98 They include texts such as the De magia mathematica (ca 1590; Giordano Bruno 1999) and
Theses de magia (in Id. 2000).
99 De��nitive and most complete impression Bergamo: Ventura 1599 (reprint Pietro Bongo
1983); cf. Ernst 1983; Piccinini 1984.
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476 Brach
Canon of the local Sant’Alessandro cathedral, this thick quarto tome is entirely
dedicated to the tradition of “Pythagoreanism,” and draws from every conceiv-
able source available at the time, including magical, Hermetic, kabbalistic and
esoteric writings (Lull, Cusa, Pico, Ficino, Lefèvre d’Etaples, Bovelles, Zorzi,
Dee, etc). The book was frequently criticized for its motley and untidy charac-
ter, which often degenerates in a mere mosaic of quotations.100 Bongo never-
theless remained aware in it of certain theoretical issues at stake in his days.
For instance, the growing opposition between traditional thinking (based on
analogy, correspondences and the powers hidden in the essence of things) and
a more modern trend of thought, which attempted to read the world through
the lenses of experience and of a scienti��c mathesis, was not lost on him.
Bongo contrasted the Book of Nature with that of Scripture, and exhibited
an understanding of pythagorica disciplina as based on Tradition and author-
ity, and as essentially concerned with scrutinizing the divine mysteries. Such
a perspective naturally retained a strong theological ��avor, insisting on the
supposed consensus between Pythagoreanism (as Bongo understood it) and
post-Tridentine Catholic perspectives. The symbolical use of numbers is here
viewed not just as a general key to the harmony of reality and of spiritual life
but also as an ontological principle at work behind the layout of creation.
Through its several editions and the echo it found in other contemporary
publications, Bongo’s treatise was instrumental in establishing number mys-
ticism as a speci��c and relevant humanistic topic, of which it became one of
the foremost textbooks, thus strongly contributing to the acceptance of such
speculations into the body of mainstream scholarly culture.101
Thirty years later, the then archbishop of Milano Federico Borromeo
(1564–1631) had an extremely limited number of copies of his De pythagoricis
numeris102 printed by the press established in the archbishopric by his distant
cousin and predecessor on the Milan seat, the more famous Carlo Borromeo
(1538–1584).103 Here again, Pythagoreanism is considered as standing in the
midst between religion and science, and viewed from a dual, contemplative
and scienti��c, perspective on nature, typical of the early 17th century, a period
sometimes as wary of esoteric speculations (both Borromeos were cham-
pions of the Catholic Counter-Reform in Italy) as it was de��ant of certain
100 Seen from the opposite perspective, this feature helps making the book a useful dictio-
nary of the allegorical meanings of numbers, which almost all artistic or intellectual
trades could indi�ferently tap into.
101 Baroni 2012.
102 Federico Borromeo 2016.
103 Burgio and Ceriotti 2002.
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Pythagorean Number Mysticism in the Renaissance 477
requirements of scienti��c methods. The book examines the nature and prop-
erties of numbers, as well as their usefulness in the rational study of natural
mechanisms, while leaving aside or criticizing their “occult,” magical, divina-
tory or kabbalistic aspects, for which the author had entertained a strong inter-
est in his youth but which he now scorned.104 As an aside, we may note that,
following a collaboration between the two men which apparently started in
late 1610 or early 1611, F. Borromeo became the dedicatee of the Taumatologia105
written by Giovan Battista Della Porta (1535–1615). Parts of this work deal with
the natural powers attributed to numbers and music, a topic certainly reminis-
cent of Pico della Mirandola and consonant with Della Porta’s famous interest
in natural magic.106 The De pythagoricis numeris enjoyed almost no circula-
tion at all and was therefore virtually unknown; it was, however, rediscovered
and quoted in recent times by the Florentine mathematician and specialist of
Pythagoreanism Arturo Reghini (1878–1946).107
Another contemporary encyclopedic presentation of Pythagorean number
philosophy108 – albeit of a very di�ferent kind – is that of the famous English
theosopher Robert Fludd (1574–1637).109 Chapters on this topic open the sec-
ond volume of his Utriusque cosmi … historia,110 dedicated to the “microcosm,”
according to the leading theme and structural principle of the entire opus,
which is the fundamental analogy between the two corresponding worlds, the
universe and man. The analogy is in fact tripartite, according to Fludd, and
includes the divine sphere, of which both the macro- and microcosm are sup-
posedly perfect images. Following a classical (since Augustine) interpretation
of this theory, the pattern of creation is essentially modelled on the ternary,
as the expression of the three-fold operation of the Trinity. Beginning with
“divine numbers,” which he also calls “supersubstantial numbers,” naturally
104 In the same year and place, F. Borromeo also published his De cabbalisticis inventis
libri duo (Federico Borromeo 1978); see Campanini 2002. The famous Neoplatonic phi-
losopher Francesco Patrizi (1529–1597) has left a hitherto unpublished manuscript De
numerorum mysteriis (On the Mysteries of Numbers, 1594) dedicated to F. Borromeo, who
was his pupil at the time (a critical edition of the text was announced a long time ago by
Maria Muccillo).
105 It is possible that this work remained uncompleted and unpublished; extant fragments in
Giovan Battista Della Porta 2013.
106 Bertolini 2017 (my thanks to M. Ghione for this reference); Verardi 2018, 138–140.
107 Reghini 2004, 46�f.
108 Akin, to a certain extent, to Zorzi’s Harmonia mundi, although quite di�ferent of course in
many respects.
109 Hu�fman 1988 and 2001; Janacek 2011, 43–74.
110 Robert Fludd 1617–1619.
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478 Brach
extolling the importance of the Monad and of its created counterpart, the
geometrical point, Fludd goes on to examine the mystical Dyad, and then
the Ternary. He expands on the relation of the Trinity to the Monad, and on the
manifold triadic correspondences within both worlds. Numbers and musical/
harmonic proportions rule the general layout of the cosmic structure as well as
the ratios between its di�ferent tiers, the whole argument being superbly illus-
trated by many engravings which have vastly contributed to making Fludd’s
work famous and helped initiate (along with Khunrath and a few others) the
trend of “cosmo-theosophical” illustrations in 17th-century alchemical and
Rosicrucian books.111
The author does make use of the expression “formal numbers” and, in his
quest for universal knowledge,112 imitates Agrippa in applying the primary
Decad to the Godhead and the ��rst, essential principles, the tens to the angelic
spheres, the hundreds to the celestial world and the thousands to the sublunar
universe and its basic elements.
The same tripartite blueprint necessarily applies to Man as microcosm,
organized according to the ternary of intellect, soul and body and their hier-
archy ruled by musical proportions and harmony. Divine in��uences on both
the lesser and greater worlds are mediated by the celestial forces and this uni-
versal vitalism reminds us that the network of natural correspondences is to
Fludd a basic component of reality, embedded into the machina mundi and
essential to both its life and operation. The same goes for Pythagorean num-
bers which, for him, exert an action which is far from being merely symbolical
or abstract; they constitute, on the contrary, an integral part of the intimate
nature of the universe and of its workings, as well as an essential tool for their
understanding.
Although more limited in scope and bulk than Bongo’s or Fludd’s books, Jan
van Meurs the Elder’s (1579–1639) Denarius Pythagoricus (Pythagorean Decad)113
and Athanasius Kircher’s (1602–1680) Arithmologia114 represent typical ency-
clopedic treatments of number symbolism.
The former work is essentially a systematic inventory of classical sources
concerning Pythagorean number theory. It consists mostly of an array of quo-
tations about the nature and de��nition of number, its basic constitution (odd
and even, male and female, perfect and imperfect, etc.) and the characteristics
111 Szulakowska 2011; Forshaw 2016.
112 Akin to Kircher’s in this respect but of course quite di�ferent in tone, spirit and intentions.
113 Johannes Meursius 1631.
114 Athanasius Kircher 1665 (the full title in English reads: Arithmology, or the Hidden
Mysteries of Numbers). See Leinkauf 1993, 192–235.
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Pythagorean Number Mysticism in the Renaissance 479
and mythological correspondences attached to the components of the Decad,
examined according to their natural order. Unsurprisingly, the references are
chie��y taken from pagan sources (literary, poetical, philosophical, historical)
and a good number of Greek and Latin Church Fathers, who have frequently
expressed theological views about scriptural numbers. By contrast, the major-
ity of medieval authorities – with the exception of Boethius and a few other
Western and Byzantine writers – are shunned by this Protestant historian,
famous for his erudition but lacking in philosophical creativity. Speculation,
moreover, is not the goal of the present opus, which is mainly descriptive, and
aims at a didactic presentation of the topic, enhanced by several useful refer-
ence indexes.
One of the greatest and most famous polymaths of the 17th century, the
Jesuit A. Kircher has dedicated a speci��c treatise to number symbolism.
Although not one of his best-known books (probably because it is also of
much less value to book-lovers than some of his other, richly illustrated
productions115), the Arithmologia nevertheless reveals its author’s interest for
“occult” speculations – an interest Kircher had to rein in prudently, given the
context of post-Tridentine Catholicism.
The book is divided in six parts, and deals with all sorts of topics linked to
number symbolism: digits or numerical characters and their symbolism; the
so-called “magic squares” and their astrological use in Antiquity, as well as in
Judaic and Arabic religious cultures; divination by numbers, using magical
seals and number combinations; amulets, angelic seals and magical alphabets
based on numerals and geometrical ��gures. The last chapter, entitled “The
mystical signi��cation of numbers,” considers the Decad and its multiple analo-
gies and correspondences in Nature.
In an age thirsting for univeral knowledge, the Arithmologia intends to be
an encyclopedic presentation of its topic, synthesizing the di�ferent doctrinal,
magical and astrological aspects of number mysticism, as Kircher understands
it. Apart from its vast erudition, the book clearly betrays its author’s fascination
for the kind of unorthodox speculations he is examining. Kircher justi��es his
interest in number magic and symbolism by assuming a dual necessity: ��rst,
to bring back to light this material by extracting it from its ancient, more or
less reputable pagan or Christian sources; second, to salvage it from “heretical”
contexts and criticize its eventual denaturation. Finally, his ultimate goal is
to reintegrate these views within the scope of contemporary knowledge, and
115 Such as the Mundus subterraneus, published in the same year, or his Oedipus Aegyptiacus
(1652–1654).
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480 Brach
present them henceforth as acceptable and legitimate from the points of view
of theology, science and natural philosophy.116
9 Pythagoras: Stranger in a Strange Land
From what we have seen above, pythagorean tenets about number and/or
geometry, as understood during the Renaissance, are generally reinterpreted
through neoplatonic lenses, which root the study of natural philosophy and
cosmology in an ontological and theological viewpoint. Central, here, is the
christianized idea of numbers being essentially a divine model, the essential
principles of things, present in God’s intellect and which serve as a pattern for
the organization of the cosmos.
Conversely, numbers and geometrical ��gures are equally perceived as a sca-
lar support for the ascension of the human mind from earthly matters towards
the unitive contemplation of the immaterial being (theosis, dei��catio), thus
blending an ontological and a cognitive approach to the nature of reality and
of the Godhead. Such a stance, in which theological considerations actually
govern scienti��c knowledge, paves the way for doctrines which treat the quali-
tative aspects of number as superior to and ruling over the quantitative and
material ones, yet maintaining a strict relationship between both: physical
and metaphysical numbers are never very far removed, let alone independent,
from one another.
Thus, Pythagorean arithmology is linked to a conception of number as “e���-
cient cause,” as well as to the doctrines of the unicity of creation and of the
analogies and correspondences linking its di�ferent planes, of which man him-
self is a mirror, on an obviously smaller scale.
The progressive decline of such an organic worldview within European
culture, from the late 16th and 17th century onwards, inevitably entailed the
increasing scienti��c irrelevance of the currents of thought which depended on
it, including of course that of arithmology and of other esoteric tenets which
frequently resorted to it. Gradually, number found itself reduced to the status
of a mere logical operator, devoid of any reference to a living, inner essence of
things, thus rendering meaningless its previous role as a “factor of enchant-
ment” within creation, mediating between material and spiritual realities.
Harmony and proportions are no longer construed as key elements in the lan-
guage of Nature – a language which is henceforth treated as both physically
116 Fletcher 2011, 53, 161–170, 174.
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Pythagorean Number Mysticism in the Renaissance 481
and metaphysically autonomous vis-à-vis the theological discourse. While ana-
lyzing the geometrical and quantitative aspects of space and of natural order,
mathematicians develop a new mathesis universalis which aims at renovating
the understanding of the relationship between knowledge and being. The
components of the universe are therefore viewed as immanent, mechanical
constructs submitted to quantitative laws, in lieu of elements of a pattern in
the mind of God; accordingly, their study may no longer be conducted in terms
of a quest for the mystic harmonies of numbers and of geometrical propor-
tions, nor expressed cogently as the unfolding of a providential design, already
inscribed in the nature of things by way of their mathematical structure.
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