The present chapter focuses, first of all, on mathematical sciences, such as mathematical astronomy and astrology, their history in Byzantium and the Constantinopolitan scholars’ contribution to their development. Second, it illustrates how mathematics provided the foundation and enhanced a number of related disciplines and technologies whose purpose was the successful and accurate measurement of the world, such as geography and pharmacology. For instance, astronomical instruments were employed not only to observe the sky, but also to measure time. Geography and cartography were dependent on mathematical methods and astronomical knowledge. Alchemy and medicine used a system of measurements and proportions derived from the mathematical theory and relied to some extent on symbolic mathematics and astrology.

There are four major points one ought to emphasize with respect to the history of science in Byzantium. First, the mathematical sciences were studied and practiced as theoretical rather than experimental sciences, whence the certainty and truthfulness of their results were derived. Other types of knowledge, such as medicine, pharmacology, and alchemy relied much more on experience, observation, and practice.

Second, scientific study and production grew out of the classical heritage of Greek science and aimed at its preservation, clarification and emendation. A case in point is the period after 1204, famously characterized by the increased production of compilations of scientific works whose chief purpose was the preservation of the ancient knowledge on the subject, as well as the renewal of its circulation. It is in this period of proliferation of collections and compilations that a codification of a “cannon of authorities” took place: Nikomachus of Gerasa (fl. ca. 100), together with Diophantus of Alexandria (fl. ca. 250) became the main reference for those interested in arithmetic, Euclid (fl. ca. 300 BCE) for the study of geometry, Heron of Alexandria (1st century CE), and Ptolemy (fl. ca. 130-175) for music and astronomy. It is worth noting that the period after 1261 until the conquest of Constantinople in 1453 is the period most saturated with scientific production during the Byzantine millennium.

Third, one has to bear in mind the lack of institutionalization and support on behalf of the Byzantine imperial government for the study and practice of the higher mathematical sciences. This was not the case with medicine, for instance, since the Byzantine emperors invested in the creation and maintenance of medical schools and hospitals.

The fourth main feature characterizing Byzantine science in particular, as well as Byzantine erudite culture in general, consists in the lack of specialization on behalf of the scholars. The higher education in Byzantium was not university-based and did not follow an established curriculum. Thus, those educated Byzantines, who dedicated themselves to mathematics, typically left their contributions in the fields of music, astronomy, and even philosophy. Two Byzantine terms conceptually express the attitude of the Byzantine scholar towards learning, be it properly scientific (in the fields of mathematics, harmonics, and astronomy), or quasi-scientific (with respect to astrology, magic, dream interpretation, and so on): philomatheia and polymatheia. Though their meaning vary from the positive zeal for learning (philomatheia) to the sometimes objectionable and unhealthy curiosity (polymatheia is generally meant positively, but on occasion it can be synonymous with periergasia and polypragmosyne), they both indicate general and all-encompassing knowledge rather than specialized learning.

It has been argued that polymathy, usually attributed to those well-versed in various or all disciplines of the trivium and quadrivium, is a characteristic feature of Byzantine culture. The notion of polymathy also indicated the intersection of scientific knowledge and rhetoric. Thus, scientific works differed not only in terms of their topic, but also in terms of their literary style. There are, generally speaking, two major groups of scientific texts with respect to the register they were written in, namely those composed in classicizing Greek and those written in the vernacular. The first group usually deals with the so-called ‘noble’ matters, i.e. the advanced theoretical levels of the mathematical sciences. The second group includes practical and ‘reader-friendly’ manuals such as botanical lists, astrological prescriptions, and collections of arithmetical problems. The rough division of the Byzantine scientific texts according to style should be complemented by the addition of the category of translated works, e.g. from Arabic or Persian. Often times the Byzantine translations rendered the original word by word and in the case of foreign technical vocabulary, they preserved it in transliteration instead of providing an equivalent Greek term.

Before proceeding to the discussion of different branches of Byzantine mathematical sciences and related disciplines and technologies, it is necessary to introduce their numerical foundation, namely the number systems used by the Byzantines, as well as to note the additional symbolic meaning attributed to numbers which was reflected in various products of Byzantine culture - from texts to architectural monuments.

1. Numerical Foundation

Three different numerical systems were employed at various points of the Byzantine millennium: 1) the Greek mathematical notation system; 2) the sexagesimal place value system; 3) and the Indian decimal place value system. The first denoted the numbers with the twenty-four letters of the Greek alphabet plus three archaic letters (digamma/stigma, koppa and sampi). With the help of the resulting twenty-seven characters and the addition of diacritic marks, one could express units, tens, and hundreds, as well as thousands (a stroke was added to the lower left), ten thousands (the smaller number was written above the letter M), and fractional numbers. The sexagesimal place value system played a significant role in astronomical calculations, as well as in horology and trigonometry. It operated with letter numbers from one to fifty-nine. This system represented both negative and positive numbers, distinguished by their position. It also denoted the absence of a number (i.e. zero) by the symbol ō. The Indian decimal place value system, which employed Indian numerals, commonly referred to as Arabic numerals today, was introduced in Byzantine science in the middle of the thirteenth century. It coexisted with the Greek mathematical notation system until after 1453.

Number symbolism found multiple uses in Byzantine culture as it was a popular device employed by rhetoricians, philosophers, politicians, writers, artists, and architects. Byzantine number symbolism inherited its main principles from the Pythagorean and Neoplatonic philosophy, as well as from the subsequently developed Christian exegesis and theology which also had to explain the origin of multiplicity in a world with monadic beginning, i.e. God. Particular significance was ascribed to various numbers, such as one (e.g. God is one, and so is the emperor), two (e.g. concerning the two natures in Christ, namely divine and human), and three (e.g. with respect to the angelic hierarchy being structured into three orders, or referring to the Trinitarian doctrine of God’s one substance and three hypostases). Besides a mere rhetorical or allegorical device, number symbolism was the subject matter of a specific literary genre, the so-called theologoumena arithmetikēs or ‘theology of arithmetic.’ At least three different theologoumena are preserved, though partially: 1) by Nikomachos of Gerasa; 2) by Anatolius of Laodikeia (3rd century); 3) and by someone from the circle of Iamblichus (d. ca. 325). They were very well received in Byzantium and continuously copied and reused, as Christian examples and exegesis were introduced into the corpus. The theologoumena were structured as brief textbooks of ten chapters. Each chapter was dedicated to one of the numbers in the decade. The interpretation of a given number’s symbolic meaning included material from mathematics, musical theory, astronomy, medicine, grammar, and so forth.

2. Mathematical Foundation

The mathematical sciences in Byzantium inherited their material and methods from the Greek mathematics of antiquity and were subsequently influenced by the developments in the Arabic, Persian, Latin, and Jewish science. Mathematics was the foundation of astronomy, astrology, the computus (i.e. the calculation of the date of Easter), of financial transaction and architectural construction.

Most influential in the studies of the mathematical sciences in Byzantium were the works of Euclid, Nikomachus of Gerasa, Diophantus of Alexandria, Apollonius of Perge (d. ca. 190 BCE), Archimedes (d. 212 BCE), Ptolemy, Pappus (fl. ca. 320), Theon of Alexandria (fl. ca. 360-380), and Heron. Nikomachus famously circumscribed the cycle of the four mathematical disciplines or tetraktys tōn mathēmatōn, namely arithmetic, geometry, music and astronomy. The works of Euclid, in turn, provided the basis for the study of geometry and were continuously read throughout the Byzantine millennium.



The importance of Euclidean mathematics in Byzantium is comparable only to the influence Ptolemaic astronomy exerted on its medieval Greek counterpart. The systematic exposition of mathematical astronomy in Ptolemy’s Almagest and Handy Tables, as well as Theon’s commentaries were read continuously in Byzantium and though during the thirteenth century the study of the higher mathematical sciences was interrupted for about hundred years, astronomy was revitalized and reintroduced towards the end of this period.

Two main trends in the development of Palaiologan science can be distinguished: on the one hand, Ptolemaic astronomy was consciously reintroduced in practice and publicized by several generations of scholars, most of them connected to the Chora monastery in Constantinople. The main driving force behind this enterprise was Theodore Metochites (d. 1332), though his work was already prepared by the efforts of Maximos Planudes (d. ca. 1305) and Manuel Bryennios (fl. ca. 1300). Nikephorus Gregoras (d. ca. 1360) continued Metochites’ efforts and then handed over the task to his own students, notably to Isaac Argyros (d. ca. 1375). On the other hand, an alternative trend in the study and practice of astronomy emerged under the influence of Islamic astronomical works coming mainly from Tabriz and introduced in Byzantium by Gregory Chioniades (d. ca. 1320) and later on popularized by scholars such as George Chrysokokkes (fl. ca. 1335-1350), Theodore Meliteniotes (d. 1393), and John Abramios (fl. 1370-1390). Moreover, through the court of Hugh IV (r. 1324-1359) of Lusignan those who maintained connection with Cyprus, like Nikephorus Gregoras, had access also to Latin astronomical treatises.

1. Astronomical Instruments

In order to study the configurations of the fixed stars, the movements and conjunctions of the five planets, the positions of the two luminaries, the sun and the moon, with respect to the earth and to each other, the Byzantines used the astrolabe, an astronomical instrument which converted with the help of stereographical projection the three-dimensional celestial sphere visible from a defined geographical latitude into a dynamic two-dimensional map of the sky projected on the equatorial plane. Though only one Byzantine astrolabe survives today, there are descriptions of the instrument, depictions, as well as treatises and diagrams dedicated to its construction and usage preserved in numerous Byzantine codices. Ptolemy himself described the principles of the astrolabe in his Projection of the Surface of a Sphere. His work, however, was not known in Constantinople after the early Byzantine period. Nevertheless, commentaries of the Almagest, such as Pappus’ and Theon’s, provided instructions for the construction of the astrolabe and various other observational instruments listed in the Almagest, e.g. meridional and equinoctial armillaries, a plinth, an armillary sphere, a parallactic instrument, a diopter. The treatise on the astrolabe composed by John Philoponus (d. ca. 570), as well as the earlier description of the instrument by Synesios (d. ca. 413), served as models for Palaiologan contributions on the subject such as Nikephorus Gregoras’ On the Construction of the Astrolabe (in two redactions), as well as the works by Isaak Argyros and Theodore Meliteniotes. Astrolabes found their use not only in measuring the longitudes of the stars, but also in time-keeping, and probably in navigation. Importantly, they were portable and they could be used both by night and day.

The actual observational use of astronomical instruments in Byzantium is scarcely attested. One such instance is contained in a lengthy marginal note on f. 275 in codex Laurentianus 28, 16, authored probably in 1389 in Constantinople, by the astronomer and astrologer John Abramios. John mentioned that with the help of a diopter, he observed one of the fixed stars, namely the Southern Crown, and calculated its longitude. Then, he reported adjusting his astrolabe accordingly and calculating the time of night when his observation was recorded. The estimation of the precise hour was confirmed by the sound of a clock. He repeated the same procedure in his observation of other stars.

2. Horoscopes

Byzantine mathematical astronomy, as well as its counterpart, the pseudo-scientific astrology, strove to produce accurate representations of the heavens. The astrolabe depicted the sky and the configurations of the heavenly bodies for a given geographical latitude, while a horoscope, for instance, provided a map of the positions of the heavenly bodies in the zodiac at a given moment in time. Some Byzantine horoscopes are simple lists of longitudes; others include diagrams and interpretation. Casting political horoscopes, such as the horoscopes of emperors, cities, and even religions (e.g. the horoscope concerning the future of Islam cast by Stephanus of Alexandria in the late sixth/early seventh century) was not uncommon in Byzantium. A handful of political horoscopes are preserved, among them the horoscope of Constantinople for May 11, 330, cast in ca. 990 by a certain Demophilos (the name is possibly a pseudonym, or it indicates that the method of an eponymous ancient astrologer has been applied) which predicted the end of the city 696 years after its foundation, that is, in 1026. An anonymous eleventh-century astrologer extended the foretold life of the city with a hundred years, i.e. to altogether 796 years. In the twelfth-century, the authorship of Constantinople’s horoscope has been attributed to a certain Valens who was allegedly commissioned to cast the horoscope by emperor Constantine himself, on the eight day of Constantinople’s inaugural festivities.


As illustrated by the example of John Abramios using an astrolabe to determine the precise time, Byzantine scholars used astronomical instruments and related technology for the purposes of timekeeping. In Byzantium the term horologion was applied to any timekeeping device used to measure time or to indicate a specific moment in time. More often than not, a horologion meant a sundial or a water clock. Timekeeping was essential for regulating the administrative and ceremonial life of a given community. For instance, the Rule of the monastery of St. John Stoudius in Constantinople (ninth century) mentions the use of a water clock equipped with an alarm to rouse the “waker,” a monk in charge of awakening the rest of his brothers. In addition, the existence and use of several public horologia in Constantinople (both sundials and water clocks) are attested in textual sources, though no material evidence survives. Perhaps the most well-known is the horologion at the southwestern corner of Hagia Sophia erected in 838/39 under emperor Theophilos and patriarch John the Grammarian. According to Hārūn Ibn Yaḥyā’s description (ca. 900), the construction had twenty-four little square doors, one for each hour of the day and the night. At the end of every hour one door was opening on its own. Another monumental clock was erected earlier by Justinian I, in 535 next to the Milion, while until the sixth century, a horologion was positioned between the Augusteion and the Basilike. The latter was subsequently moved to the Chalke where it remained at least through the seventh century, and probably also through the eighth, when it was restored by Constantine V (r. 741-775). Under the reign of Justin II (r. 565-578), another monumental clock (perhaps a sundial) was installed at the northeastern corner of the Basilike and presumably it was functioning up to the ninth century. Patriarch Sergius I (610-638) installed a sundial in the garden of the Patriarchate, between Hagia Sophia and the Augustaion. Textual sources mention three other horologia: 1) a clock, probably a sundial, located in the imperial palace in a hall across from the Tripeton; 2) a clock positioned on the forum of Constantine; 3) and a horologion in the church of the Holy Apostles, probably erected in the basilica’s atrium. Among the service personnel that maintained the imperial palace, there were clock attendants who belonged to the larger group of the diaitarioi under the supervision of the eunuch papias, a sort of supreme concierge of the palace.

1. Mechanics and Automata

While several public clocks were on display in Costantinople, a related type of fine technology was employed for the purposes of the imperial display of power at court. During the reign of Constantine VII Porphyrogennetos (r. 945-959) there were at least three elaborate automata, or self-operating machines, engaged in the presentation of the emperor, in particular during audiences with foreign visitors. Liutprand of Cremona, who visited Constantine’s court in 948 and 966 described a tree with singing birds, mechanical lions, and an imperial throne, the so-called “throne of Solomon,” that could raise up from the ground. The tree was located in front of the throne and it was made of gilded bronze. Its branches were filled with birds of the same material twittering with different sounds according to their species. The mechanical gilded bronze lions guarded the imperial throne and were able to strike the ground with their tails and to roar with open mouth and quivering tongue. The throne itself was of immense size and could rise towards the ceiling. Other examples of Byzantine fine technology included self-regulating fountains, trick vessels that were able to contain different liquids without mixing them, vessels that always kept the same amount of liquid, mechanical theatres, pipe organs, and astronomical computing devices among others.


The ancient cartographic tradition the Byzantines inherited was based on mathematics and practical observation and found its ultimate manifestation in the works of Ptolemy. Map-drawing required both geographical and astronomical knowledge and found an immediate application in navigation. Though no Byzantine maps earlier than the end of the thirteenth century survive, the textual evidence suggests that maps existed and were sometimes associated with books of sailing directions for navigators. The so-called periploi usually describe sea travel from port to port, mentioning the distances between ports, providing information about the coasts, the winds, the nearby fortresses and even about the local produce and customs. Several early Byzantine periploi survive today and none includes maps, thus it has been suggested that the usage of maps for practical purposes in Byzantium was in decline during the early life of the empire.

Maps were employed not only for practical purposes, but also for display of imperial power. A case in point is the so-called Theodosian map, a map of the eastern Roman empire commissioned by emperor Theodosius II (emperor of the East 408-450). Though the map itself has not survived, it was probably still extant in the ninth century. Moreover, the poem in Latin hexameters attached to it was preserved. World maps were not used in navigation or travel; instead, regional maps assumed this function. However, with the exception of a sixth-century mosaic map of Palestine, no regional Byzantine maps survive before the thirteenth century.

Specific feature in the development of Byzantine geography and cartography is the neglect of Ptolemy’s Geography on behalf of Byzantine scholarship and its rediscovery in the end of the thirteenth century. The driving force behind the revival of Ptolemaic geography in Palaiologan Byzantium was the activity of Maximos Planudes who in 1295 successfully acquired and reedited Ptolemy’s treatise. Worth mentioning are two codices containing the Geography: 1) Vat. gr. 177, dated to the end of the thirteenth century, which was in Planoudes’ possession while he was residing at the monastery of Christ Saviour in Chora; 2) and Vat. gr. 191, a thirteenth or fourteenth-century manuscript containing in addition a number of astronomical works. Both manuscripts do not include any maps; however, they both contain notes indicating that the codices were supposed to comprise twenty-six or twenty-seven maps respectively. The three oldest manuscript witnesses of Ptolemy’s Geography containing maps date to the late thirteenth century and are also associated with Planudes’ editorial activity. These are codices Urbinas gr. 82 with twenty-seven maps, Seragliensis 57, and Fragmentum Fabricianum Graecum. Another branch of the Ptolemaic manuscript tradition transmits the Geography accompanied by sixty-five maps. One of the earliest examples is the early fourteenth-century codex Laurentianus Plut. 28. 49.


Alchemy is primarily based on the theory of the possibility of transmutation of metals into gold and silver. Alchemical texts were produced in Byzantium and they could be either practical lists of recipes or highly theoretical and allegorical mystical works. One collection that contains both types of texts is the so-called ‘alchemical corpus’ which was put together at some point between the seventh and the eleventh centuries. The principal manuscript witnesses of the collection date respectively to the end of the tenth or the beginning of the eleventh century (Marcianus gr. 299), to the thirteenth century (Parisinus gr. 2325), and to 1478 (Parisinus gr. 2327). They contain a large number of works dating from the beginning of our era to the fifteenth century, such as the writings of Pseudo-Democritus (2nd century CE), Zosimus of Panopolis (fl. 300 CE), Synesius, Olympiodorus (d. after 564/5), Stephanus of Alexandria, the Anonymous Philosopher (7th-9th centuries) and others.

The ‘alchemical corpus’ reflects three major trends characteristic of the practice of alchemy in Byzantium. First, the Corpus transmits the works of Zosimus who was considered the chief authority on the subject and exerted a significant influence on later authors. Second, the collection’s content alludes to the growing interest in the study of alchemy in seventh-century Byzantium during the reign of emperor Heraclius (r. 610-641). Not only the Corpus contains, among other texts, four alchemical poems dated to this period, but also its version preserved in Marcianus gr. 299 included three alchemical writings authored by Heraclius himself and subsequently lost. Finally, among the middle and late Byzantine additions to the Corpus, one finds both purely theoretical works such as Michael Psellos’ letter On How to Make Gold addressed to patriarch Michael I Cerularius in ca. 1045/6, and fairly practical recipes and technical treatises which comment, among other things, on the silver and goldsmiths’ practices of tempering and dyeing of metals (e.g. of copper and iron), glass-making, processing and imitating precious stones, cleaning and imitating pearls, purifying and welding gold and silver, mold-making, and even illuminating books with gold and silver. Thus, the Corpus provides useful information for the production of luxury goods in Byzantium. Importantly, even if technical Byzantine recipes are preserved, they rarely provide all the information needed for their successful use. More often than not, the recipe included a general description of the working method and of the materials, but omitted the most significant detail, namely the exact proportions of the ingredients, thus preserving part of the alchemical art and/or the metallurgical craft secret, to be orally transmitted from master to student.

The imperial workshop in Constantinople, associated with the palace, deserves a special mentioning. The manufacture, storage and distribution of goldwork for palace use, of certain copied or illuminated books, and most importantly, of coins was a subject of state monopoly and it took place in special workshops scattered throughout the empire. After the seventh century, however, it seems that the provincial workshops vanished and this specialized production remained restricted to Constantinople. Thus, the activity of the imperial goldsmith is well-attested in the medieval sources. For instance, it manufactured the crowns the emperors ordered for personal use, as well as for votive offerings or diplomatic gifts.


Medicine in Byzantium, both theoretical and practical, carried on and developed the Greco-Roman tradition of Hippocrates and Galen and additionally, it employed the means of astrology, magic, and folk medicine. Byzantine medical manuscripts, as well as saints’ lives list a number of illnesses such as malaria, tuberculosis, blindness and deafness, dropsy, intestinal problems, ulcers, paralysis, leprosy, mental disorders, urinary problems and hemorrhage, menstrual anomalies and problems with lactation in the case of women, as well as cancerous lesions. Byzantine pharmacology provided variety of drugs to treat the ill, as it is attested by the medical encyclopedias of Alexander of Tralles (ca. 525-605) and Paul of Aegina (fl. ca. 640). Drug lists were also inherited from the works of Galen, as well as from Dioscorides’ De materia medica. Additionally, by the eleventh century one finds Arabic, and Hindu spices mentioned in Byzantine medical texts, such as the works of Simeon Seth (fl. ca. 1071-1078). Byzantine drug lore used approximately 700 herbal, animal and mineral simples and applied traditional drugs such as opium poppy, hellebore, blister beetle solution, caustic mineral wash, soft emollients based on rose oil, kaolin, and so forth.

Hospitals, that is, charitable foundations providing the sick with overnight accommodation and medical service, existed not only in Constantinople, but also in the provinces. With the transformation of Constantinople from a late antique into a Christian city and the related proliferation of churches after 450, hospitals and other philanthropic institutions (e.g. old-age homes, poor-hostels, etc.) were established in the capital. The anonymous collection of miracles of St. Artemius written ca. 660, for instance, described the healing wonders performed by the martyr at his shrine at the Church of St. John Prodromos in Constantinople, primarily related to the treatment of genital tumors. In addition, the forty-five miracle stories provide some information on the hospitals in the capital at the time, e.g. the xenon associated with the Church of St. John Prodromos. The Miracles also comment in passim on surgical practices. One story describes an unsuccessful groin surgery performed at the Sampson Xenon (the oldest philanthropic medical institution in Constantinople opened towards the end of the fourth century), while another tells the story of St. Artemius himself conducting a surgical intervention. One of the better-documented medical institutions in Constantinople was the hospital at the monastery of Christ Pantokrator founded in 1136 by emperor John II Komnenos. According to the Pantokrator’s typikon, the monastery hosted and maintained two charitable institutions, namely a nursing home for twenty-four aged or infirm men and a hospital for fifty patients. Importantly, Byzantine hospitals not only provided medical care for the sick, but also organized and sustained the education and training of prospective physicians.


Throughout the Byzantine millennium, Constantinople acted as a major center of scientific production, consumption and exchange. Despite the lack of established higher-education curriculum and corresponding institutions, the proximity to the center of imperial power facilitated the preservation of ancient knowledge and technologies and in some cases enhanced their development, thanks to or in reaction to the corresponding developments in Latin, Persian, Indian, and Jewish science. A case in point is the revival of Ptolemaic studies during the Palaiologan period, notably in the fields of astronomy and geography, connected with the activity of several Constantinopolitan scholars based in the monastery of Christ Saviour in Chora. The sciences in Byzantium, both the mathematical and the related disciplines of geography, alchemy, and medicine, advanced and employed technologies that could be used for multiple purposes, as for instance, in the case of astronomy and timekeeping, or in the case of alchemy and metallurgy. In terms of their methods, the present article argues, Byzantine sciences shared a common mathematical foundation they consequently employed in measuring and mapping the earth, the heavens, and the human body.




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This article was originally written in English for History of Istanbul and its Turkish translation was published in 2015.