Regiomontanus's oration: overview, context, legacy and relevance

Regiomontanus held a course on astronomical studies at the University of Padua in 1464. From that series of lectures, what has come down to us is the inaugural speech – an oration that introduced the topic of the course, namely the astronomer al-Farghani, who was known in the Latin world as Alfraganus or Alfarganus, while simultaneously praising the mathematical sciences and their utility. The oration provided some accounts of the background of each of the sciences according to Regiomontanus's contemporary classification and personal taste – with an emphasis on the continuity of the mathematical tradition, portrayed as a transfer of knowledge from one culture to another through the efforts of translation.Footnote ⁵ According to Regiomontanus, the origins of mathematics can be traced back to the flooding of the Nile – a natural event that forced the Egyptians to develop techniques of land surveying and geometry. From Egypt, it was received by the Greeks, who produced works that remain fundamental: Euclid's Elements and the work of Hypsicles (translated into Latin by Boethius), as well as the works of Apollonius and Archimedes (translated into Latin by Jacob of Cremona). As for number theory (arithmetica), it is followed through all the way to Pythagoras. Regiomontanus goes on to mention Euclid's Elements (Books 7–9) and the Latin Jordanus Nemorarius as well as Diophantus and the Byzantine Barlaam of Calabria. Diophantus, who is remembered as the founding father of algebra, survived only in Greek, and Regiomontanus wished to have him translated into Latin as soon as possible.Footnote ⁶

Regarding astronomy and stargazing, its initiators are identified as biblical or mythical figures such as Abraham, Moses, Prometheus and Hercules, but it is the Greek Hipparchus who is named as the founder of proper mathematical–astronomical studies. Astronomy is then shown to reach a peak with Ptolemy and his Almagest. Regiomontanus relates the achievements of prominent Arabic astronomers, and mentions al-Battani, Jabir ibn Aflah and al-Farghani by name. Noted in due course are the Persian astronomical tables and the Indian observation of the obliquity of the ecliptic. Among contemporary astronomers, two Paduans are lauded: Pietro d'Abano and Giovanni de Dondi, along with Antonio de Montulmo, as well as scholars of Germanic origins, such as Albertus Magnus and Georg Peuerbach: the latter had been Regiomontanus's master at the University of Vienna. After brief sections devoted to music and optics, astrology is celebrated as the queen of mathematical sciences owing to its capacity to connect the heavenly and the earthly realms. However, Regiomontanus stresses the importance of possessing a solid mathematical background prior to practising astrology. Contrary to the prevailing fashion of his time, which held that basic knowledge sufficed for aspiring astrologers who needed only to read John of Hollywood (better known under the Latinized name Sacrobosco), Regiomontanus advised far stricter standards. He recommended making detailed observations of the celestial bodies as a prerequisite for arriving at correct predictions.

Although Regiomontanus's oration contains brief accounts of the history of each science, the text does not belong to the genres of either historiography or biography. Instead, its proper genre is demonstrative, or epideictic, oratory. Rooted in ancient Greek rhetoric, this evaluative genre aims to show why its topic is worthy of either praise or condemnation. In this case, Regiomontanus aimed at praising the sciences by tracing their ancestry, invoking their most prominent exponents and works, and expounding on why the arduous study of the subject is worth the effort – a not insignificant detail for a university course. Accordingly, when he recounts the scientific contributions of Greeks, Indians, Arabs and Latins, he is not so much investigating the transmission of knowledge proper as he is showing the genealogy, and hence the prestige, of the sciences practised in his own time.

In spite of the limitations of the literary genre, the importance of Regiomontanus's oration for the history of science was immediately obvious to his contemporaries: the text, in fact, survives thanks to a widely circulated printed edition of a compendium of al-Farghani (Rudimenta Astronomica Alfragani), published in Nuremberg in 1537 by Johannes Schöner for the Petreius Press, in which the lecture was published as an additional introductory piece (the city of Nuremberg was chosen by Regiomontanus to establish a press devoted to the printing of scientific works).Footnote ⁷ This edition spread all over Europe and influenced the next generations of scholars. Already by 1549, Erasmus Reinhold, prominent sixteenth-century astronomer and professor of mathematics at the University of Wittenberg, had Regiomontanus's oration reprinted and praised him as a leading and exemplary scholar of mathematics and the humanities at large.Footnote ⁸

Pierre Gassendi recalls passages of the oration in his biography of Regiomontanus, published in 1654 in a volume containing the biographies of eminent astronomers, such as Tycho Brahe, Nicolaus Copernicus and the Viennese astronomer (and master of Regiomontanus) Georg Peuerbach. A genealogy of anti-Scholastic learned men was thus constructed through this publication.Footnote ⁹ The relevance of Gassendi's biographical sketch lies in the methodology of evaluating Regiomontanus's works from his text. Gassendi acknowledges that the principal value of the text resides in its praising of mathematical sciences as superior to other disciplines for the certitude they provide. He also commends Regiomontanus's efforts to study Latin, Greek and Arabic astronomy as necessary for correcting the errors of the past and reaching a contemplative status of knowledge.Footnote ¹⁰ The emphasis he places on the highest degree of certitude provided by mathematics reflects Gassendi's own agenda.

In addition to appreciating the mathematical sciences, the oration also praised the traditional arts – as a traditional humanist literary product extolling the virtues of learning. It is important to keep in mind that valuing mathematics for its certitude, although an established view in the scientific literature of the time, was not the done thing in an institutional context, where the highest degree of certitude was usually ascribed to theology. This cultural climate makes the oration all the more interesting.Footnote ¹¹ In light of all of this, the oration is a unicum – there are no previous lectures of this kind.

Another key aspect of the document, already acknowledged by Gassendi, is the cross-cultural character of Regiomontanus's interests. On this account, Gassendi considered Regiomontanus and Peuerbach as rediscoverers of the astronomical sciences.Footnote ¹² Indeed, another point of relevance is that the history of the oration is linked to the reception of Arabic astronomy in the Latin world, especially that of al-Farghani and al-Battani. As previously noted, the printed edition of the oration appeared in the compendium of al-Farghani (which contained a translation of al-Battani as well) in 1537, in Nuremberg.Footnote ¹³

Another point raised by Regiomontanus deserves our attention, namely his treatment of algebra (ars rei et census). He is the first Latin scholar to mention Diophantus of Alexandria as the founder of algebra – a fact that would soon enough give rise to an inquiry into the history of algebra: whether it was born of Greek or Arabic mathematics.Footnote ¹⁴ Cardinal Bessarion, Regiomontanus's patron, was likely acquainted with Diophantine mathematics, given that his master in Constantinople, John Chortasmenos (c.1370–1431/7), is remembered as the Byzantine scholar who, in a marginal note of a manuscript, cursed Diophantus for the difficulty of his problem and sent his soul to the Devil.Footnote ¹⁵

The enthusiasm for algebra which Regiomontanus expressed in the oration significantly influenced the subsequent history of mathematics in the Latin-speaking world. Several arithmetic books published across Western Europe cited and reprised Regiomontanus's view on the history of algebra. For instance, Johann Scheubel's Algebra (1550) took that view for granted and Petrus Ramus in his Scholae mathematicae (1569) argued about a lineage leading from ancient Greece through Byzantium to Western Europe, again in line with Regiomontanus's authoritative view.Footnote ¹⁶

According to historians of mathematics such as Jens Høyrup, the failure to acknowledge Arabic sources on algebra was an intentional move, influenced by the political propaganda of humanists with whom Regiomontanus had contact in Italy. This strategic omission, alongside the mythologizing of Archimedes, served to emphasize the utility of mathematics to Italian and European patrons of the arts and sciences.Footnote ¹⁷ Nevertheless, it should first be noted that most humanists were not as knowledgeable about mathematics as Regiomontanus was, so they might have given his words an uncritical reception. Second, Regiomontanus spoke of algebraic literature that was accessible in Arabic, but it is not clear whether or what aspects of that literature were available in Latin translations. If the most advanced Arabic algebraic texts were unavailable in Latin, then it would make no sense to argue that Regiomontanus was siding with an anti-Arabic agenda.

Regiomontanus's oration: Bessarion's influence

Regiomontanus's enthusiasm for Greek mathematics and his own study of the Greek sources reflect his ongoing contact with his patron, Bessarion. Like many other Byzantine scholars, Bessarion became part of the Byzantine scholarly diaspora, which had begun long before the fall of the Byzantine Empire in 1453. This diaspora provided a decisive impetus to the scholarly interest in Greek studies in early modern Italy and initiated the race to build renowned humanist libraries, which, compared to their medieval counterparts, would not run out of Greek originals. Euclid and Archimedes, for instance, were a must-have in both Latin and Greek.

The most important event for the study of Greek in Italy was the Council of Florence in 1438–9, convened to discuss the unification of the Churches of Rome and Constantinople. This forum saw prominent Byzantine scholars, such as George Gemistus Pletho and Bessarion, meet de visu with humanists like Poggio Bracciolini, Lorenzo Valla and Nicholas of Cusa. On the face of it, a union of the churches was tentatively accomplished, but de facto it failed. That convention marked the beginning of the humanist forays into Byzantine territories for the purposes of manuscript hunting. The new acquisitions made Italian libraries the most important in the Western world. Notable amongst these were the library of Pope Nicholas V (1397–1455) in Rome. However, the manuscripts collection of Regiomontanus's patron, Cardinal Bessarion, came to symbolize the merging of knowledge between the East and the West and the preservation of civilization from what contemporaries perceived as the threatening, barbarous enemies of Christianity, the Ottoman Turks.

Bessarion had shown scientific inclinations since his youth. In 1438, he travelled to Florence with his master, the Neoplatonic philosopher George Gemistus Pletho. Pope Eugene IV appreciated Bessarion's conciliatory viewpoints (favouring the union of the churches) and invested him with the rank of cardinal. From 1440 onwards, a Catholic convert and a cardinal, Bessarion lived in Italy and dedicated immense effort to Greek studies, including the sciences. His manuscripts collection, donated to the Republic of Venice in 1468, contained all major Greek mathematical writings.Footnote ¹⁸

In 1460 Bessarion arrived in Vienna as papal legate whose mission was to obtain imperial support for the war against the Ottomans. There he met Peuerbach and his student Regiomontanus and acquainted them with his project to translate the Almagest into Latin. He then invited them to travel back to Italy with him and to assist him in the task of translation. Peuerbach died not long afterwards, but Regiomontanus joined the Cardinal's patronage for the years to follow. During this period, Regiomontanus completed Peuerbach's Epitoma Almagesti (Epitome of the Almagest) and wrote, among other works, his renowned treatise on trigonometry, De triangulis (On Triangles).

Thanks to Bessarion and his circle of Greek scholars, Regiomontanus learned Greek in order to inspect scientific texts in their source language. This enthusiasm explains why in his oration the mathematical tradition is constellated by ancient Greek scholars, while the Arabs (whether intentionally or not) are not fully acknowledged. As for the astronomical tradition, Regiomontanus did indeed praise the Arabic contribution, devoting the very topic of the course at the University of Padua to an Arab astronomer. The discrepancy between the treatments of the Arabic tradition in other fields of mathematics and in astronomical studies is another potential indication in support of the claim that Regiomontanus adheres to the ideological programme of the humanists as far as pure mathematics is concerned; that is, the programme to construct a narrative of the rebirth of Greek mathematics by emphasizing the relevance of Archimedes and excising the achievements of Islamic mathematical tradition.Footnote ¹⁹

It is true that Regiomontanus was likely influenced by the humanists he met through Bessarion and by Bessarion himself, and that Bessarion stressed the Greekness of scientific knowledge, especially after the capture of Constantinople in 1453. However, there are facts that stand contrary to the claim that Regiomontanus and Bessarion adhered to a Greek purist, anti-Arabic agenda. First, astronomical tables of the Islamic tradition are preserved in several good-quality manuscripts in Bessarion's collection, including one penned by Bessarion himself.Footnote ²⁰ Second, Bessarion's education included not only Ptolemy, but also Islamic astronomy. The advancements of the Arabic tradition were officially acknowledged by major institutions in late Byzantium.Footnote ²¹ Third, the topic of Regiomontanus's lecture does not indicate an anti-Arabic agenda.

Moreover, it is also worth recalling again that: (1) modern philological sensitivity at the time of Regiomontanus is non-existent, thus his statements on the nature of textual transmission must be accepted with caution; (2) it is not clear what Latin translations of advanced Arabic algebra were at Regiomontanus's disposal. All of this begs the question: was Bessarion completely in line with the Latin humanists? To what extent did the Graeco-Arabic astronomical heritage, preserved by Bessarion, influence Regiomontanus? Does this heritage coincide with the humanist views?

Contained in the oration are three lesser-known elements which, in light of research on the Byzantine heritage in early modern Italy, could also clarify to what extent Regiomontanus was influenced by Bessarion and the latter's intellectual background. First, there is the praise for astrology. As Darrel Rutkin points out, Regiomontanus considered astrology, not astronomy, the queen of mathematical sciences, because its method allowed for the provision of meaningful insights into the natural and human realms and into the divine realms.Footnote ²² As we shall see below, astrology was a sensitive topic in late Byzantium. In addition, there are two significant works of Byzantine astronomy, namely Barlaam's Logistic and the Byzantine versions of The Persian Tables, mentioned in the Paduan oration.Footnote ²³ Together, these three elements provide insights into a preliminary understanding of the influence of the Byzantine intellectual heritage in the advancement and institutionalization of astronomical studies in the Italian university context. For this reason, a more in-depth examination is warranted.

Astrology and physical properties of the heavens in fourteenth-century Byzantium

Regiomontanus's praise for astrology likely reflects Bessarion's own views. Bessarion's patronage was not merely financial, but also intellectual. The close bond between the two men was evident in astronomical research, manifesting itself more specifically in their shared interest in understanding the Greek of Ptolemy's Almagest or the computational intricacies that went into the composition of the Epitoma Almagesti.Footnote ²⁴ Given the fact that astrology was removed from the official branches of knowledge in Byzantium after the Council of Constantinople of 1351, Regiomontanus's support for it becomes all the more significant.

The debate over the legitimacy of astrology had a profound impact on fourteenth-century Byzantium. Astrology, a practice present throughout Byzantine history and in numerous other cultures, has been extensively examined by scholars in the fields of intellectual history and philology.Footnote ²⁵ Summing up the collective insights from previous scholarly inquiries, it is clear that the most difficult task remains the development of critical tools with which to understand the writings of these Byzantine scholars and their transcriptions of astronomical works. This work is essential in understanding the enterprise of writing astrology or astronomy through their eyes, thus attaining an aspect of the historicity of astrology and, in so doing, avoiding applying our categories to the past.Footnote ²⁶ Some Byzantine scholars decided to treat the celestial bodies as mere abstract objects, whereas others continued to advocate investigating the physical properties of the planets, alongside the abstract properties, seeing in this a means to attain the contemplation of God and God's providence, which at that time was the ultimate goal of astronomical studies in the East and the West. Eventually, the former came to view the latter as heretics and at risk of the damnation of their souls.

In other words, the key distinction between groups of Byzantine scholars active in astronomy lay in the properties of the celestial bodies considered relevant when contemplating the heavens. This choice had a decisive influence on the future developments of astronomical studies in Byzantium from the second half of the fourteenth century. It was a time that coincided with a massive crisis in both foreign policy and internal social cohesion – the empire was a pale shadow of its former glory. Nevertheless, learned men continued to extensively practise astronomical studies and most of them were aware that the study of the heavens was problematic in the fourteenth century.Footnote ²⁷ The solution to astronomical problems and their relationship with theological concerns was likely to be found in correcting or reforming Ptolemy in a way tantamount to establishing a new model – intellectual challenges which, as the Latin world was about to experience a few years later, provoked debates and had major repercussions in politics, economics and society at large. Those Byzantines agitating for reforms or new models were in favour of astrology and the possibility to investigate the celestial bodies in their physical properties. Due to their non-Orthodox views, however, these scholars were precluded from having a career in the official echelons of the church and the empire (the Byzantine deep state) in Constantinople. Notably, Bessarion's master, the Neoplatonic philosopher Georgius Gemistus Pletho, was one of those longing for innovation in astronomical studies as well as wider social renewal. Pletho was convinced that the solution for the resurrection of the Roman Empire would come through a revival of Greek philosophy and mythology as well as through Platonic cosmology, thus establishing Platonic philosophy as the basis for both metaphysical speculation and physical science.Footnote ²⁸ It is in this spirit that Pletho's pupil was taking to Europe the so-called Greek knowledge, alongside the will to investigate the heavens in their physical properties.

Besides reprising the Vienna academic astronomical tradition of Langenstein, von Gmunden, and Peuerbach, Regiomontanus's praise for astrology speaks to an important shared intellectual basis with Bessarion.Footnote ²⁹ But the origins of this common basis are distinct, and an analysis of the two Byzantine works mentioned by Regiomontanus will elucidate this intellectual scenario.

Barlaam of Calabria and the core Byzantine problem on astronomical sciences

Barlaam of Calabria (c.1290–1348), whom Regiomontanus praises in the oration, was a Greek monk from southern Italy and one of the best mathematicians among all late Byzantine scholars.Footnote ³⁰ He is, notably, the only one to have produced an original mathematical work, the Logistic, a theoretical treatise on arithmetic organized in six books.Footnote ³¹ Testimony to the relevance of Barlaam's work to the European Renaissance are two printed versions of his Logistic: one by the Swiss mathematician Conrad Dasypodius (1572, Strasbourg) and another by the English mathematician John Chamber (Paris, 1600).Footnote ³² Moreover, Barlaam is the key figure through which to interpret the consequences for astronomical studies of the decisions that the Byzantine Orthodox authorities took at the 1351 Council of Constantinople on the question of the Filioque. That convention sanctioned the theological doctrine of the Byzantine scholar Gregory Palamas (1296–1359) on divine substance and energies as official for the Orthodox Church, thus irredeemably widening the divide between the Eastern and Western Churches.Footnote ³³ This solution to a theological controversy coincided with a socio-historical turning point that involved a well-known political dispute within Byzantine society, culminating in the hegemony of the hesychasts in formal Byzantine culture. Here it is worth keeping in mind that, most of the time, hesychasts were anti-Latin.Footnote ³⁴

In the first half of the fourteenth century, the hesychasts, a group of monks from Mount Athos, became very influential in the Byzantine political sphere. One of their distinctive claims was that their practice of prayer and ascetic struggle allowed them to see God with their own eyes in the form of light (uncreated light). Around 1337, this specific claim of theirs was ridiculed as insane by Barlaam, who at the time was lecturing on philosophy in Constantinople. Barlaam's attack itself was a reaction to previous attacks against him. Some Orthodox exponents had accused him of adopting non-Orthodox philosophical arguments in his theological works. One of these exponents, Gregory Palamas, had criticized Barlaam before 1337 for using unacceptable terms in discussing the problem of the insertion of the Filioque into the Nicene Creed. On the basis of Aristotelian demonstrative philosophy, Barlaam had claimed that, given that God was unknowable and non-demonstrable to humans, it would not be possible to demonstrate the procession of the Holy Spirit either. This meant that the Latin views on the Filioque were indefensible, and the Orthodox view was proven right.Footnote ³⁵

Notwithstanding the use of Aristotelian philosophy on the Filioque and the subsequent attack of the hesychasts, Barlaam had not contradicted Orthodox positions. But these interrelated issues touched an extremely sensitive point of Orthodoxy: for Palamas, the question of the possibility of demonstrating the procession of the Holy Spirit triggered the problem of whether God is the subject of certain knowledge, and denying that demonstrability was equivalent to the claim that God is not the subject of certain knowledge.Footnote ³⁶ Therefore Gregory Palamas responded to Barlaam by developing a doctrine explaining, in philosophical terms, how the transcendent God could be visible to human eyes.Footnote ³⁷ His arguments were based on two notions stemming from the Greek philosophical vocabulary, namely the terms ousia (substance, essence) and energeia (activity, operation): the divine ousia is unknowable to any human intellect, but the divine energeia (such as the uncreated light the hesychasts claimed to see) can be reached through prayer and ascetic struggle. By reaching the contemplative status of a divine energeia, human beings became godlike inasmuch as they participated in it. The hesychast monks could have access to energeia through the purification of the heart, a goal to be pursued through prayer, asceticism and obedience to the divine commandments. The Council of 1351 was the final chapter of a series of synods convened at Constantinople to discuss and evaluate Palamas's doctrine, the defence of the hesychasts and related theological and political problems. At any rate, the core problem that triggered all the subsequent discussion between Barlaam and Palamas lay in the vexata quaestio of the Filioque.

The debates on hesychasm came to coincide with the discussion on whether ascetic practice and prayer are superior to secular scientific knowledge with regard to the contemplation of God, and whether and to what extent secular knowledge is worth pursuing.Footnote ³⁸ With regard to astronomical studies, traditionally considered a useful tool in striving towards the contemplation of God, it was a question of identifying which properties of the heavens and the celestial bodies allowed for the attainment of the contemplative state. As a result, astrology was radically rejected in favour of mathematical astronomy, and these two parts of astronomical studies were, in the eyes of radical hesychasts, irreconcilable.

The controversy over Barlaam's defence of the Orthodox, anti-Latin position on the Filioque belied a politically extremely sensitive topic for Byzantine Orthodoxy. Indeed, it is on the Filioque question that the Church of Constantinople based its distinctions and conflicts with the Church of Rome – the controversies surrounding the hesychasts and the theology of Palamas are ultimately a consequence of the overriding drive to be anti-Latin. As a result, as we shall see further on, the political success of the hesychasts calcified into an irreversibly negative view as regards the inquiry into the physical properties of the heavens. Barlaam was excommunicated by the Orthodox Church in 1341 and had to leave Constantinople permanently. By the end of the same year, he had renounced Orthodoxy and become Catholic. He met Petrarch and taught him some Greek, and probably made contact with Giovanni Boccaccio and other Italian literati. Given the humanist connection running alongside the transmission channel of Bessarion, it is no accident that Barlaam is the sole Byzantine scholar mentioned by Regiomontanus.

The Persian Tables

The concerns raised by Barlaam about the Filioque and its implicit impact on the dichotomy between asceticism and science are evident in the historical narrative of a Byzantine astronomical work with Islamic origins, referred to as the Persian Tables. This work was widely circulated among scholars during the fourteenth and fifteenth centuries and was preserved in European astronomical traditions largely due to the influence of Byzantine expatriates during the Renaissance.Footnote ³⁹

After the triumph of hesychasm in 1351, the status of astronomical knowledge was problematic, and non-Byzantine sources on astronomy were more disfavoured than ever. The debate, in essence, centred on two issues: (1) whether it was worth translating Islamic sources (Arabic or Persian) into Greek and (2) whether their study and use were worthwhile. Byzantine scholars in fourteenth-century Byzantium had at their disposal astronomical knowledge with Islamic provenance thanks to Gregory Chioniades (c.1240–1320).Footnote ⁴⁰ He is known as a translator of works of Islamic astronomy from Persian and Arabic into Greek and such activity drew a fair amount of criticism. Due to his acquaintance with such materials, Chioniades was accused of heresy and had to defend himself through an official profession of faith.Footnote ⁴¹ Some fifty years later the Persian Tables, likely brought to Constantinople by Chioniades, had spread among scholars and amateur astrologers. Quite a few authors wrote commentaries on the Tables, the most notable being Theodoros Meliteniotes (c.1320–93), who was an influential churchman and a proponent of hesychasm and of Palamas's doctrine.

Active around the middle of the fourteenth century in Constantinople, Meliteniotes was the rector of the Patriarchal School, which was the official educational establishment of Orthodoxy.Footnote ⁴² He composed the Three Books of Astronomy right after the Council of 1351.Footnote ⁴³ This work was conceived as a textbook for the Patriarchal School: the first two books deal with Ptolemaic astronomy, while the third is devoted to the Persian Tables.Footnote ⁴⁴ In accordance with Byzantium's hesychast hegemony, Meliteniotes wrote preambles to provide a programmatic overview of astronomical studies that complied with the hesychast agenda and incorporated, in an appropriate manner, Islamic astronomical knowledge into the school's teaching programme. In his view, Orthodox astronomical studies allow for the investigation of the abstract properties of the celestial bodies by way of mathematics (universal properties extracted from celestial objects), while the inquiry into physical properties is worthless, because the realm of physics (natural philosophy) deals with corruptible things, thus generating false or uncertain knowledge.Footnote ⁴⁵ Mathematics, on the other hand, provides the highest degree of certitude among the sciences, with only theology surpassing it in this respect. As some physical properties of celestial bodies can be wholly or partially connected to human behaviour and considered as causes of actions, at a distance, between human actions and earthly events (astrology), this reasoning would have led to a deterministic mindset, in which the existence of free will is denied. As this would have questioned a basic principle of faith, astrology was rejected in toto, on the grounds of determinism, by the hesychast astronomical agenda. On these counts, Meliteniotes banned astrology as an illicit activity leading to damnation. The usefulness of astronomy lay only in its mathematical aspect, in the ability to compute the positions of the planets and predict eclipses. This the Orthodox faith deemed commendable as it helped in the contemplation of the cosmic order, and in reflecting on God's wisdom. This was made possible, once again, by mathematical certitude found in the abstract properties of celestial objects, the highest degree of certitude among sciences, second only to theology in Meliteniotes's classification.

The relevance of Meliteniotes's Three Books on Astronomy is that they led to the institutionalization of a specific form of knowledge, reflecting the doctrinal rules of 1351, hence securing a view on science in accordance with the hesychast agenda – this means also in accordance with the implications of the Byzantine views on the question of the Filioque. This process of institutionalization generated a negative view not of astronomical studies per se, but rather of such studies in the service of astrology. The main assumption was the idea (and misinterpretation of Palamas's writings) that religious knowledge is superior to natural knowledge, which can therefore be pursued only within the limits of faith. It is likely that this may have prevented possible developments in the science of the heavens in Byzantium, as astrology was a major driver of astronomical inquiry elsewhere. For non-hesychast scholars like Pletho and Bessarion, it was impossible to access the milieu of the official Byzantine state. From around the time of Meliteniotes's work, a Byzantine dialogue has come down to us – Hermippus Dialogue on Astrology – offering a defence of astrology as a discipline that enables one to reach the divine realms by combining Christian and Platonic doctrines. This work was banned by the hesychast Byzantine Orthodoxy.Footnote ⁴⁶

Meliteniotes's approach towards celestial bodies allowed the Persian Tables to enter the programme of the Patriarchal School and granted them legitimation while insulating them from astrological concerns. The authoritative status of the Persian Tables was guaranteed by the genealogy that they outlined: from Ptolemy to Persian and Arabic scholars, all deserving of mention for having improved Ptolemy, the founding father of astronomy. Al-Battani and al-Tusi figure among the scholars mentioned by Meliteniotes.Footnote ⁴⁷ Most Byzantine scholars after 1351, Bessarion included, were trained both in Ptolemaic astronomy and on the Persian Tables. These tables were so popular that Byzantine scholars took copies of them on their travels to Ferrara and Florence in the 1430s, at the time of the Council for the Union of the Churches. Cusanus records that he received a copy of the Persian Tables from Bessarion.Footnote ⁴⁸ Despite the limitations of the abstractionist approach to astronomical studies, Meliteniotes's Three Books on Astronomy sanctioned the Graeco-Arabic roots of astronomy as officially recognized in Byzantium.

Bessarion's cultural background and Regiomontanus's oration

Bessarion was born in Trebizond, a city on the Black Sea, in 1400/8. The local religious leader, fascinated by Bessarion's talent, sent him to be educated in Constantinople. Here, under the guidelines set by Meliteniotes, astronomical studies was a compulsory part of the curriculum in the 1420s. Among Bessarion's teachers in Constantinople was John Chortasmenos, to whom he owed his knowledge of Meliteniotes and the Persian Tables. Given his astronomical proclivities, it was suggested that Bessarion move to the Peloponnese, to the town of Mistra, where he could benefit from the teaching of George Gemistus Pletho, a non-conventional Neoplatonic philosopher who did not side with the hesychast Orthodoxy of Constantinople. Bessarion moved to Mistra in 1431.Footnote ⁴⁹ The fact that Bessarion had to move to study astronomy is more than telling. His wish to reform astronomical studies and sciences in general could not be reconciled with the expectations of the Constantinopolitan intellectuals, but found ideal ground for growth in Pletho, who authored an innovative work on astronomy, aimed at reforming the discipline.Footnote ⁵⁰

In light of the close intellectual relationship between Bessarion and Regiomontanus, it is reasonable to see in the Paduan oration a reflection of the aims of Bessarion's scientific agenda. As evinced by the oration, Regiomontanus had privileged access to Bessarion's manuscripts, which included works not only on mathematical astronomy, but also on celestial physics, such as Proclus's Hypotyposis astronomicarum positionum, as well as works of a rather astrological character by Ptolemy, Vettius Valens and Hermes Trismegistos.Footnote ⁵¹ Regiomontanus also single-handedly copied some astrological texts from Bessarion's manuscripts and there is evidence of Regiomontanus having had access to astrological materials in Bessarion's manuscripts to study astrology and learn Greek.Footnote ⁵² Such is the case, for instance, of a Byzantine text on astrology relating to the hand.Footnote ⁵³

Bessarion likely inherited a taste for astrology already in his birthplace of Trebizond. An Almanac for the city has come down to us giving evidence of the astronomical activity practised there at the time.Footnote ⁵⁴ Unlike Constantinople, Trebizond did not suffer from strenuous politico-theological debates in the fourteenth century. Moreover, the Persian Tables arrived at Constantinople through Trebizond, for Byzantines an essential outpost on the eastern trade routes. In light of Bessarion's cultural background as reflected in Regiomontanus's oration, we can better assess the reasons behind Bessarion's moving to Italy. It is not only the disappointment with the narrow-mindedness of Byzantine officials after the failure of the 1439 Council of Florence and their decision against the Union with the Church of Rome – something that could have been life-saving in the fight with the Muslim Ottoman Turks who were about to conquer Constantinople. It is very likely that the passage to the West for Bessarion also offered a golden opportunity to develop a broader investigation of astronomical studies including astrology, a path that had been denied him in his homeland due to the political–theological choices of his compatriots.

As for Regiomontanus's approach in the oration, his claims about the highest degree of certitude granted by mathematical sciences, especially his praising of astrology to reach divine realms, without any mention of theology, might lead one to think of him as an anti-Scholastic scholar. While this conclusion remains tentative, his account is certainly a non-Orthodox Scholastic approach, and it remains to be determined whether this might have been influenced by Bessarion. Regiomontanus's contact with humanists came through Bessarion and it is likely that his acquaintance with Leon Battista Alberti and Paolo Toscanelli was formative for his non-Orthodox Scholastic approach to the sciences. However, it would be an exaggeration to view Bessarion as an anti-Scholastic philosopher tout court. Before moving to Italy and converting to Catholicism, he had not perceived his commitment to Orthodoxy and to Thomism as contradictory. His reception of the works of Thomas Aquinas was mediated by Greek translations of Summa contra Gentiles and Summa Theologiae by Demetrios Cydones. His manuscripts collection reflects his interest in the works of Aquinas, but after moving to Italy he did not use Thomism to face the theological and scientific issues he was dealing with.Footnote ⁵⁵

Concluding remarks

Unquestionably, as anticipated, certain facets of the arguments presented in this research remain speculative, necessitating additional scrutiny and exploration of primary source materials. Notwithstanding these constraints, this article is based on an innovative interpretation that may catalyse a significant historiographic reinterpretation of Regiomontanus and his intellectual context.

As has been shown, it is possible to use the Paduan academic context of the 1460s to reveal unfamiliar aspects of Byzantine influence on astronomical studies and their institutionalization in early modern Italy. It is no accident that the university hailed Regiomontanus as lecturer in the sciences and welcomed another protégé of Cardinal Demetrios Chalkondylas as teacher of Greek from 1463 on.Footnote ⁵⁶ The consequences of hesychasm and Palamism on astronomical studies, as evinced by Meliteniotes's Three Books on Astronomy, provide some as yet unexplored pieces in the puzzle of Bessarion's stance on astronomical studies: Meliteniotes fostered the study of astronomy but isolated it from astrological issues. The significance of Bessarion's patronage of Regiomontanus and of his fostering of the study of the Almagest in Italy lies in the fact that he was heir to a lineage of scholars (especially Pletho) who did not align with Orthodox views on the importance of studying astronomy without astrology after the Council of 1351. On this account, Bessarion identified in Regiomontanus a figure who could both propound non-Orthodox views and reform astronomical studies. He stressed the importance of having Regiomontanus teach at the University of Padua, because he saw in that institution the capacity to support investigations of the physical properties of the heavens, both in the form of celestial physics and for astrological purposes tout court.

As demonstrated by Michael Shank, in the Defensio Theonis Regiomontanus made significant claims about the physical properties of the heavens.Footnote ⁵⁷ Alongside Regiomontanus's unquestionable talent, Bessarion's patronage and his intellectual background provided an ideal framework on which this programme could unfold. It was not only the opportunity proffered by the patronage, but also the intellectual heritage Bessarion was granting his mentee that allowed Regiomontanus to conceive of astronomy as physical and not just fictional.

Regiomontanus's inaugural lecture reflects his enthusiasm for the Greek scientific literature he had accessed thanks to his patron.Footnote ⁵⁸ Bessarion's astronomical heritage, as evidenced by examinations of his manuscripts, is a hybrid collection of astronomical knowledge, namely the Graeco-Arabic tradition (e.g. Ptolemy and the Persian Tables).Footnote ⁵⁹ This coexistence was regulated in Byzantium through Meliteniotes and his abstractionist and anti-astrological approach. It was a hybrid culture that merged happily with Regiomontanus's background, which had benefited from the Viennese Latin tradition of Peuerbach and his predecessors – a tradition which had questioned Ptolemaic astronomy and taken into account Arabic innovations. On this account, the programme of astronomical studies at the University of Padua reflected a Viennese–Byzantine conception of astronomy; that is, the confluence of two traditions congenial to Graeco-Arabic astronomical studies.

Regiomontanus emphasized the Greek origins of mathematics but stressed the various influences of astronomy's development. In Høyrup's view, Regiomontanus intentionally excludes the Arabic tradition and the importance it is due. However, Regiomontanus probably was simply unacquainted with Arabic algebraic developments. Given that he acknowledges Arabic advancements in astronomy, it is rather reasonable to suppose that he would have acknowledged Arabic algebra too, had he been aware of the content. If he and Bessarion had set out to pursue an anti-Arabic humanist agenda, they would not have bestowed such lavish praise on Arabic astronomy – such praise would have been counterproductive. Regiomontanus had at his disposal neither the knowledge of Arabic, nor Greek or Latin translations of the advanced algebraic works of the Islamic tradition.

While some exponents of humanism have worked for the suppression of Arabic science in Europe and have constructed a purist vision of society through the unification of Greek science with Christian faith, Regiomontanus and Bessarion, as glimpsed through the oration, did acknowledge the Graeco-Arabic roots of astronomy and inserted them into an institutional context.Footnote ⁶⁰ Furthermore, it would be hard to see Bessarion and Regiomontanus as humanist adherents of an anti-Scholastic programme. The extent of the oration's anti-Scholastic character is nothing compared to the anti-Scholasticism of one renowned scholar based in Padua, namely Galileo Galilei. Although certainly sharing Regiomontanus's view on the superiority of mathematical sciences, Bessarion was a man of faith, and as such he very likely distinguished between the truths provided by mathematical sciences and those truths not mathematically provable. It is difficult to believe that he would have allowed his protégé to state that mathematics is superior to theology. Not only was he a churchman, but his collection of manuscripts testifies to a strong interest in theological and philosophical questions, making a thesis on the superiority of mathematics to theology historically incongruous and misleading. The same applies to Regiomontanus.

The question of the certitude provided by mathematical sciences is detectable in the backgrounds of both Regiomontanus and Bessarion. The former likely stressed that concept under the influence of the anti-Scholastic philosophers with whom he was in contact, whereas Bessarion's familiarity with the idea hails from Byzantium. As the previous sections of this article have demonstrated, the certitude of mathematics as guaranteeing the superiority of astronomy to the other sciences was common knowledge during his years of study in Constantinople in the 1420s. At any rate, the humanistic character of the oration was well suited to the intellectual environment at the University of Padua. In Padua, in contrast to other university contexts, such as Paris, the teaching of theology was not treated as superior to the arts, medicine or law. This made Padua, indeed, the perfect venue for the oration.