Stefan Zieme

About

I am a historian of astronomy with a focus on mathematical practices and visual culture from antiquity to the early modern period. Currently, I am a CNRS postdoc at the Observatoire de Paris / PSL University, where I am a member of the Laboratoire Temps Espace. My research investigates the structure and composition of numerical tables and geometrical diagrams in sets of astronomical tables and zījes, with a specific focus on the transmission of astronomical knowledge across space, time, and cultures. My work, with a strong emphasis on data analysis, resides in the digital humanities and includes methods based on artificial intelligence.

I am currently writing a book entitled The Equation of Time: A History of Tables and Practices in Medieval Astronomy. The book investigates the mathematical and tabular practices related to determining the table of the equation of time across Greek, Arabic, Hebrew, and Latin astronomical sources from the 2nd to the 17th century CE. The equation of time stands among the few tables in mathematical astronomy that required periodic renewal, offering a unique lens for cross-cultural analysis of mathematical practice over the longue durée.

Originally, I studied theoretical physics at Humboldt University Berlin and earned my PhD at the Max Planck Institute for Gravitational Physics in Potsdam, Germany, in 2010, specialising in mathematical physics and string theory. After a postdoctoral position at the Nordic Institute for Theoretical Physics in Stockholm, Sweden, I joined the history of science and became a postdoctoral research fellow at the Cluster of Excellence Image Knowledge Gestaltung at Humboldt University Berlin in 2014.

From February 2019 until December 2025, I was a Research Associate at the Cluster of Excellence Matters of Activity and an Assistant Professor in the Department for Cultural History and Theory, both at Humboldt University Berlin.

fields of interest: history of astronomy, history of science, digital humanities, AI

Publications

Books

The Equation of Time: A History of Tables and Practices in Medieval Astronomy

Stefan Zieme

(Turnhout: Brepols, 2027), forthcoming.

Journal articles

Lewis Caerleon and the equation of time: tabular astronomical practices in late fifteenth-century England

Laure Miolo and Stefan Zieme

Archive for History of Exact Sciences 78, No. 2 (2024): 183-243.

doi

abstract

The manuscripts and writings of the fifteenth-century astronomer and physician Lewis Caerleon (d. c. 1495) have been largely overlooked. To fill this gap, this article focuses on his writings and working methods through a case study of his canons and table for the equation of time. In the first part, an account of his life and writings is given on the basis of new evidence. The context in which his work on the equation of time was produced is explored in detail by reviewing the three key periods of his scientific production. His heavy reliance on Simon Bredon’s Commentum super Almagesti is also analyzed. The article also provides editions of Lewis Caerleon’s canons for calculating his table for the equation of time and a critical edition of Simon Bredon’s Commentum super Almagesti, III, 22–24. In the second part of this article, we analyze the table for the equation of time derived by Lewis around 1485. In addition to the final table, there is a unique table with intermediate results that records every step of his derivation. By following and discussing the details of this derivation, we shed a new light on tabular practices in mathematical astronomy. Following Lewis in his historical mathematical procedure, we argue, offers a novel historiographical approach that allows us to identify different sources and practices used by historical actors. Therefore, beyond the exchange of parameters residing in modern mathematical analysis, this novel approach offers a promising refinement for the analysis of the transmission of knowledge across space, time, and culture.

Gerard of Cremona's Latin translation of the Almagest and the revision of tables

Stefan Zieme

Journal for the History of Astronomy 54, No. 1 (2023): 3-33.

doi

abstract

Until the late 15th century, knowledge of Ptolemy’s Almagest in the Latin West was constituted by Gerard of Cremona’s translation from Arabic into Latin. The text of Gerard’s translation has been examined carefully and its dependence on two different Arabic versions is well studied. However, the tables of Gerard’s Latin Almagest have not been scrutinized, and the relation to their Arabic or Greek counterparts has not been examined. In this article, I will analyze the historical mathematical structure of tables in Gerard’s Latin Almagest translated from the Arabic in comparison to their Arabic and Greek precursors. While Gerard’s text has proved to be a faithful translation from Arabic templates, some of the tables will turn out to be different. Fundamental tables for, for example, the chord interpolation values, declination, and rising times appear to have been recomputed in order to match Ptolemy’s proofs and paradigm computations, which, in contrast, generally diverge in both Greek and Arabic tradition with the tables. It remains unclear if Gerard himself or someone in his company recalculated these tables and thus deliberately aimed to correct the ancient classic of astronomy. By a systematic analysis of these tables, I intend to provide a novel perspective on the medieval transmission and translation of knowledge, its cross-cultural exchange, and especially the practice of Gerard of Cremona and his collaborator(s).

Imagining the Heavens: Adam Elsheimer's Flight into Egypt and the Renaissance Night Sky

Stefan Zieme

Journal for the History of Knowledge 2, No. 1 (2021): 1-18.

doi

abstract

Adam Elsheimer’s The Flight into Egypt (1609) has triggered a longstanding debate among art historians. For the last five decades, Elsheimer’s novel naturalistic representation of the night sky in his painting on copper has been linked to Galileo’s telescopic observations. To explain the astronomical details of this painting, scholars have contended that Elsheimer observed, before Galileo, the night sky with one of the first telescopes available in Rome. So far, the debate has lacked input from the history of astral science. This article presents a case study that examines the relationship between the visual arts and astronomical knowledge. It offers a contextualized analysis of the technical details of the artwork within the prevailing astronomical knowledge— before the appearance of Galileo’s Sidereus Nuncius—and frames it within the network of and debates among prominent figures of Galileo’s and Elsheimer’s time. It proposes a revisionist interpretation of Elsheimer’s most famous artwork based on an analysis of the technical and cultural practices of discerning and imagining the night sky around 1600.

Book chapters

Regiomontanus on the Equation of Time: Computational Practices of an Alfonsine Astronomer

Eleonora Andriani and Stefan Zieme

Alfonsine Astronomy: Computational Practices, ed. by Matthieu Husson, José Chabás, and Richard L. Kremer (Turnhout: Brepols, 2026), 307-43.

doi

introduction

The equation of time is an essential tabular quantity in all sets of historical astronomical tables. While astronomical computations were performed in mean solar time, daily cultural life from antiquity to the early modern period was ordained by apparent solar time, which could be read on a sundial. This difference between mean and apparent time is determined by the equation of time. It is considerably small, but can amount to about half of an hour of time over the course of a year. Therefore, the difference is irrelevant when determining the positions of slow-moving celestial bodies such as Jupiter or Saturn, but it becomes pivotal for the position of the Moon and thus for the determination of solar and lunar eclipses. For astrological purposes, for example nativities and horoscopes, the equation of time may have presented a crucial component for the determination of the ascendant and the linked house divisions, as a time difference of about half an hour can amount to shifts of about eight degrees for the ascendant. Notably, when a specific point in time was sought as part of an astrological inquiry, the equation of time may have been taken into account by diligent practitioners. Regiomontanus (1436–76), one of the most renowned astronomers in early modern Europe, was a diligent practitioner and used the equation of time whenever he cast a horoscope...

Journal articles (physics)

Fine Structure of String Spectrum in AdS(5)xS(5)

Konstantin Zarembo and Stefan Zieme

JETP Lett. 95, (2012): 219–23.

arXiv doi

abstract

The spectrum of an infinite spinning string in AdS(5) does not precisely match the spectrum of dual gauge theory operators, interpolated to the strong coupling regime with the help of Bethe-ansatz equations. We show that the mismatch is due to interactions in the string sigma-model which cannot be neglected even at asymptotically large 't Hooft coupling.

From weak coupling to spinning strings

Lisa Freyhult, Adam Rej, and Stefan Zieme

JHEP 02 (2010): 50.

arXiv doi

abstract

We identify the gauge theory dual of a spinning string of minimal energy with spins S_1, S_2 on AdS_5 and charge J on S^5. For this purpose we focus on a certain set of local operators with two different types of covariant derivatives acting on complex scalar fields. We analyse the corresponding nested Bethe equations for the ground states in the limit of large spins. The auxiliary Bethe roots form certain string configurations in the complex plane, which enable us to derive integral equations for the leading and sub-leading contribution to the anomalous dimension. The results can be expressed through the observables of the sl(2) sub-sector, i.e. the cusp anomaly f(g) and the virtual scaling function B_L(g), rendering the strong-coupling analysis straightforward. Furthermore, we also study a particular sub-class of these operators specialising to a scaling limit with finite values of the second spin at weak and strong coupling.

Analytic solution of the multiloop Baxter equation

Matteo Beccaria, Andrei Belitsky, Anatoly Kotikov, and Stefan Zieme

Nuclear Physics B 827, No. 3 (2010): 565-606.

arXiv doi

abstract

The spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang-Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2) subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.

Twist-three at five loops, Bethe Ansatz and wrapping

Matteo Beccaria, Valentina Forini, Tomasz Lukowski, and Stefan Zieme

JHEP 03 (2009): 129.

arXiv doi

abstract

We present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large values of the spin.

The virtual scaling function of AdS/CFT

Lisa Freyhult and Stefan Zieme

Phys. Rev. D 79 (2009): 105009.

arXiv doi

abstract

We write an integral equation that incorporates finite corrections to the large spin asymptotics of N=4 SYM twist operators from the non-linear integral equation. We show that these corrections are an all-loop result, not affected by wrapping effects, and agree, after determining the strong coupling expansion, with string theory predictions.

Analytic three-loop Solutions for N=4 SYM Twist Operators

Anatoly V. Kotikov, Adam Rej, and Stefan Zieme

Nuclear Physics B 813, No. 3 (2009): 460-83.

arXiv doi

abstract

We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N=4 SYM. Our result proofs the conjectured formula for the three-loop anomalous dimension of twist-two operators. As such we derive the maximally transcendental part of the corresponding three-loop QCD result from the maximal supersymmetric gauge theory in four dimension purely by methods of integrability.

Nesting and Dressing

Adam Rej, Matthias Staudacher, and Stefan Zieme

J. Stat. Mech. 0708 (2007): P08006.

arXiv doi

abstract

We compute the anomalous dimensions of field strength operators Tr F^L in N=4 SYM from an asymptotic nested Bethe ansatz to all-loop order. Starting from the exact solution of the one-loop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic L → ∞ limit of these dimensions. We also include the recently proposed phase factor for the S-matrix of the planar AdS/CFT system. The terms in the effective equation corresponding to, respectively, the nesting and the dressing are structurally very similar. This hints at the physical origin of the dressing phase, which we conjecture to arise from the hidden presence of infinitely many auxiliary Bethe roots describing a non-trivial “filled” structure of the theory’s BPS vacuum. We finally show that the mechanism for creating effective nesting/dressing kernels is quite generic by also deriving the integral equation for the all-loop dimension of a certain one-loop so(6) singlet state.

Talks

(selection)

• Jul 2026 Gerard of Cremona and the Toledan Tables 2026 Joint Meeting of the European Society for the History of Science (ESHS) and History of Science Society (HSS), Edinburgh.
• Jun 2026 The Diagrams of the First Appendix of al-Ṭūsī’s Taḥrīr al-Majisṭī Image Making as Knowledge Production, Bibliotheca Hertziana, Max Planck Institute for Art History, Rome.
• Apr 2025 Diagram Transformations in George of Trebizond’s Translation of the Almagest A long history of diagrammatization in the astral sciences, 3rd International EIDA Conference, Observatoire de Paris, Paris.
• Sep 2024 45°: The Toledan Tables and the Latitude of Cremona Perspectives on Gerard of Cremona, 2nd International Conference of the Project Ptolemaeus Arabus et Latinus, Würzburg.
• Sep 2024 On the Transmission of the Almagest 11th Conference of the European Society for the History of Science (ESHS), Barcelona.
• Nov 2023 On the Translations and Transmission of the Almagest VIIIth Workshop de Epistemología e Historia de la Astronomía, Universidad Pedagógica Nacional Buenos Aires, Buenos Aires.
• Apr 2023 Manuscript Culture and the Early Modern Editions of the Almagest XIVe Congrès de la Société française d’histoire des sciences et des techniques, Université de Bordeaux, Bordeaux.

Teaching

(last five courses)